CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : LCL759-1 : TPTP v9.2.1. Released v4.1.0.
% 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 : n005.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 04:44:57 PM UTC 2026

% Result   : Unsatisfiable 1.81s 2.67s
% Output   : CNFRefutation 1.86s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_637)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_conjecture_4,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(cls_Suc__eq__plus1_0,axiom,
    c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).

cnf(cls_conjecture_1,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X1))),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_subst__subst_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
    | ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).

cnf(cls_mod__mult__self4_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).

cnf(cls_shift__commute_0,axiom,
    c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4) = c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).

cnf(cls_split__div__lemma_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Suc(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat)),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div__lemma_2) ).

cnf(cls_Suc__mult__less__cancel1_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).

cnf(cls_one__less__mult_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).

cnf(cls_Suc__mult__less__cancel1_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

cnf(cls_mod__Suc__eq__Suc__mod_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).

cnf(cls_dB_Osize_I5_J_0,axiom,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I5_J_0) ).

cnf(cls_lift__lift_0,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X2)),c_Suc(X3)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X3)),X2)
    | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).

cnf(cls_n__less__n__mult__m_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).

cnf(cls_n__less__m__mult__n_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).

cnf(cls_mod__Suc_1,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat))
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).

cnf(cls_Suc__times__mod__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).

cnf(cls_power__Suc__less__one_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).

cnf(cls_mod__Suc_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).

cnf(cls_upt_Oinduct_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upt_Oinduct_1) ).

cnf(cls_nat_Oinduct_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinduct_1) ).

cnf(cls_nat_Oinducts_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinducts_1) ).

cnf(cls_replicate_Oinduct_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate_Oinduct_1) ).

cnf(cls_nat__induct_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__induct_1) ).

cnf(cls_lexn_Oinduct_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lexn_Oinduct_1) ).

cnf(cls_less__iff__Suc__add_1,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

cnf(cls_less__add__Suc1_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

cnf(cls_less__add__Suc2_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

cnf(cls_dB_Osize_I2_J_0,axiom,
    c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I2_J_0) ).

cnf(cls_Suc__mult__cancel1_0,axiom,
    ( X2 = X3
    | c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).

cnf(cls_add__Suc_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).

cnf(cls_power__gt1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).

cnf(cls_Suc__less__eq_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

cnf(cls_add__Suc__shift_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).

cnf(cls_add__Suc__right_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

cnf(cls_zero__induct_0,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))))
    | ~ hBOOL(hAPP(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__induct_0) ).

cnf(cls_Suc__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

cnf(cls_less__Suc__eq__0__disj_3,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

cnf(cls_mult__eq__1__iff_2,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).

cnf(cls_add__is__1_4,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).

cnf(cls_one__is__add_4,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).

cnf(cls_power__Suc2_0,axiom,
    ( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).

cnf(cls_power__Suc_0,axiom,
    ( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Power_Opower(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).

cnf(cls_class__semiring_Opwr__Suc_0,axiom,
    ( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).

cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom,
    ( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_Power_Opower__class_Opower(X2,c_Suc(X3),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(X2,c_Suc(X3),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).

cnf(cls_not__less__eq_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

cnf(cls_less__trans__Suc_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

cnf(cls_dvd__1__iff__1_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__iff__1_0) ).

cnf(cls_mult__Suc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).

cnf(cls_mult__Suc__right_0,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).

cnf(cls_less__SucE_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).

cnf(cls_not__less__less__Suc__eq_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

cnf(cls_less__antisym_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

cnf(cls_Suc__lessD_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

cnf(cls_Suc__lessI_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | c_Suc(X1) = X2
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

cnf(cls_one__is__add_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).

cnf(cls_add__is__1_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).

cnf(cls_dvd__1__iff__1_1,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__iff__1_1) ).

cnf(cls_less__Suc0_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

cnf(cls_less__SucI_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

cnf(cls_nat__power__eq__Suc__0__iff_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_0) ).

cnf(cls_mult__eq__1__iff_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).

cnf(cls_mult__eq__1__iff_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).

cnf(cls_one__is__add_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).

cnf(cls_one__is__add_3,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

cnf(cls_add__is__1_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).

cnf(cls_add__is__1_3,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).

cnf(cls_dB_Osize_I6_J_0,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).

cnf(cls_power__Suc__0_0,axiom,
    c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__0_0) ).

cnf(cls_nat__power__eq__Suc__0__iff_2,axiom,
    c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_2) ).

cnf(cls_add__is__1_5,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).

cnf(cls_one__is__add_5,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).

cnf(cls_of__nat__Suc_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_Oof__nat(X2,X1))
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).

cnf(cls_not__less__less__Suc__eq_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

cnf(cls_not__less__eq_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

cnf(cls_dB_Osize_I3_J_0,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).

cnf(cls_power__0__Suc_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).

cnf(cls_one__is__add_2,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).

cnf(cls_add__is__1_2,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).

cnf(cls_less__Suc0_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).

cnf(cls_mod__1_0,axiom,
    c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).

cnf(cls_div__1_0,axiom,
    c_Divides_Odiv__class_Odiv(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__1_0) ).

cnf(cls_dvd__1__left_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).

cnf(cls_Suc__inject_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

cnf(cls_nat_Oinject_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

cnf(cls_gr0__conv__Suc_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

cnf(cls_zero__less__Suc_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

cnf(cls_lessI_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).

cnf(cls_less__Suc__eq_2,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

cnf(cls_nat__power__eq__Suc__0__iff_1,axiom,
    c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_1) ).

cnf(cls_Suc__eq__plus1__left_0,axiom,
    c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

cnf(cls_nat_Osimps_I3_J_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

cnf(cls_Suc__neq__Zero_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

cnf(cls_nat_Osimps_I2_J_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

cnf(cls_Zero__neq__Suc_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

cnf(cls_Suc__n__not__n_0,axiom,
    c_Suc(X1) != X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

cnf(cls_n__not__Suc__n_0,axiom,
    X1 != c_Suc(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

cnf(cls_not0__implies__Suc_0,axiom,
    ( X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not0__implies__Suc_0) ).

cnf(cls_nat_Onchotomy_0,axiom,
    ( X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Onchotomy_0) ).

cnf(cls_nat_Oexhaust_0,axiom,
    ( X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oexhaust_0) ).

cnf(cls_One__nat__def_0,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).

cnf(cls_subst__map_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__map_0) ).

cnf(cls_substs__lemma_0,axiom,
    ( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X3,X6,tc_Type_Otype),X4,X5)
    | ~ c_Type_Otyping(X1,X2,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substs__lemma_0) ).

cnf(cls_Beta_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).

cnf(cls_lift__map_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__map_0) ).

cnf(cls_var__app__type__eq_0,axiom,
    ( X1 = X2
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).

cnf(cls_lift__types_0,axiom,
    ( c_Type_Otypings(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | ~ c_Type_Otypings(X1,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__types_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_lifts__IT_0,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lifts__IT_0) ).

cnf(cls_IT_OVar_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).

cnf(cls_apps__preserves__beta_0,axiom,
    ( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB))
    | ~ c_Lambda_Obeta(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).

cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).

cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).

cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom,
    ( X2 = X4
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).

cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom,
    ( X2 = X4
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).

cnf(cls_foldl__assoc_0,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).

cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).

cnf(cls_apps__eq__tail__conv_0,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).

cnf(cls_foldl__absorb0_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).

cnf(cls_split__mod_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hBOOL(hAPP(X3,X1))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)),X1),X2,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_1) ).

cnf(cls_split__div_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hBOOL(hAPP(X3,X4))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)),X1),X2,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_1) ).

cnf(cls_div__mod__equality_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).

cnf(cls_div__mod__equality2_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).

cnf(cls_div__add1__eq_0,axiom,
    c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X1,X3,tc_nat)),c_Divides_Odiv__class_Odiv(X2,X3,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X1,X3,tc_nat)),c_Divides_Odiv__class_Omod(X2,X3,tc_nat)),X3,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add1__eq_0) ).

cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom,
    hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).

cnf(cls_COMBC__def_0,axiom,
    hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

cnf(cls_App__eq__foldl__conv_0,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).

cnf(cls_Abs__App__neq__Var__apps_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).

cnf(cls_Abs__eq__apps__conv_0,axiom,
    ( c_Lambda_OdB_OAbs(X1) = X2
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).

cnf(cls_Var__eq__apps__conv_0,axiom,
    ( c_Lambda_OdB_OVar(X1) = X2
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).

cnf(cls_apps__eq__Abs__conv_0,axiom,
    ( X1 = c_Lambda_OdB_OAbs(X3)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).

cnf(cls_lift__subst_0,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X2),X4)),X3)
    | ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).

cnf(cls_apps__eq__Abs__conv_1,axiom,
    ( X2 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).

cnf(cls_Abs__eq__apps__conv_1,axiom,
    ( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).

cnf(cls_Var__eq__apps__conv_1,axiom,
    ( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).

cnf(cls_mod__mult2__eq_0,axiom,
    c_Divides_Odiv__class_Omod(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X3,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult2__eq_0) ).

cnf(cls_mod__lemma_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat)),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X4,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__lemma_0) ).

cnf(cls_div__mult1__eq_0,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X3,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult1__eq_0) ).

cnf(cls_sum__squares__gt__zero__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

cnf(cls_combine__common__factor_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X4,X3,X1)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)),X5)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

cnf(cls_left__add__mult__distrib_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).

cnf(cls_App__eq__foldl__conv_4,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).

cnf(cls_not__sum__squares__lt__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

cnf(cls_lift__subst__lt_0,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X4)),hAPP(hAPP(c_Lambda_Olift,X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).

cnf(cls_apps__eq__Abs__conv_2,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).

cnf(cls_Abs__eq__apps__conv_2,axiom,
    c_Lambda_OdB_OAbs(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).

cnf(cls_Var__eq__apps__conv_2,axiom,
    c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).

cnf(cls_foldl__Nil_0,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).

cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
    ( X3 = X5
    | X2 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X5,X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X5,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).

cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
    ( X3 = X5
    | X2 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X5,X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X5,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).

cnf(cls_subst__lemma_0,axiom,
    ( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).

cnf(cls_natgb_Oadd__mul__solve_0,axiom,
    ( X2 = X4
    | X1 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).

cnf(cls_natgb_Onoteq__reduce_0,axiom,
    ( X2 = X4
    | X1 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).

cnf(cls_mod__add__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).

cnf(cls_subst__App_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).

cnf(cls_sum__squares__gt__zero__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

cnf(cls_sum__squares__gt__zero__iff_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),X1)
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

cnf(cls_mod__div__equality_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).

cnf(cls_mod__div__equality2_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1)) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).

cnf(cls_mod__div__decomp_0,axiom,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__decomp_0) ).

cnf(cls_subst__Abs_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).

cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).

cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).

cnf(cls_mod__mult__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).

cnf(cls_zmod__simps_I1_J_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).

cnf(cls_mod__add__left__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).

cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

cnf(cls_div__mult__div__if__dvd_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_Divides_Odiv__class_Odiv(X4,X5,X1),X1) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).

cnf(cls_natgb_Oadd__mul__solve_1,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).

cnf(cls_natgb_Onoteq__reduce_1,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).

cnf(cls_div__add_0,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X2,X4,X1)),c_Divides_Odiv__class_Odiv(X3,X4,X1))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add_0) ).

cnf(cls_lift__type_0,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X4),X2),X5)
    | ~ c_Type_Otyping(X1,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).

cnf(cls_power__Suc__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).

cnf(cls_mod__mult__cong_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
    | c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).

cnf(cls_mod__add__cong_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X2),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X6),X4),X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
    | c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).

cnf(cls_div__dvd__div_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X4,X1),c_Divides_Odiv__class_Odiv(X3,X4,X1),X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).

cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

cnf(cls_mod__mult__self3_0,axiom,
    c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).

cnf(cls_shift__gt_0,axiom,
    ( hAPP(c_Type_Oshift(X1,X2,X3,X4),X5) = hAPP(X1,X5)
    | ~ c_HOL_Oord__class_Oless(X5,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).

cnf(cls_sum__squares__eq__zero__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

cnf(cls_sum__squares__eq__zero__iff_1,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).

cnf(cls_power__less__power__Suc_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).

cnf(cls_mult__less__cancel__left__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

cnf(cls_mult__less__cancel__left__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

cnf(cls_power__less__imp__less__exp_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).

cnf(cls_power__strict__increasing__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).

cnf(cls_nat__mod__eq__iff_1,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X4,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).

cnf(cls_nat__power__less__imp__less_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,tc_nat),c_Power_Opower__class_Opower(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__less__imp__less_0) ).

cnf(cls_nat__mult__less__cancel1_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).

cnf(cls_dvd__mult__cancel_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel_0) ).

cnf(cls_nat__mult__dvd__cancel1_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_0) ).

cnf(cls_power__strict__decreasing_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).

cnf(cls_mult__less__cancel__left__disj_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

cnf(cls_mult__less__cancel__right__disj_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

cnf(cls_mult__less__cancel__right__disj_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

cnf(cls_mult__less__cancel__left__disj_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

cnf(cls_mult__less__cancel__left__disj_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

cnf(cls_mult__less__cancel__right__disj_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

cnf(cls_zmod__simps_I4_J_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).

cnf(cls_mod__mult__left__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).

cnf(cls_mod__mult__right__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).

cnf(cls_div__mult__self2_0,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),c_Divides_Odiv__class_Odiv(X2,X3,X1))
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).

cnf(cls_div__mult__self1_0,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_Divides_Odiv__class_Odiv(X2,X4,X1))
    | X4 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).

cnf(cls_mult__less__cancel__right__disj_3,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

cnf(cls_mult__less__cancel__left__disj_3,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).

cnf(cls_comm__semiring__class_Odistrib_0,axiom,
    ( c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1))
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

cnf(cls_class__semiring_Omul__d_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

cnf(cls_div__dvd__div_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_Divides_Odiv__class_Odiv(X4,X3,X1),X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).

cnf(cls_zmod__simps_I2_J_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).

cnf(cls_mod__add__right__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).

cnf(cls_div__power_0,axiom,
    ( c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__power_0) ).

cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
    ( X4 = X5
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X5,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

cnf(cls_shift__eq_0,axiom,
    hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).

cnf(cls_add__mult__distrib_0,axiom,
    c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).

cnf(cls_add__mult__distrib2_0,axiom,
    c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).

cnf(cls_dvd__mult__cancel__right_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | X4 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).

cnf(cls_dvd__mult__cancel__left_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | X4 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).

cnf(cls_power__gt1__lemma_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).

cnf(cls_substn_Osimps_I2_J_0,axiom,
    c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).

cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom,
    ( X3 = X4
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).

cnf(cls_add__less__cancel__right_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

cnf(cls_add__less__cancel__left_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

cnf(cls_nat__mult__dvd__cancel__disj_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).

cnf(cls_mult__less__cancel1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).

cnf(cls_mult__less__cancel2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).

cnf(cls_mult__less__cancel2_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).

cnf(cls_mult__less__cancel1_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).

cnf(cls_mult__strict__left__mono__comm_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

cnf(cls_mult__strict__left__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

cnf(cls_mult__less__cancel__left__disj_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

cnf(cls_mult__less__cancel__left__pos_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

cnf(cls_mult__strict__right__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

cnf(cls_mult__less__cancel__right__disj_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

cnf(cls_mult__less__cancel__left__disj_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).

cnf(cls_mult__strict__left__mono__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).

cnf(cls_mult__less__cancel__left__neg_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

cnf(cls_mult__less__cancel__right__disj_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).

cnf(cls_mult__strict__right__mono__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

cnf(cls_sum__squares__eq__zero__iff_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

cnf(cls_power__strict__increasing_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).

cnf(cls_power__strict__increasing__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).

cnf(cls_mult__dvd__mono_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).

cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),X3) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

cnf(cls_div__add__self1_0,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X3,X2,X1)),c_HOL_Oone__class_Oone(X1))
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).

cnf(cls_div__add__self2_0,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X2,X3,X1)),c_HOL_Oone__class_Oone(X1))
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).

cnf(cls_add__strict__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

cnf(cls_mod__mult__mult2_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).

cnf(cls_mod__mult__mult1_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).

cnf(cls_power__mult__distrib_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).

cnf(cls_class__semiring_Opwr__mul_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).

cnf(cls_nat__mult__less__cancel1_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).

cnf(cls_mult__less__mono2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).

cnf(cls_mult__less__cancel1_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).

cnf(cls_mult__less__mono1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).

cnf(cls_mult__less__cancel2_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).

cnf(cls_nat__mult__dvd__cancel1_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_1) ).

cnf(cls_lift_Osimps_I2_J_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

cnf(cls_mod__mult__self2_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).

cnf(cls_mod__mult__self1_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).

cnf(cls_split__div_0,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_0) ).

cnf(cls_zero__less__mult__pos2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

cnf(cls_zero__less__mult__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

cnf(cls_split__mod_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_0) ).

cnf(cls_nat__add__left__cancel__less_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

cnf(cls_power__add_0,axiom,
    ( c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__add_0) ).

cnf(cls_class__semiring_Omul__pwr_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1) = c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).

cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

cnf(cls_class__semiring_Oadd__a_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

cnf(cls_mod__mult__distrib_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).

cnf(cls_mod__mult__distrib2_0,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).

cnf(cls_dvd__div__mult_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).

cnf(cls_dvd__mod__iff_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).

cnf(cls_dvd__mod__imp__dvd_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).

cnf(cls_nat__mult__div__cancel1_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel1_0) ).

cnf(cls_add__less__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

cnf(cls_map__is__Nil__conv_0,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Omap(X1,X2,X3,X4) != c_List_Olist_ONil(X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).

cnf(cls_Nil__is__map__conv_0,axiom,
    ( X3 = c_List_Olist_ONil(X4)
    | c_List_Olist_ONil(X1) != c_List_Omap(X2,X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).

cnf(cls_conjecture_3,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_add__cancel__21_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

cnf(cls_subst__preserves__beta_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X2),X3))
    | ~ c_Lambda_Obeta(X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

cnf(cls_subst__lift_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).

cnf(cls_mult__neg__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).

cnf(cls_mult__pos__neg2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).

cnf(cls_mult__pos__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

cnf(cls_less__1__mult_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

cnf(cls_mult__pos__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

cnf(cls_mult__neg__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

cnf(cls_substn_Osimps_I3_J_0,axiom,
    c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).

cnf(cls_nat__add__assoc_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

cnf(cls_add__neg__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

cnf(cls_add__pos__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

cnf(cls_dvd__power__same_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).

cnf(cls_dvd__mult__cancel__left_2,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).

cnf(cls_dvd__mult__cancel__right_2,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).

cnf(cls_one__less__power_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).

cnf(cls_dvd_Oless__trans_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__trans_1) ).

cnf(cls_add__less__cancel__left_1,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

cnf(cls_add__strict__left__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

cnf(cls_add__less__cancel__right_1,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

cnf(cls_add__strict__right__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

cnf(cls_pos__add__strict_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

cnf(cls_nat__mult__dvd__cancel__disj_2,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).

cnf(cls_add__gr__0_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

cnf(cls_dvd__mod_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod_0) ).

cnf(cls_dvd__mod__iff_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).

cnf(cls_dvd__mult__cancel2_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_0) ).

cnf(cls_dvd__mult__cancel1_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_0) ).

cnf(cls_nat__0__less__mult__iff_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

cnf(cls_dvd__add_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).

cnf(cls_div__mult__mult1_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_Divides_Odiv__class_Odiv(X3,X4,X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).

cnf(cls_div__mult__mult2_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_Divides_Odiv__class_Odiv(X2,X4,X1)
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).

cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1)),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

cnf(cls_div__less__dividend_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less__dividend_0) ).

cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

cnf(cls_power__commutes_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).

cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

cnf(cls_class__semiring_Omul__a_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

cnf(cls_dvd_Oless__trans_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__trans_0) ).

cnf(cls_power__mult_0,axiom,
    ( c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).

cnf(cls_class__semiring_Opwr__pwr_0,axiom,
    ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).

cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

cnf(cls_even__less__0__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

cnf(cls_nat__add__left__cancel__less_1,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

cnf(cls_add__less__mono1_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

cnf(cls_nat__mult__div__cancel__disj_1,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_1) ).

cnf(cls_lift_Osimps_I3_J_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X1)),X2) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).

cnf(cls_dvd__mult__left_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).

cnf(cls_dvd__mult__right_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).

cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

cnf(cls_add__cancel__21_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

cnf(cls_nat__mult__assoc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).

cnf(cls_div__mult2__eq_0,axiom,
    c_Divides_Odiv__class_Odiv(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X3,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult2__eq_0) ).

cnf(cls_nat__zero__less__power__iff_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_0) ).

cnf(cls_mod__mod__cancel_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).

cnf(cls_nat__0__less__mult__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

cnf(cls_nat__0__less__mult__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

cnf(cls_split__div_5,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_5) ).

cnf(cls_split__div_H_6,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_H_6) ).

cnf(cls_dvd_Ole__less__trans_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_1) ).

cnf(cls_dvd_Oless__le__trans_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_1) ).

cnf(cls_div__mult__mult1__if_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).

cnf(cls_dvd__mult__cancel__left_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).

cnf(cls_dvd__mult__cancel__right_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X1),X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).

cnf(cls_split__mod_5,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_5) ).

cnf(cls_beta_0,axiom,
    c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

cnf(cls_less__add__eq__less_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

cnf(cls_add__lessD1_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

cnf(cls_dvd__reduce_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_0) ).

cnf(cls_power__inject__exp_0,axiom,
    ( X3 = X4
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

cnf(cls_nat__mult__div__cancel__disj_0,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_0) ).

cnf(cls_dvd_Ole__less__trans_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_0) ).

cnf(cls_dvd_Oless__le__trans_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_0) ).

cnf(cls_nat__mult__dvd__cancel__disj_1,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).

cnf(cls_nat__add__left__commute_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

cnf(cls_not__square__less__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

cnf(cls_zero__less__power_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

cnf(cls_even__less__0__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

cnf(cls_map__is__Nil__conv_1,axiom,
    c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).

cnf(cls_Nil__is__map__conv_1,axiom,
    c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).

cnf(cls_dvd__power_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_0) ).

cnf(cls_nat__mult__eq__cancel1_0,axiom,
    ( X2 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).

cnf(cls_nat__dvd__not__less_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__not__less_0) ).

cnf(cls_dvd__div__mult__self_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1) = X2
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).

cnf(cls_dvd__mult__div__cancel_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1) = X3
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).

cnf(cls_dvd__mult2_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).

cnf(cls_dvd__mult_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).

cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

cnf(cls_dvd__mult__cancel2_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_1) ).

cnf(cls_dvd__mult__cancel1_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_1) ).

cnf(cls_nat__zero__less__power__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_1) ).

cnf(cls_div__mult__self1__is__m_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__m_0) ).

cnf(cls_div__mult__self__is__m_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self__is__m_0) ).

cnf(cls_mod__less__divisor_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).

cnf(cls_of__nat__add_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1)),c_Nat_Osemiring__1__class_Oof__nat(X3,X1))
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).

cnf(cls_add__gr__0_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).

cnf(cls_add__gr__0_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).

cnf(cls_order__less__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

cnf(cls_xt1_I10_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

cnf(cls_dvd__trans_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).

cnf(cls_of__nat__mult_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).

cnf(cls_of__nat__less__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

cnf(cls_div__if_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__if_0) ).

cnf(cls_trans__less__add1_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

cnf(cls_termination__basic__simps_I1_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

cnf(cls_trans__less__add2_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

cnf(cls_termination__basic__simps_I2_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

cnf(cls_dvd__reduce_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).

cnf(cls_not__add__less1_0,axiom,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

cnf(cls_not__add__less2_0,axiom,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

cnf(cls_mod__mod__trivial_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).

cnf(cls_mult__left__idem_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).

cnf(cls_dvd_Oorder__trans_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).

cnf(cls_mod__add__self1_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).

cnf(cls_mod__add__self2_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).

cnf(cls_lift__IT_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).

cnf(cls_zero__less__two_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

cnf(cls_of__nat__power_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X2,X3,tc_nat),X1) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X3,X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__power_0) ).

cnf(cls_lift_Osimps_I1_J_1,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).

cnf(cls_of__nat__0__less__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

cnf(cls_subst__lt_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).

cnf(cls_of__nat__less__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

cnf(cls_nat__less__cases_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

cnf(cls_dvd__power_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_1) ).

cnf(cls_of__nat__0__less__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

cnf(cls_class__ringb_Oadd__cancel_0,axiom,
    ( X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

cnf(cls_appR_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3))
    | ~ c_Lambda_Obeta(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).

cnf(cls_appL_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))
    | ~ c_Lambda_Obeta(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).

cnf(cls_lift__preserves__beta_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X1),X2),hAPP(hAPP(c_Lambda_Olift,X3),X2))
    | ~ c_Lambda_Obeta(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

cnf(cls_not__less__iff__gr__or__eq_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

cnf(cls_order__less__asym_H_0,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

cnf(cls_order__less__asym_0,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

cnf(cls_xt1_I9_J_0,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

cnf(cls_less__add__one_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

cnf(cls_div__mult__self1__is__id_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = X3
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).

cnf(cls_div__mult__self2__is__id_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = X2
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).

cnf(cls_add__right__cancel_0,axiom,
    ( X2 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

cnf(cls_add__left__cancel_0,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

cnf(cls_add__imp__eq_0,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

cnf(cls_mult__cancel2_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).

cnf(cls_nat__mult__eq__cancel__disj_0,axiom,
    ( X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).

cnf(cls_mult__cancel1_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).

cnf(cls_mod__div__trivial_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).

cnf(cls_mod__mult__self1__is__0_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).

cnf(cls_mod__mult__self2__is__0_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).

cnf(cls_dvd_Oneq__le__trans_0,axiom,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oneq__le__trans_0) ).

cnf(cls_dvd_Ole__neq__trans_0,axiom,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).

cnf(cls_dvd_Oantisym__conv_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oantisym__conv_0) ).

cnf(cls_dvd__antisym_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__antisym_0) ).

cnf(cls_dvd_Oless__le_0,axiom,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le_0) ).

cnf(cls_dvd_Oantisym_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).

cnf(cls_dvd_Oeq__iff_2,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).

cnf(cls_subst__Var_2,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
    | X1 = X3
    | c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).

cnf(cls_dvdI_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Odvd(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).

cnf(cls_dvd__triv__left_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).

cnf(cls_dvd__triv__right_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).

cnf(cls_nat__zero__less__power__iff_2,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_2) ).

cnf(cls_subst__Var_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).

cnf(cls_subject__reduction_0,axiom,
    ( c_Type_Otyping(X1,X2,X3)
    | ~ c_Lambda_Obeta(X4,X2)
    | ~ c_Type_Otyping(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).

cnf(cls_mod__eq__0__iff_1,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).

cnf(cls_dvd__eq__mod__eq__0_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).

cnf(cls_dvd__imp__mod__0_0,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).

cnf(cls_zero__induct_1,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__induct_1) ).

cnf(cls_nat__add__right__cancel_0,axiom,
    ( X1 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

cnf(cls_nat__add__left__cancel_0,axiom,
    ( X2 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

cnf(cls_natgb_Oadd__cancel_0,axiom,
    ( X2 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

cnf(cls_substn__subst__0_0,axiom,
    c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).

cnf(cls_of__nat__less__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

cnf(cls_div__less_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less_0) ).

cnf(cls_mod__if_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).

cnf(cls_lift_Osimps_I1_J_0,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

cnf(cls_upt_Oinduct_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upt_Oinduct_0) ).

cnf(cls_nat_Oinduct_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinduct_0) ).

cnf(cls_nat_Oinducts_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinducts_0) ).

cnf(cls_replicate_Oinduct_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate_Oinduct_0) ).

cnf(cls_nat__induct_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__induct_0) ).

cnf(cls_lexn_Oinduct_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lexn_Oinduct_0) ).

cnf(cls_power__eq__0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

cnf(cls_power__eq__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).

cnf(cls_substn_Osimps_I1_J_2,axiom,
    ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
    | X1 = X3
    | c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).

cnf(cls_linorder__antisym__conv3_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

cnf(cls_linorder__less__linear_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

cnf(cls_linorder__neqE_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | X3 = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

cnf(cls_not__less__iff__gr__or__eq_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

cnf(cls_linorder__neqE__ordered__idom_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | X3 = X2
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

cnf(cls_dB_Osimps_I2_J_0,axiom,
    ( X1 = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

cnf(cls_dB_Osimps_I2_J_1,axiom,
    ( X2 = X4
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

cnf(cls_class__semiring_Omul__c_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

cnf(cls_not__one__less__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

cnf(cls_mult__cancel1_1,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).

cnf(cls_mult__cancel2_1,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).

cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

cnf(cls_class__semiring_Oadd__c_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

cnf(cls_subst__eq_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).

cnf(cls_typing__elims_I1_J_0,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).

cnf(cls_mult__eq__0__iff_0,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
    | c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

cnf(cls_no__zero__divisors_0,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).

cnf(cls_no__zero__divirors__neq0_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

cnf(cls_linorder__neqE__nat_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

cnf(cls_nat__neq__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

cnf(cls_dvd__0__left_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).

cnf(cls_nat__mult__commute_0,axiom,
    c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).

cnf(cls_field__power__not__zero_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
    | c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

cnf(cls_double__eq__0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

cnf(cls_power__eq__0__iff_2,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | ~ class_Power_Opower(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).

cnf(cls_mult__is__0_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).

cnf(cls_linorder__neq__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

cnf(cls_order__less__irrefl_0,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

cnf(cls_order__less__le_1,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

cnf(cls_neq0__conv_1,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

cnf(cls_mult__eq__self__implies__10_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Oone__class_Oone(tc_nat)
    | X1 != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).

cnf(cls_nat__dvd__1__iff__1_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).

cnf(cls_nat__add__commute_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

cnf(cls_nat__mult__eq__1__iff_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).

cnf(cls_nat__mult__eq__1__iff_1,axiom,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).

cnf(cls_nat__1__eq__mult__iff_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).

cnf(cls_nat__1__eq__mult__iff_1,axiom,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).

cnf(cls_not__less0_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

cnf(cls_gr__implies__not0_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

cnf(cls_typing_OVar_0,axiom,
    c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).

cnf(cls_less__not__refl_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

cnf(cls_nat__less__le_1,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

cnf(cls_power__0__left_1,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).

cnf(cls_Lambda_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).

cnf(cls_power__0__left_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).

cnf(cls_double__eq__0__iff_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

cnf(cls_add__is__0_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

cnf(cls_add__is__0_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

cnf(cls_add__eq__self__zero_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

cnf(cls_natgb_Oadd__r0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

cnf(cls_zero__less__one_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

cnf(cls_add__0__left_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

cnf(cls_comm__monoid__add_Omult__1_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

cnf(cls_class__semiring_Oadd__0_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

cnf(cls_div__0_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).

cnf(cls_power__one_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).

cnf(cls_mult__eq__0__iff_1,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

cnf(cls_mult__zero__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

cnf(cls_class__semiring_Omul__0_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

cnf(cls_mod__0_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).

cnf(cls_div__by__0_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).

cnf(cls_mult__eq__0__iff_2,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

cnf(cls_mult__zero__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

cnf(cls_mod__by__1_0,axiom,
    ( c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).

cnf(cls_div__self_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).

cnf(cls_power__0_0,axiom,
    ( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).

cnf(cls_class__semiring_Opwr__0_0,axiom,
    ( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

cnf(cls_mult__1_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).

cnf(cls_class__semiring_Omul__1_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).

cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

cnf(cls_mult__1__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

cnf(cls_div__by__1_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).

cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

cnf(cls_mult__1__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

cnf(cls_mod__by__0_0,axiom,
    ( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).

cnf(cls_one__dvd_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).

cnf(cls_dvd__0__right_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).

cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom,
    ( c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).

cnf(cls_power__one__right_0,axiom,
    ( c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).

cnf(cls_mod__self_0,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).

cnf(cls_dB_Osimps_I8_J_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).

cnf(cls_dB_Osimps_I5_J_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

cnf(cls_dB_Osimps_I9_J_0,axiom,
    c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).

cnf(cls_dB_Osimps_I4_J_0,axiom,
    c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).

cnf(cls_mult__idem_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X2,X1) = X2
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).

cnf(cls_dvd__refl_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).

cnf(cls_nat__mult__eq__1__iff_2,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).

cnf(cls_nat__1__eq__mult__iff_2,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).

cnf(cls_listsp_ONil_0,axiom,
    c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).

cnf(cls_gr0I_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

cnf(cls_nat__dvd__1__iff__1_1,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).

cnf(cls_mult__is__0_1,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).

cnf(cls_power__eq__if_0,axiom,
    c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__if_0) ).

cnf(cls_mult__is__0_2,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).

cnf(cls_add__is__0_2,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).

cnf(cls_nat__mult__1_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).

cnf(cls_nat__mult__1__right_0,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).

cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
    c_fequal(X1,X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

cnf(cls_of__nat__eq__iff_0,axiom,
    ( X2 = X3
    | ~ class_Nat_Osemiring__char__0(X1)
    | c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

cnf(cls_plus__nat_Oadd__0_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

cnf(cls_dvd_Oeq__iff_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).

cnf(cls_Nat_Oadd__0__right_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

cnf(cls_natgb_Oadd__r0__iff_1,axiom,
    X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

cnf(cls_abs_0,axiom,
    ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

cnf(clsarity_fun__Orderings_Opreorder,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

cnf(clsarity_fun__Orderings_Oorder,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

cnf(cls_beta__cases_I1_J_0,axiom,
    ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

cnf(cls_of__nat__1_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).

cnf(cls_of__nat__0_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

cnf(cls_conjecture_2,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_dB_Osize_I4_J_0,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).

cnf(cls_zero__neq__one_0,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

cnf(cls_one__neq__zero_0,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

cnf(cls_dB_Osimps_I3_J_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

cnf(cls_dB_Osimps_I1_J_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

cnf(cls_dB_Osimps_I7_J_0,axiom,
    c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).

cnf(cls_dB_Osimps_I6_J_0,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

cnf(cls_dB_Osize_I1_J_0,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

cnf(clsarity_nat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

cnf(clsarity_nat__Ring__and__Field_Odvd,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).

cnf(clsarity_nat__Power_Opower,axiom,
    class_Power_Opower(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

cnf(clsarity_nat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

cnf(clsarity_nat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

cnf(clsarity_nat__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).

cnf(i_0_636,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    cls_conjecture_4 ).

cnf(i_0_637,axiom,
    c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
    cls_Suc__eq__plus1_0 ).

cnf(i_0_638,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X1))),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    cls_conjecture_1 ).

cnf(i_0_639,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
    | ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    cls_subst__subst_0 ).

cnf(i_0_640,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
    cls_mod__mult__self4_0 ).

cnf(i_0_641,axiom,
    c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4) = c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4),
    cls_shift__commute_0 ).

cnf(i_0_642,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,c_Suc(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat)),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_split__div__lemma_2 ).

cnf(i_0_643,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
    cls_Suc__mult__less__cancel1_0 ).

cnf(i_0_644,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    cls_one__less__mult_0 ).

cnf(i_0_645,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    cls_Suc__mult__less__cancel1_1 ).

cnf(i_0_646,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat),
    cls_mod__Suc__eq__Suc__mod_0 ).

cnf(i_0_647,axiom,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_dB_Osize_I5_J_0 ).

cnf(i_0_648,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X2)),c_Suc(X3)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X3)),X2)
    | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    cls_lift__lift_0 ).

cnf(i_0_649,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    cls_n__less__n__mult__m_0 ).

cnf(i_0_650,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    cls_n__less__m__mult__n_0 ).

cnf(i_0_651,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat))
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2 ),
    cls_mod__Suc_1 ).

cnf(i_0_652,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    cls_Suc__times__mod__eq_0 ).

cnf(i_0_653,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_power__Suc__less__one_0 ).

cnf(i_0_654,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
    cls_mod__Suc_0 ).

cnf(i_0_655,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_upt_Oinduct_1 ).

cnf(i_0_656,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_nat_Oinduct_1 ).

cnf(i_0_657,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_nat_Oinducts_1 ).

cnf(i_0_658,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_replicate_Oinduct_1 ).

cnf(i_0_659,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_nat__induct_1 ).

cnf(i_0_660,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_lexn_Oinduct_1 ).

cnf(i_0_661,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
    cls_less__iff__Suc__add_1 ).

cnf(i_0_662,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
    cls_less__add__Suc1_0 ).

cnf(i_0_663,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
    cls_less__add__Suc2_0 ).

cnf(i_0_664,axiom,
    c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_dB_Osize_I2_J_0 ).

cnf(i_0_665,axiom,
    ( X2 = X3
    | c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat) ),
    cls_Suc__mult__cancel1_0 ).

cnf(i_0_666,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
    cls_add__Suc_0 ).

cnf(i_0_667,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    cls_power__gt1_0 ).

cnf(i_0_668,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
    cls_Suc__less__eq_0 ).

cnf(i_0_669,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
    cls_add__Suc__shift_0 ).

cnf(i_0_670,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
    cls_add__Suc__right_0 ).

cnf(i_0_671,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))))
    | ~ hBOOL(hAPP(X1,X2)) ),
    cls_zero__induct_0 ).

cnf(i_0_672,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_Suc__mono_0 ).

cnf(i_0_673,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_less__Suc__eq__0__disj_3 ).

cnf(i_0_674,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_mult__eq__1__iff_2 ).

cnf(i_0_675,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_add__is__1_4 ).

cnf(i_0_676,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_one__is__add_4 ).

cnf(i_0_677,axiom,
    ( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    cls_power__Suc2_0 ).

cnf(i_0_678,axiom,
    ( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Power_Opower(X1) ),
    cls_power__Suc_0 ).

cnf(i_0_679,axiom,
    ( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Opwr__Suc_0 ).

cnf(i_0_680,axiom,
    ( c_Power_Opower__class_Opower(X2,c_Suc(X3),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I35_J_0 ).

cnf(i_0_681,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_Power_Opower__class_Opower(X2,c_Suc(X3),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I28_J_0 ).

cnf(i_0_682,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(X2,c_Suc(X3),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I27_J_0 ).

cnf(i_0_683,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    cls_not__less__eq_1 ).

cnf(i_0_684,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_less__trans__Suc_0 ).

cnf(i_0_685,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    cls_dvd__1__iff__1_0 ).

cnf(i_0_686,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
    cls_mult__Suc_0 ).

cnf(i_0_687,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
    cls_mult__Suc__right_0 ).

cnf(i_0_688,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    cls_less__SucE_0 ).

cnf(i_0_689,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    cls_not__less__less__Suc__eq_0 ).

cnf(i_0_690,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    cls_less__antisym_0 ).

cnf(i_0_691,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
    cls_Suc__lessD_0 ).

cnf(i_0_692,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | c_Suc(X1) = X2
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_Suc__lessI_0 ).

cnf(i_0_693,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    cls_one__is__add_1 ).

cnf(i_0_694,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_1 ).

cnf(i_0_695,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    cls_dvd__1__iff__1_1 ).

cnf(i_0_696,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    cls_less__Suc0_0 ).

cnf(i_0_697,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_less__SucI_0 ).

cnf(i_0_698,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_nat__power__eq__Suc__0__iff_0 ).

cnf(i_0_699,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_mult__eq__1__iff_0 ).

cnf(i_0_700,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_mult__eq__1__iff_1 ).

cnf(i_0_701,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    cls_one__is__add_0 ).

cnf(i_0_702,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    cls_one__is__add_3 ).

cnf(i_0_703,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_0 ).

cnf(i_0_704,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_3 ).

cnf(i_0_705,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_dB_Osize_I6_J_0 ).

cnf(i_0_706,axiom,
    c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_power__Suc__0_0 ).

cnf(i_0_707,axiom,
    c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_nat__power__eq__Suc__0__iff_2 ).

cnf(i_0_708,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_add__is__1_5 ).

cnf(i_0_709,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_one__is__add_5 ).

cnf(i_0_710,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_Oof__nat(X2,X1))
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__Suc_0 ).

cnf(i_0_711,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
    cls_not__less__less__Suc__eq_1 ).

cnf(i_0_712,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    cls_not__less__eq_0 ).

cnf(i_0_713,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_dB_Osize_I3_J_0 ).

cnf(i_0_714,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    cls_power__0__Suc_0 ).

cnf(i_0_715,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    cls_one__is__add_2 ).

cnf(i_0_716,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_2 ).

cnf(i_0_717,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    cls_less__Suc0_1 ).

cnf(i_0_718,axiom,
    c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_mod__1_0 ).

cnf(i_0_719,axiom,
    c_Divides_Odiv__class_Odiv(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
    cls_div__1_0 ).

cnf(i_0_720,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
    cls_dvd__1__left_0 ).

cnf(i_0_721,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_Suc__inject_0 ).

cnf(i_0_722,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_nat_Oinject_0 ).

cnf(i_0_723,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    cls_gr0__conv__Suc_1 ).

cnf(i_0_724,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    cls_zero__less__Suc_0 ).

cnf(i_0_725,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_lessI_0 ).

cnf(i_0_726,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_less__Suc__eq_2 ).

cnf(i_0_727,axiom,
    c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_nat__power__eq__Suc__0__iff_1 ).

cnf(i_0_728,axiom,
    c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
    cls_Suc__eq__plus1__left_0 ).

cnf(i_0_729,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_nat_Osimps_I3_J_0 ).

cnf(i_0_730,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_Suc__neq__Zero_0 ).

cnf(i_0_731,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_nat_Osimps_I2_J_0 ).

cnf(i_0_732,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_Zero__neq__Suc_0 ).

cnf(i_0_733,axiom,
    c_Suc(X1) != X1,
    cls_Suc__n__not__n_0 ).

cnf(i_0_734,axiom,
    X1 != c_Suc(X1),
    cls_n__not__Suc__n_0 ).

cnf(i_0_735,axiom,
    ( X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_not0__implies__Suc_0 ).

cnf(i_0_736,axiom,
    ( X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_nat_Onchotomy_0 ).

cnf(i_0_737,axiom,
    ( X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_nat_Oexhaust_0 ).

cnf(i_0_738,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_One__nat__def_0 ).

cnf(i_0_739,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ia),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ja),c_HOL_Oone__class_Oone(tc_nat))))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_636,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_740,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_638,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_741,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    cls_subst__map_0,
    [final] ).

cnf(i_0_742,axiom,
    ( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X3,X6,tc_Type_Otype),X4,X5)
    | ~ c_Type_Otyping(X1,X2,X6) ),
    cls_substs__lemma_0,
    [final] ).

cnf(i_0_743,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    cls_Beta_0,
    [final] ).

cnf(i_0_744,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    cls_lift__map_0,
    [final] ).

cnf(i_0_745,axiom,
    ( X1 = X2
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X1) ),
    cls_var__app__type__eq_0,
    [final] ).

cnf(i_0_746,axiom,
    ( c_Type_Otypings(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | ~ c_Type_Otypings(X1,X4,X5) ),
    cls_lift__types_0,
    [final] ).

cnf(i_0_747,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    cls_conjecture_0,
    [final] ).

cnf(i_0_748,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    cls_lifts__IT_0,
    [final] ).

cnf(i_0_749,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB) ),
    cls_IT_OVar_0,
    [final] ).

cnf(i_0_750,axiom,
    ( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB))
    | ~ c_Lambda_Obeta(X1,X3) ),
    cls_apps__preserves__beta_0,
    [final] ).

cnf(i_0_751,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
    | ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_639,c_0_637]),
    [final] ).

cnf(i_0_752,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Abs__apps__eq__Abs__apps__conv_0,
    [final] ).

cnf(i_0_753,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Var__apps__eq__Var__apps__conv_0,
    [final] ).

cnf(i_0_754,axiom,
    ( X2 = X4
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Abs__apps__eq__Abs__apps__conv_1,
    [final] ).

cnf(i_0_755,axiom,
    ( X2 = X4
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Var__apps__eq__Var__apps__conv_1,
    [final] ).

cnf(i_0_756,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    cls_foldl__assoc_0,
    [final] ).

cnf(i_0_757,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
    cls_Var__apps__neq__Abs__apps_0,
    [final] ).

cnf(i_0_758,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_apps__eq__tail__conv_0,
    [final] ).

cnf(i_0_759,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_foldl__absorb0_0,
    [final] ).

cnf(i_0_760,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hBOOL(hAPP(X3,X1))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)),X1),X2,tc_nat))) ),
    cls_split__mod_1,
    [final] ).

cnf(i_0_761,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hBOOL(hAPP(X3,X4))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ hBOOL(hAPP(X3,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)),X1),X2,tc_nat))) ),
    cls_split__div_1,
    [final] ).

cnf(i_0_762,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__mod__equality_0,
    [final] ).

cnf(i_0_763,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__mod__equality2_0,
    [final] ).

cnf(i_0_764,axiom,
    c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X1,X3,tc_nat)),c_Divides_Odiv__class_Odiv(X2,X3,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X1,X3,tc_nat)),c_Divides_Odiv__class_Omod(X2,X3,tc_nat)),X3,tc_nat)),
    cls_div__add1__eq_0,
    [final] ).

cnf(i_0_765,axiom,
    hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
    cls_ATP__Linkup_OCOMBC__def_0,
    [final] ).

cnf(i_0_766,axiom,
    hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
    cls_COMBC__def_0,
    [final] ).

cnf(i_0_767,plain,
    c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3)),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_640,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_768,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_App__eq__foldl__conv_0,
    [final] ).

cnf(i_0_769,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
    cls_Abs__App__neq__Var__apps_0,
    [final] ).

cnf(i_0_770,axiom,
    ( c_Lambda_OdB_OAbs(X1) = X2
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Abs__eq__apps__conv_0,
    [final] ).

cnf(i_0_771,axiom,
    ( c_Lambda_OdB_OVar(X1) = X2
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Var__eq__apps__conv_0,
    [final] ).

cnf(i_0_772,axiom,
    ( X1 = c_Lambda_OdB_OAbs(X3)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    cls_apps__eq__Abs__conv_0,
    [final] ).

cnf(i_0_773,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X2),X4)),X3)
    | ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    cls_lift__subst_0,
    [final] ).

cnf(i_0_774,axiom,
    ( X2 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    cls_apps__eq__Abs__conv_1,
    [final] ).

cnf(i_0_775,axiom,
    ( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Abs__eq__apps__conv_1,
    [final] ).

cnf(i_0_776,axiom,
    ( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Var__eq__apps__conv_1,
    [final] ).

cnf(i_0_777,axiom,
    c_Divides_Odiv__class_Omod(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X3,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),
    cls_mod__mult2__eq_0,
    [final] ).

cnf(i_0_778,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat)),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X4,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    cls_mod__lemma_0,
    [final] ).

cnf(i_0_779,plain,
    c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4) = c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X3,X4),
    inference(rw,[status(thm)],[i_0_641,c_0_637]),
    [final] ).

cnf(i_0_780,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X3,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X3,tc_nat)),
    cls_div__mult1__eq_0,
    [final] ).

cnf(i_0_781,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),X1) ),
    cls_sum__squares__gt__zero__iff_0,
    [final] ).

cnf(i_0_782,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X4,X3,X1)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)),X5)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    cls_combine__common__factor_0,
    [final] ).

cnf(i_0_783,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)),X4),
    cls_left__add__mult__distrib_0,
    [final] ).

cnf(i_0_784,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    cls_App__eq__foldl__conv_4,
    [final] ).

cnf(i_0_785,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_not__sum__squares__lt__zero_0,
    [final] ).

cnf(i_0_786,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X2,X1,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[i_0_642,c_0_637]),
    [final] ).

cnf(i_0_787,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X4)),hAPP(hAPP(c_Lambda_Olift,X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    cls_lift__subst__lt_0,
    [final] ).

cnf(i_0_788,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
    cls_apps__eq__Abs__conv_2,
    [final] ).

cnf(i_0_789,axiom,
    c_Lambda_OdB_OAbs(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    cls_Abs__eq__apps__conv_2,
    [final] ).

cnf(i_0_790,axiom,
    c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    cls_Var__eq__apps__conv_2,
    [final] ).

cnf(i_0_791,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
    cls_foldl__Nil_0,
    [final] ).

cnf(i_0_792,axiom,
    ( X3 = X5
    | X2 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X5,X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X5,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) ),
    cls_class__ringb_Onoteq__reduce_0,
    [final] ).

cnf(i_0_793,axiom,
    ( X3 = X5
    | X2 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X5,X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X5,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) ),
    cls_class__ringb_Oadd__mul__solve_0,
    [final] ).

cnf(i_0_794,axiom,
    ( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    cls_subst__lemma_0,
    [final] ).

cnf(i_0_795,axiom,
    ( X2 = X4
    | X1 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)) ),
    cls_natgb_Oadd__mul__solve_0,
    [final] ).

cnf(i_0_796,axiom,
    ( X2 = X4
    | X1 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)) ),
    cls_natgb_Onoteq__reduce_0,
    [final] ).

cnf(i_0_797,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X1,tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_643,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_798,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__eq_0,
    [final] ).

cnf(i_0_799,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),
    cls_subst__App_0,
    [final] ).

cnf(i_0_800,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_sum__squares__gt__zero__iff_1,
    [final] ).

cnf(i_0_801,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),X1)
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_sum__squares__gt__zero__iff_2,
    [final] ).

cnf(i_0_802,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__div__equality_0,
    [final] ).

cnf(i_0_803,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1)) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__div__equality2_0,
    [final] ).

cnf(i_0_804,axiom,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__div__decomp_0,
    [final] ).

cnf(i_0_805,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    cls_subst__Abs_0,
    [final] ).

cnf(i_0_806,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_644,c_0_637]),c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_807,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Onoteq__reduce_1,
    [final] ).

cnf(i_0_808,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Oadd__mul__solve_1,
    [final] ).

cnf(i_0_809,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__eq_0,
    [final] ).

cnf(i_0_810,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_zmod__simps_I1_J_0,
    [final] ).

cnf(i_0_811,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__left__eq_0,
    [final] ).

cnf(i_0_812,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_645,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_813,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I20_J_0,
    [final] ).

cnf(i_0_814,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_Divides_Odiv__class_Odiv(X4,X5,X1),X1) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    cls_div__mult__div__if__dvd_0,
    [final] ).

cnf(i_0_815,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
    cls_natgb_Oadd__mul__solve_1,
    [final] ).

cnf(i_0_816,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
    cls_natgb_Onoteq__reduce_1,
    [final] ).

cnf(i_0_817,plain,
    c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_646,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_818,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X2,X4,X1)),c_Divides_Odiv__class_Odiv(X3,X4,X1))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,X1) ),
    cls_div__add_0,
    [final] ).

cnf(i_0_819,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X4),X2),X5)
    | ~ c_Type_Otyping(X1,X4,X5) ),
    cls_lift__type_0,
    [final] ).

cnf(i_0_820,plain,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[i_0_647,c_0_637]),
    [final] ).

cnf(i_0_821,plain,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X3)),X2)
    | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_648,c_0_637]),
    [final] ).

cnf(i_0_822,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_power__Suc__less_0,
    [final] ).

cnf(i_0_823,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
    | c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
    cls_mod__mult__cong_0,
    [final] ).

cnf(i_0_824,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_649,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_825,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_650,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_826,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_651,c_0_637]),c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_827,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X2),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X6),X4),X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
    | c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
    cls_mod__add__cong_0,
    [final] ).

cnf(i_0_828,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X4,X1),c_Divides_Odiv__class_Odiv(X3,X4,X1),X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X2,X1) ),
    cls_div__dvd__div_0,
    [final] ).

cnf(i_0_829,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[i_0_652,c_0_637]),
    [final] ).

cnf(i_0_830,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I15_J_0,
    [final] ).

cnf(i_0_831,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I14_J_0,
    [final] ).

cnf(i_0_832,axiom,
    c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X3),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
    cls_mod__mult__self3_0,
    [final] ).

cnf(i_0_833,axiom,
    ( hAPP(c_Type_Oshift(X1,X2,X3,X4),X5) = hAPP(X1,X5)
    | ~ c_HOL_Oord__class_Oless(X5,X2,tc_nat) ),
    cls_shift__gt_0,
    [final] ).

cnf(i_0_834,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_sum__squares__eq__zero__iff_0,
    [final] ).

cnf(i_0_835,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_sum__squares__eq__zero__iff_1,
    [final] ).

cnf(i_0_836,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_semiring__div__class_Omod__div__equality_H_0,
    [final] ).

cnf(i_0_837,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    cls_power__less__power__Suc_0,
    [final] ).

cnf(i_0_838,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
    cls_mult__less__cancel__left__pos_0,
    [final] ).

cnf(i_0_839,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__less__cancel__left__neg_0,
    [final] ).

cnf(i_0_840,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X4,X1) ),
    cls_power__less__imp__less__exp_0,
    [final] ).

cnf(i_0_841,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X4,X1) ),
    cls_power__strict__increasing__iff_0,
    [final] ).

cnf(i_0_842,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X4,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat)) ),
    cls_nat__mod__eq__iff_1,
    [final] ).

cnf(i_0_843,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    inference(rw,[status(thm)],[i_0_653,c_0_637]),
    [final] ).

cnf(i_0_844,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != X2 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_654,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_845,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X1,tc_nat),c_Power_Opower__class_Opower(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    cls_nat__power__less__imp__less_0,
    [final] ).

cnf(i_0_846,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    cls_nat__mult__less__cancel1_0,
    [final] ).

cnf(i_0_847,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    cls_dvd__mult__cancel_0,
    [final] ).

cnf(i_0_848,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    cls_nat__mult__dvd__cancel1_0,
    [final] ).

cnf(i_0_849,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    cls_power__strict__decreasing_0,
    [final] ).

cnf(i_0_850,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    cls_mult__less__cancel__left__disj_0,
    [final] ).

cnf(i_0_851,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    cls_mult__less__cancel__right__disj_0,
    [final] ).

cnf(i_0_852,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    cls_mult__less__cancel__right__disj_1,
    [final] ).

cnf(i_0_853,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    cls_mult__less__cancel__left__disj_1,
    [final] ).

cnf(i_0_854,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    cls_mult__less__cancel__left__disj_2,
    [final] ).

cnf(i_0_855,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    cls_mult__less__cancel__right__disj_2,
    [final] ).

cnf(i_0_856,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I13_J_0,
    [final] ).

cnf(i_0_857,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_zmod__simps_I4_J_0,
    [final] ).

cnf(i_0_858,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__left__eq_0,
    [final] ).

cnf(i_0_859,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__right__eq_0,
    [final] ).

cnf(i_0_860,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),c_Divides_Odiv__class_Odiv(X2,X3,X1))
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__mult__self2_0,
    [final] ).

cnf(i_0_861,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_Divides_Odiv__class_Odiv(X2,X4,X1))
    | X4 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__mult__self1_0,
    [final] ).

cnf(i_0_862,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    cls_mult__less__cancel__right__disj_3,
    [final] ).

cnf(i_0_863,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    cls_mult__less__cancel__left__disj_3,
    [final] ).

cnf(i_0_864,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I1_J_0,
    [final] ).

cnf(i_0_865,axiom,
    ( c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1))
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    cls_comm__semiring__class_Odistrib_0,
    [final] ).

cnf(i_0_866,axiom,
    ( c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I8_J_0,
    [final] ).

cnf(i_0_867,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__d_0,
    [final] ).

cnf(i_0_868,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X3,X1),c_Divides_Odiv__class_Odiv(X4,X3,X1),X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    cls_div__dvd__div_1,
    [final] ).

cnf(i_0_869,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_zmod__simps_I2_J_0,
    [final] ).

cnf(i_0_870,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__right__eq_0,
    [final] ).

cnf(i_0_871,axiom,
    ( c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    cls_div__power_0,
    [final] ).

cnf(i_0_872,axiom,
    ( X4 = X5
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X5,X1)) ),
    cls_class__ringb_Oadd__scale__eq__noteq_0,
    [final] ).

cnf(i_0_873,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I23_J_0,
    [final] ).

cnf(i_0_874,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__List__Xupt__Xinduct__1(X1)),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(rw,[status(thm)],[i_0_655,c_0_637]),
    [final] ).

cnf(i_0_875,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__Nat__Xnat__Xinduct__1(X1)),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(rw,[status(thm)],[i_0_656,c_0_637]),
    [final] ).

cnf(i_0_876,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__Nat__Xnat__Xinducts__1(X1)),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(rw,[status(thm)],[i_0_657,c_0_637]),
    [final] ).

cnf(i_0_877,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__List__Xreplicate__Xinduct__1(X1)),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(rw,[status(thm)],[i_0_658,c_0_637]),
    [final] ).

cnf(i_0_878,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(rw,[status(thm)],[i_0_659,c_0_637]),
    [final] ).

cnf(i_0_879,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__List__Xlexn__Xinduct__1(X1)),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(rw,[status(thm)],[i_0_660,c_0_637]),
    [final] ).

cnf(i_0_880,plain,
    c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_661,c_0_637]),
    [final] ).

cnf(i_0_881,plain,
    c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_662,c_0_637]),
    [final] ).

cnf(i_0_882,plain,
    c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_663,c_0_637]),
    [final] ).

cnf(i_0_883,axiom,
    hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
    cls_shift__eq_0,
    [final] ).

cnf(i_0_884,axiom,
    c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)),
    cls_add__mult__distrib_0,
    [final] ).

cnf(i_0_885,axiom,
    c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),
    cls_add__mult__distrib2_0,
    [final] ).

cnf(i_0_886,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | X4 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    cls_dvd__mult__cancel__right_0,
    [final] ).

cnf(i_0_887,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | X4 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_dvd__mult__cancel__left_0,
    [final] ).

cnf(i_0_888,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    cls_power__gt1__lemma_0,
    [final] ).

cnf(i_0_889,plain,
    c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[i_0_664,c_0_637]),
    [final] ).

cnf(i_0_890,axiom,
    c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)),
    cls_substn_Osimps_I2_J_0,
    [final] ).

cnf(i_0_891,axiom,
    ( X3 = X4
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) ),
    cls_natgb_Oadd__scale__eq__noteq_0,
    [final] ).

cnf(i_0_892,plain,
    ( X2 = X3
    | c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) != c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X3,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_665,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_893,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
    cls_add__less__cancel__right_0,
    [final] ).

cnf(i_0_894,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
    cls_add__less__cancel__left_0,
    [final] ).

cnf(i_0_895,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_666,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_896,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    cls_nat__mult__dvd__cancel__disj_0,
    [final] ).

cnf(i_0_897,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    cls_mult__less__cancel1_0,
    [final] ).

cnf(i_0_898,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
    cls_mult__less__cancel2_0,
    [final] ).

cnf(i_0_899,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    cls_mult__less__cancel2_1,
    [final] ).

cnf(i_0_900,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    cls_mult__less__cancel1_1,
    [final] ).

cnf(i_0_901,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    inference(rw,[status(thm)],[i_0_667,c_0_637]),
    [final] ).

cnf(i_0_902,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_mult__strict__left__mono__comm_0,
    [final] ).

cnf(i_0_903,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_mult__strict__left__mono_0,
    [final] ).

cnf(i_0_904,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__less__cancel__left__disj_4,
    [final] ).

cnf(i_0_905,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__less__cancel__left__pos_1,
    [final] ).

cnf(i_0_906,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_mult__strict__right__mono_0,
    [final] ).

cnf(i_0_907,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_mult__less__cancel__right__disj_4,
    [final] ).

cnf(i_0_908,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__less__cancel__left__disj_5,
    [final] ).

cnf(i_0_909,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    cls_mult__strict__left__mono__neg_0,
    [final] ).

cnf(i_0_910,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__less__cancel__left__neg_1,
    [final] ).

cnf(i_0_911,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__less__cancel__right__disj_5,
    [final] ).

cnf(i_0_912,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X1) ),
    cls_mult__strict__right__mono__neg_0,
    [final] ).

cnf(i_0_913,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_sum__squares__eq__zero__iff_2,
    [final] ).

cnf(i_0_914,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    cls_power__strict__increasing_0,
    [final] ).

cnf(i_0_915,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    cls_power__strict__increasing__iff_1,
    [final] ).

cnf(i_0_916,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    cls_mult__dvd__mono_0,
    [final] ).

cnf(i_0_917,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),X3) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I2_J_0,
    [final] ).

cnf(i_0_918,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X3,X2,X1)),c_HOL_Oone__class_Oone(X1))
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__add__self1_0,
    [final] ).

cnf(i_0_919,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Odiv(X2,X3,X1)),c_HOL_Oone__class_Oone(X1))
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__add__self2_0,
    [final] ).

cnf(i_0_920,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_668,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_921,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__strict__mono_0,
    [final] ).

cnf(i_0_922,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__mult2_0,
    [final] ).

cnf(i_0_923,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__mult1_0,
    [final] ).

cnf(i_0_924,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    cls_power__mult__distrib_0,
    [final] ).

cnf(i_0_925,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Opwr__mul_0,
    [final] ).

cnf(i_0_926,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__mult__less__cancel1_1,
    [final] ).

cnf(i_0_927,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    cls_mult__less__mono2_0,
    [final] ).

cnf(i_0_928,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_mult__less__cancel1_2,
    [final] ).

cnf(i_0_929,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_mult__less__mono1_0,
    [final] ).

cnf(i_0_930,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_mult__less__cancel2_2,
    [final] ).

cnf(i_0_931,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__mult__dvd__cancel1_1,
    [final] ).

cnf(i_0_932,axiom,
    hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)),
    cls_lift_Osimps_I2_J_0,
    [final] ).

cnf(i_0_933,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__self2_0,
    [final] ).

cnf(i_0_934,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__self1_0,
    [final] ).

cnf(i_0_935,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    cls_split__div_0,
    [final] ).

cnf(i_0_936,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    cls_zero__less__mult__pos2_0,
    [final] ).

cnf(i_0_937,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
    cls_zero__less__mult__pos_0,
    [final] ).

cnf(i_0_938,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    cls_split__mod_0,
    [final] ).

cnf(i_0_939,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
    cls_nat__add__left__cancel__less_0,
    [final] ).

cnf(i_0_940,axiom,
    ( c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    cls_power__add_0,
    [final] ).

cnf(i_0_941,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1) = c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__pwr_0,
    [final] ).

cnf(i_0_942,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__assoc_0,
    [final] ).

cnf(i_0_943,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
    [final] ).

cnf(i_0_944,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I21_J_0,
    [final] ).

cnf(i_0_945,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__a_0,
    [final] ).

cnf(i_0_946,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I25_J_0,
    [final] ).

cnf(i_0_947,axiom,
    c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    cls_mod__mult__distrib_0,
    [final] ).

cnf(i_0_948,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    cls_mod__mult__distrib2_0,
    [final] ).

cnf(i_0_949,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    cls_dvd__div__mult_0,
    [final] ).

cnf(i_0_950,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    cls_dvd__mod__iff_0,
    [final] ).

cnf(i_0_951,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1) ),
    cls_dvd__mod__imp__dvd_0,
    [final] ).

cnf(i_0_952,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__mult__div__cancel1_0,
    [final] ).

cnf(i_0_953,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_add__less__mono_0,
    [final] ).

cnf(i_0_954,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Omap(X1,X2,X3,X4) != c_List_Olist_ONil(X4) ),
    cls_map__is__Nil__conv_0,
    [final] ).

cnf(i_0_955,axiom,
    ( X3 = c_List_Olist_ONil(X4)
    | c_List_Olist_ONil(X1) != c_List_Omap(X2,X3,X4,X1) ),
    cls_Nil__is__map__conv_0,
    [final] ).

cnf(i_0_956,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2))),
    cls_conjecture_3,
    [final] ).

cnf(i_0_957,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
    cls_add__cancel__21_0,
    [final] ).

cnf(i_0_958,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_669,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_959,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X2),X3))
    | ~ c_Lambda_Obeta(X1,X4) ),
    cls_subst__preserves__beta_0,
    [final] ).

cnf(i_0_960,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
    cls_subst__lift_0,
    [final] ).

cnf(i_0_961,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_670,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_962,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__neg__pos_0,
    [final] ).

cnf(i_0_963,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_mult__pos__neg2_0,
    [final] ).

cnf(i_0_964,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__pos__neg_0,
    [final] ).

cnf(i_0_965,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    cls_less__1__mult_0,
    [final] ).

cnf(i_0_966,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__pos__pos_0,
    [final] ).

cnf(i_0_967,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__neg__neg_0,
    [final] ).

cnf(i_0_968,axiom,
    c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    cls_substn_Osimps_I3_J_0,
    [final] ).

cnf(i_0_969,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
    cls_nat__add__assoc_0,
    [final] ).

cnf(i_0_970,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__neg__neg_0,
    [final] ).

cnf(i_0_971,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__pos__pos_0,
    [final] ).

cnf(i_0_972,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    cls_dvd__power__same_0,
    [final] ).

cnf(i_0_973,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1) ),
    cls_dvd__mult__cancel__left_2,
    [final] ).

cnf(i_0_974,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    cls_dvd__mult__cancel__right_2,
    [final] ).

cnf(i_0_975,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    cls_one__less__power_0,
    [final] ).

cnf(i_0_976,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    cls_dvd_Oless__trans_1,
    [final] ).

cnf(i_0_977,plain,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1)),c_HOL_Oone__class_Oone(tc_nat))))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_671,c_0_637]),
    [final] ).

cnf(i_0_978,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_add__less__cancel__left_1,
    [final] ).

cnf(i_0_979,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_add__strict__left__mono_0,
    [final] ).

cnf(i_0_980,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__less__cancel__right_1,
    [final] ).

cnf(i_0_981,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__strict__right__mono_0,
    [final] ).

cnf(i_0_982,axiom,
    ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_pos__add__strict_0,
    [final] ).

cnf(i_0_983,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    cls_nat__mult__dvd__cancel__disj_2,
    [final] ).

cnf(i_0_984,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    cls_add__gr__0_0,
    [final] ).

cnf(i_0_985,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
    cls_dvd__mod_0,
    [final] ).

cnf(i_0_986,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    cls_dvd__mod__iff_1,
    [final] ).

cnf(i_0_987,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_dvd__mult__cancel2_0,
    [final] ).

cnf(i_0_988,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_dvd__mult__cancel1_0,
    [final] ).

cnf(i_0_989,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__0__less__mult__iff_2,
    [final] ).

cnf(i_0_990,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
    cls_dvd__add_0,
    [final] ).

cnf(i_0_991,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_Divides_Odiv__class_Odiv(X3,X4,X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__mult__mult1_0,
    [final] ).

cnf(i_0_992,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_Divides_Odiv__class_Odiv(X2,X4,X1)
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__mult__mult2_0,
    [final] ).

cnf(i_0_993,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1)),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I3_J_0,
    [final] ).

cnf(i_0_994,axiom,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat) ),
    cls_div__less__dividend_0,
    [final] ).

cnf(i_0_995,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I16_J_0,
    [final] ).

cnf(i_0_996,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    cls_power__commutes_0,
    [final] ).

cnf(i_0_997,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,
    [final] ).

cnf(i_0_998,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I17_J_0,
    [final] ).

cnf(i_0_999,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__a_0,
    [final] ).

cnf(i_0_1000,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I18_J_0,
    [final] ).

cnf(i_0_1001,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I19_J_0,
    [final] ).

cnf(i_0_1002,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_672,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1003,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_673,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1004,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    cls_dvd_Oless__trans_0,
    [final] ).

cnf(i_0_1005,axiom,
    ( c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    cls_power__mult_0,
    [final] ).

cnf(i_0_1006,axiom,
    ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Opwr__pwr_0,
    [final] ).

cnf(i_0_1007,plain,
    c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_674,c_0_637]),c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1008,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
    cls_zero__less__double__add__iff__zero__less__single__add_0,
    [final] ).

cnf(i_0_1009,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_even__less__0__iff_0,
    [final] ).

cnf(i_0_1010,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__less__zero__iff__single__less__zero_0,
    [final] ).

cnf(i_0_1011,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_675,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1012,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_676,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1013,plain,
    ( c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(rw,[status(thm)],[i_0_677,c_0_637]),
    [final] ).

cnf(i_0_1014,plain,
    ( c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Power_Opower(X1) ),
    inference(rw,[status(thm)],[i_0_678,c_0_637]),
    [final] ).

cnf(i_0_1015,plain,
    ( c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(rw,[status(thm)],[i_0_679,c_0_637]),
    [final] ).

cnf(i_0_1016,plain,
    ( c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X1) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(rw,[status(thm)],[i_0_680,c_0_637]),
    [final] ).

cnf(i_0_1017,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X1),X2,X1) = c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(rw,[status(thm)],[i_0_681,c_0_637]),
    [final] ).

cnf(i_0_1018,plain,
    ( c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(rw,[status(thm)],[i_0_682,c_0_637]),
    [final] ).

cnf(i_0_1019,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_683,c_0_637]),
    [final] ).

cnf(i_0_1020,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(rw,[status(thm)],[i_0_684,c_0_637]),
    [final] ).

cnf(i_0_1021,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    cls_nat__add__left__cancel__less_1,
    [final] ).

cnf(i_0_1022,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_add__less__mono1_0,
    [final] ).

cnf(i_0_1023,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_nat__mult__div__cancel__disj_1,
    [final] ).

cnf(i_0_1024,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X1)),X2) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),
    cls_lift_Osimps_I3_J_0,
    [final] ).

cnf(i_0_1025,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1) ),
    cls_dvd__mult__left_0,
    [final] ).

cnf(i_0_1026,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X2,X1),X3,X1) ),
    cls_dvd__mult__right_0,
    [final] ).

cnf(i_0_1027,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__left__commute_0,
    [final] ).

cnf(i_0_1028,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I22_J_0,
    [final] ).

cnf(i_0_1029,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_add__cancel__21_1,
    [final] ).

cnf(i_0_1030,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    cls_nat__mult__assoc_0,
    [final] ).

cnf(i_0_1031,axiom,
    c_Divides_Odiv__class_Odiv(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat),X3,tc_nat),
    cls_div__mult2__eq_0,
    [final] ).

cnf(i_0_1032,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat) ),
    cls_nat__zero__less__power__iff_0,
    [final] ).

cnf(i_0_1033,plain,
    ( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_685,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1034,axiom,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1) ),
    cls_mod__mod__cancel_0,
    [final] ).

cnf(i_0_1035,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    cls_nat__0__less__mult__iff_0,
    [final] ).

cnf(i_0_1036,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    cls_nat__0__less__mult__iff_1,
    [final] ).

cnf(i_0_1037,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_split__div_5,
    [final] ).

cnf(i_0_1038,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_split__div_H_6,
    [final] ).

cnf(i_0_1039,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    cls_dvd_Ole__less__trans_1,
    [final] ).

cnf(i_0_1040,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    cls_dvd_Oless__le__trans_1,
    [final] ).

cnf(i_0_1041,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__mult__mult1__if_0,
    [final] ).

cnf(i_0_1042,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    cls_dvd__mult__cancel__left_1,
    [final] ).

cnf(i_0_1043,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X1),X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    cls_dvd__mult__cancel__right_1,
    [final] ).

cnf(i_0_1044,plain,
    c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
    inference(rw,[status(thm)],[i_0_686,c_0_637]),
    [final] ).

cnf(i_0_1045,plain,
    c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),
    inference(rw,[status(thm)],[i_0_687,c_0_637]),
    [final] ).

cnf(i_0_1046,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    cls_split__mod_5,
    [final] ).

cnf(i_0_1047,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_688,c_0_637]),
    [final] ).

cnf(i_0_1048,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_689,c_0_637]),
    [final] ).

cnf(i_0_1049,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_690,c_0_637]),
    [final] ).

cnf(i_0_1050,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_691,c_0_637]),
    [final] ).

cnf(i_0_1051,axiom,
    c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_beta_0,
    [final] ).

cnf(i_0_1052,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = X2
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_692,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1053,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    cls_less__add__eq__less_0,
    [final] ).

cnf(i_0_1054,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
    cls_add__lessD1_0,
    [final] ).

cnf(i_0_1055,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    cls_dvd__reduce_0,
    [final] ).

cnf(i_0_1056,axiom,
    ( X3 = X4
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    cls_power__inject__exp_0,
    [final] ).

cnf(i_0_1057,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_nat__mult__div__cancel__disj_0,
    [final] ).

cnf(i_0_1058,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    cls_dvd_Ole__less__trans_0,
    [final] ).

cnf(i_0_1059,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    cls_dvd_Oless__le__trans_0,
    [final] ).

cnf(i_0_1060,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat),
    cls_nat__mult__dvd__cancel__disj_1,
    [final] ).

cnf(i_0_1061,plain,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_693,c_0_637]),c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1062,plain,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_694,c_0_637]),c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1063,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
    cls_nat__add__left__commute_0,
    [final] ).

cnf(i_0_1064,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_not__square__less__zero_0,
    [final] ).

cnf(i_0_1065,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_zero__less__power_0,
    [final] ).

cnf(i_0_1066,plain,
    c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_695,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1067,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_even__less__0__iff_1,
    [final] ).

cnf(i_0_1068,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__less__zero__iff__single__less__zero_1,
    [final] ).

cnf(i_0_1069,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_zero__less__double__add__iff__zero__less__single__add_1,
    [final] ).

cnf(i_0_1070,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_696,c_0_637]),
    [final] ).

cnf(i_0_1071,axiom,
    c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
    cls_map__is__Nil__conv_1,
    [final] ).

cnf(i_0_1072,axiom,
    c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
    cls_Nil__is__map__conv_1,
    [final] ).

cnf(i_0_1073,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    cls_dvd__power_0,
    [final] ).

cnf(i_0_1074,axiom,
    ( X2 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__mult__eq__cancel1_0,
    [final] ).

cnf(i_0_1075,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_nat__dvd__not__less_0,
    [final] ).

cnf(i_0_1076,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1) = X2
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    cls_dvd__div__mult__self_0,
    [final] ).

cnf(i_0_1077,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1) = X3
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
    cls_dvd__mult__div__cancel_0,
    [final] ).

cnf(i_0_1078,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
    cls_dvd__mult2_0,
    [final] ).

cnf(i_0_1079,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    cls_dvd__mult_0,
    [final] ).

cnf(i_0_1080,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I4_J_0,
    [final] ).

cnf(i_0_1081,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_dvd__mult__cancel2_1,
    [final] ).

cnf(i_0_1082,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_dvd__mult__cancel1_1,
    [final] ).

cnf(i_0_1083,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__zero__less__power__iff_1,
    [final] ).

cnf(i_0_1084,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_div__mult__self1__is__m_0,
    [final] ).

cnf(i_0_1085,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_div__mult__self__is__m_0,
    [final] ).

cnf(i_0_1086,axiom,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_mod__less__divisor_0,
    [final] ).

cnf(i_0_1087,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1)),c_Nat_Osemiring__1__class_Oof__nat(X3,X1))
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__add_0,
    [final] ).

cnf(i_0_1088,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_add__gr__0_1,
    [final] ).

cnf(i_0_1089,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_add__gr__0_2,
    [final] ).

cnf(i_0_1090,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_order__less__trans_0,
    [final] ).

cnf(i_0_1091,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    cls_xt1_I10_J_0,
    [final] ).

cnf(i_0_1092,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
    cls_dvd__trans_0,
    [final] ).

cnf(i_0_1093,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_697,c_0_637]),
    [final] ).

cnf(i_0_1094,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X1) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__mult_0,
    [final] ).

cnf(i_0_1095,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | c_Power_Opower__class_Opower(X1,X2,tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_698,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1096,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
    cls_of__nat__less__iff_0,
    [final] ).

cnf(i_0_1097,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_div__if_0,
    [final] ).

cnf(i_0_1098,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_trans__less__add1_0,
    [final] ).

cnf(i_0_1099,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_termination__basic__simps_I1_J_0,
    [final] ).

cnf(i_0_1100,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_trans__less__add2_0,
    [final] ).

cnf(i_0_1101,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_termination__basic__simps_I2_J_0,
    [final] ).

cnf(i_0_1102,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    cls_dvd__reduce_1,
    [final] ).

cnf(i_0_1103,plain,
    ( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_699,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1104,plain,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_700,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1105,axiom,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
    cls_not__add__less1_0,
    [final] ).

cnf(i_0_1106,axiom,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
    cls_not__add__less2_0,
    [final] ).

cnf(i_0_1107,axiom,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mod__trivial_0,
    [final] ).

cnf(i_0_1108,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
    cls_mult__left__idem_0,
    [final] ).

cnf(i_0_1109,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    cls_dvd_Oorder__trans_0,
    [final] ).

cnf(i_0_1110,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_701,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1111,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_702,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1112,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_703,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1113,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_704,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1114,plain,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[i_0_705,c_0_637]),
    [final] ).

cnf(i_0_1115,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__self1_0,
    [final] ).

cnf(i_0_1116,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__self2_0,
    [final] ).

cnf(i_0_1117,plain,
    c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_706,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1118,plain,
    c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_707,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1119,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_708,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1120,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_709,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1121,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_lift__IT_0,
    [final] ).

cnf(i_0_1122,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_Oof__nat(X2,X1))
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(rw,[status(thm)],[i_0_710,c_0_637]),
    [final] ).

cnf(i_0_1123,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_zero__less__two_0,
    [final] ).

cnf(i_0_1124,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X2,X3,tc_nat),X1) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X3,X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__power_0,
    [final] ).

cnf(i_0_1125,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_lift_Osimps_I1_J_1,
    [final] ).

cnf(i_0_1126,plain,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_711,c_0_637]),
    [final] ).

cnf(i_0_1127,plain,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_712,c_0_637]),
    [final] ).

cnf(i_0_1128,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
    cls_of__nat__0__less__iff_0,
    [final] ).

cnf(i_0_1129,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_subst__lt_0,
    [final] ).

cnf(i_0_1130,axiom,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    cls_of__nat__less__iff_1,
    [final] ).

cnf(i_0_1131,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    cls_nat__less__cases_0,
    [final] ).

cnf(i_0_1132,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_dvd__power_1,
    [final] ).

cnf(i_0_1133,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_of__nat__0__less__iff_1,
    [final] ).

cnf(i_0_1134,axiom,
    ( X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    cls_class__ringb_Oadd__cancel_0,
    [final] ).

cnf(i_0_1135,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3))
    | ~ c_Lambda_Obeta(X2,X3) ),
    cls_appR_0,
    [final] ).

cnf(i_0_1136,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))
    | ~ c_Lambda_Obeta(X1,X3) ),
    cls_appL_0,
    [final] ).

cnf(i_0_1137,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X1),X2),hAPP(hAPP(c_Lambda_Olift,X3),X2))
    | ~ c_Lambda_Obeta(X1,X3) ),
    cls_lift__preserves__beta_0,
    [final] ).

cnf(i_0_1138,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_not__less__iff__gr__or__eq_1,
    [final] ).

cnf(i_0_1139,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_order__less__asym_H_0,
    [final] ).

cnf(i_0_1140,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_order__less__asym_0,
    [final] ).

cnf(i_0_1141,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_xt1_I9_J_0,
    [final] ).

cnf(i_0_1142,plain,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[i_0_713,c_0_637]),
    [final] ).

cnf(i_0_1143,axiom,
    ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_less__add__one_0,
    [final] ).

cnf(i_0_1144,plain,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(rw,[status(thm)],[i_0_714,c_0_637]),
    [final] ).

cnf(i_0_1145,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = X3
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__mult__self1__is__id_0,
    [final] ).

cnf(i_0_1146,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = X2
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__mult__self2__is__id_0,
    [final] ).

cnf(i_0_1147,axiom,
    ( X2 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
    cls_add__right__cancel_0,
    [final] ).

cnf(i_0_1148,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    cls_add__left__cancel_0,
    [final] ).

cnf(i_0_1149,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    cls_add__imp__eq_0,
    [final] ).

cnf(i_0_1150,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    cls_mult__cancel2_0,
    [final] ).

cnf(i_0_1151,axiom,
    ( X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
    cls_nat__mult__eq__cancel__disj_0,
    [final] ).

cnf(i_0_1152,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
    cls_mult__cancel1_0,
    [final] ).

cnf(i_0_1153,axiom,
    ( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__div__trivial_0,
    [final] ).

cnf(i_0_1154,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__self1__is__0_0,
    [final] ).

cnf(i_0_1155,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__self2__is__0_0,
    [final] ).

cnf(i_0_1156,axiom,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    cls_dvd_Oneq__le__trans_0,
    [final] ).

cnf(i_0_1157,axiom,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    cls_dvd_Ole__neq__trans_0,
    [final] ).

cnf(i_0_1158,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    cls_dvd_Oantisym__conv_0,
    [final] ).

cnf(i_0_1159,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    cls_dvd__antisym_0,
    [final] ).

cnf(i_0_1160,axiom,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    cls_dvd_Oless__le_0,
    [final] ).

cnf(i_0_1161,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    cls_dvd_Oantisym_0,
    [final] ).

cnf(i_0_1162,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    cls_dvd_Oeq__iff_2,
    [final] ).

cnf(i_0_1163,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
    | X1 = X3
    | c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    cls_subst__Var_2,
    [final] ).

cnf(i_0_1164,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Odvd(X1) ),
    cls_dvdI_0,
    [final] ).

cnf(i_0_1165,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_dvd__triv__left_0,
    [final] ).

cnf(i_0_1166,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_dvd__triv__right_0,
    [final] ).

cnf(i_0_1167,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    inference(rw,[status(thm)],[i_0_715,c_0_637]),
    [final] ).

cnf(i_0_1168,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[i_0_716,c_0_637]),
    [final] ).

cnf(i_0_1169,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
    cls_nat__zero__less__power__iff_2,
    [final] ).

cnf(i_0_1170,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2 ),
    cls_subst__Var_1,
    [final] ).

cnf(i_0_1171,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_717,c_0_637]),
    [final] ).

cnf(i_0_1172,axiom,
    ( c_Type_Otyping(X1,X2,X3)
    | ~ c_Lambda_Obeta(X4,X2)
    | ~ c_Type_Otyping(X1,X4,X3) ),
    cls_subject__reduction_0,
    [final] ).

cnf(i_0_1173,plain,
    c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rw,[status(thm)],[i_0_718,c_0_637]),
    [final] ).

cnf(i_0_1174,plain,
    c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = X1,
    inference(rw,[status(thm)],[i_0_719,c_0_637]),
    [final] ).

cnf(i_0_1175,plain,
    c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1,tc_nat),
    inference(rw,[status(thm)],[i_0_720,c_0_637]),
    [final] ).

cnf(i_0_1176,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_mod__eq__0__iff_1,
    [final] ).

cnf(i_0_1177,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_721,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1178,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_722,c_0_637]),c_0_637]),
    [final] ).

cnf(i_0_1179,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_dvd__eq__mod__eq__0_1,
    [final] ).

cnf(i_0_1180,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_723,c_0_637]),
    [final] ).

cnf(i_0_1181,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_724,c_0_637]),
    [final] ).

cnf(i_0_1182,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X1) ),
    cls_dvd__imp__mod__0_0,
    [final] ).

cnf(i_0_1183,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    cls_zero__induct_1,
    [final] ).

cnf(i_0_1184,plain,
    c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_725,c_0_637]),
    [final] ).

cnf(i_0_1185,plain,
    c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_726,c_0_637]),
    [final] ).

cnf(i_0_1186,axiom,
    ( X1 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    cls_nat__add__right__cancel_0,
    [final] ).

cnf(i_0_1187,axiom,
    ( X2 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
    cls_nat__add__left__cancel_0,
    [final] ).

cnf(i_0_1188,axiom,
    ( X2 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
    cls_natgb_Oadd__cancel_0,
    [final] ).

cnf(i_0_1189,axiom,
    c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_substn__subst__0_0,
    [final] ).

cnf(i_0_1190,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_of__nat__less__0__iff_0,
    [final] ).

cnf(i_0_1191,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_div__less_0,
    [final] ).

cnf(i_0_1192,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_mod__if_0,
    [final] ).

cnf(i_0_1193,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_lift_Osimps_I1_J_0,
    [final] ).

cnf(i_0_1194,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_upt_Oinduct_0,
    [final] ).

cnf(i_0_1195,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_nat_Oinduct_0,
    [final] ).

cnf(i_0_1196,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_nat_Oinducts_0,
    [final] ).

cnf(i_0_1197,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_replicate_Oinduct_0,
    [final] ).

cnf(i_0_1198,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_nat__induct_0,
    [final] ).

cnf(i_0_1199,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    cls_lexn_Oinduct_0,
    [final] ).

cnf(i_0_1200,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_power__eq__0__iff_0,
    [final] ).

cnf(i_0_1201,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_power__eq__0__iff_1,
    [final] ).

cnf(i_0_1202,axiom,
    ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
    | X1 = X3
    | c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    cls_substn_Osimps_I1_J_2,
    [final] ).

cnf(i_0_1203,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__antisym__conv3_0,
    [final] ).

cnf(i_0_1204,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__less__linear_0,
    [final] ).

cnf(i_0_1205,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | X3 = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__neqE_0,
    [final] ).

cnf(i_0_1206,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_not__less__iff__gr__or__eq_0,
    [final] ).

cnf(i_0_1207,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | X3 = X2
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    cls_linorder__neqE__ordered__idom_0,
    [final] ).

cnf(i_0_1208,axiom,
    ( X1 = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
    cls_dB_Osimps_I2_J_0,
    [final] ).

cnf(i_0_1209,axiom,
    ( X2 = X4
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
    cls_dB_Osimps_I2_J_1,
    [final] ).

cnf(i_0_1210,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__c_0,
    [final] ).

cnf(i_0_1211,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I7_J_0,
    [final] ).

cnf(i_0_1212,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_not__one__less__zero_0,
    [final] ).

cnf(i_0_1213,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
    cls_mult__cancel1_1,
    [final] ).

cnf(i_0_1214,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_mult__cancel2_1,
    [final] ).

cnf(i_0_1215,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__commute_0,
    [final] ).

cnf(i_0_1216,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__c_0,
    [final] ).

cnf(i_0_1217,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I24_J_0,
    [final] ).

cnf(i_0_1218,plain,
    c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[i_0_727,c_0_637]),
    [final] ).

cnf(i_0_1219,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
    cls_subst__eq_0,
    [final] ).

cnf(i_0_1220,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    cls_typing__elims_I1_J_0,
    [final] ).

cnf(i_0_1221,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
    | c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_mult__eq__0__iff_0,
    [final] ).

cnf(i_0_1222,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_no__zero__divisors_0,
    [final] ).

cnf(i_0_1223,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_no__zero__divirors__neq0_0,
    [final] ).

cnf(i_0_1224,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    cls_linorder__neqE__nat_0,
    [final] ).

cnf(i_0_1225,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    cls_nat__neq__iff_0,
    [final] ).

cnf(i_0_1226,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_dvd__0__left_0,
    [final] ).

cnf(i_0_1227,axiom,
    c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
    cls_nat__mult__commute_0,
    [final] ).

cnf(i_0_1228,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
    | c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_field__power__not__zero_0,
    [final] ).

cnf(i_0_1229,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
    cls_class__ringb_Oadd__r0__iff_0,
    [final] ).

cnf(i_0_1230,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
    inference(rw,[status(thm)],[i_0_728,c_0_637]),
    [final] ).

cnf(i_0_1231,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_double__eq__0__iff_0,
    [final] ).

cnf(i_0_1232,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | ~ class_Power_Opower(X1) ),
    cls_power__eq__0__iff_2,
    [final] ).

cnf(i_0_1233,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_mult__is__0_0,
    [final] ).

cnf(i_0_1234,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__neq__iff_1,
    [final] ).

cnf(i_0_1235,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__irrefl_0,
    [final] ).

cnf(i_0_1236,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__le_1,
    [final] ).

cnf(i_0_1237,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_neq0__conv_1,
    [final] ).

cnf(i_0_1238,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Oone__class_Oone(tc_nat)
    | X1 != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    cls_mult__eq__self__implies__10_0,
    [final] ).

cnf(i_0_1239,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    cls_nat__dvd__1__iff__1_0,
    [final] ).

cnf(i_0_1240,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
    cls_nat__add__commute_0,
    [final] ).

cnf(i_0_1241,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    cls_nat__mult__eq__1__iff_0,
    [final] ).

cnf(i_0_1242,axiom,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    cls_nat__mult__eq__1__iff_1,
    [final] ).

cnf(i_0_1243,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    cls_nat__1__eq__mult__iff_0,
    [final] ).

cnf(i_0_1244,axiom,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    cls_nat__1__eq__mult__iff_1,
    [final] ).

cnf(i_0_1245,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_not__less0_0,
    [final] ).

cnf(i_0_1246,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_gr__implies__not0_0,
    [final] ).

cnf(i_0_1247,axiom,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0,
    [final] ).

cnf(i_0_1248,axiom,
    c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
    cls_typing_OVar_0,
    [final] ).

cnf(i_0_1249,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_less__not__refl_0,
    [final] ).

cnf(i_0_1250,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_nat__less__le_1,
    [final] ).

cnf(i_0_1251,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    cls_power__0__left_1,
    [final] ).

cnf(i_0_1252,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_Lambda_0,
    [final] ).

cnf(i_0_1253,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    cls_power__0__left_0,
    [final] ).

cnf(i_0_1254,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_double__eq__0__iff_1,
    [final] ).

cnf(i_0_1255,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rw,[status(thm)],[i_0_729,c_0_637]),
    [final] ).

cnf(i_0_1256,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rw,[status(thm)],[i_0_730,c_0_637]),
    [final] ).

cnf(i_0_1257,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[i_0_731,c_0_637]),
    [final] ).

cnf(i_0_1258,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[i_0_732,c_0_637]),
    [final] ).

cnf(i_0_1259,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_add__is__0_0,
    [final] ).

cnf(i_0_1260,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_add__is__0_1,
    [final] ).

cnf(i_0_1261,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != X1,
    inference(rw,[status(thm)],[i_0_733,c_0_637]),
    [final] ).

cnf(i_0_1262,plain,
    X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[i_0_734,c_0_637]),
    [final] ).

cnf(i_0_1263,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ),
    cls_add__eq__self__zero_0,
    [final] ).

cnf(i_0_1264,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    cls_natgb_Oadd__r0__iff_0,
    [final] ).

cnf(i_0_1265,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_zero__less__one_0,
    [final] ).

cnf(i_0_1266,axiom,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Oadd__r0__iff_1,
    [final] ).

cnf(i_0_1267,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_add__0__left_0,
    [final] ).

cnf(i_0_1268,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__1_0,
    [final] ).

cnf(i_0_1269,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I5_J_0,
    [final] ).

cnf(i_0_1270,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__0_0,
    [final] ).

cnf(i_0_1271,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__0_0,
    [final] ).

cnf(i_0_1272,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    cls_power__one_0,
    [final] ).

cnf(i_0_1273,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
    cls_mult__eq__0__iff_1,
    [final] ).

cnf(i_0_1274,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    cls_mult__zero__left_0,
    [final] ).

cnf(i_0_1275,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I9_J_0,
    [final] ).

cnf(i_0_1276,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__0_0,
    [final] ).

cnf(i_0_1277,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__0_0,
    [final] ).

cnf(i_0_1278,axiom,
    ( c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__by__0_0,
    [final] ).

cnf(i_0_1279,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
    cls_mult__eq__0__iff_2,
    [final] ).

cnf(i_0_1280,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    cls_mult__zero__right_0,
    [final] ).

cnf(i_0_1281,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I10_J_0,
    [final] ).

cnf(i_0_1282,axiom,
    ( c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__by__1_0,
    [final] ).

cnf(i_0_1283,axiom,
    ( c_Divides_Odiv__class_Odiv(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__self_0,
    [final] ).

cnf(i_0_1284,axiom,
    ( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1) ),
    cls_power__0_0,
    [final] ).

cnf(i_0_1285,axiom,
    ( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Opwr__0_0,
    [final] ).

cnf(i_0_1286,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    cls_mult__1_0,
    [final] ).

cnf(i_0_1287,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__1_0,
    [final] ).

cnf(i_0_1288,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I11_J_0,
    [final] ).

cnf(i_0_1289,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    cls_mult__1__left_0,
    [final] ).

cnf(i_0_1290,axiom,
    ( c_Divides_Odiv__class_Odiv(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_div__by__1_0,
    [final] ).

cnf(i_0_1291,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I12_J_0,
    [final] ).

cnf(i_0_1292,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    cls_mult__1__right_0,
    [final] ).

cnf(i_0_1293,axiom,
    ( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__by__0_0,
    [final] ).

cnf(i_0_1294,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_one__dvd_0,
    [final] ).

cnf(i_0_1295,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_dvd__0__right_0,
    [final] ).

cnf(i_0_1296,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_monoid__add__class_Oadd__0__right_0,
    [final] ).

cnf(i_0_1297,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__1__right_0,
    [final] ).

cnf(i_0_1298,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I6_J_0,
    [final] ).

cnf(i_0_1299,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[i_0_735,c_0_637]),
    [final] ).

cnf(i_0_1300,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[i_0_736,c_0_637]),
    [final] ).

cnf(i_0_1301,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[i_0_737,c_0_637]),
    [final] ).

cnf(i_0_1302,axiom,
    ( c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I33_J_0,
    [final] ).

cnf(i_0_1303,axiom,
    ( c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    cls_power__one__right_0,
    [final] ).

cnf(i_0_1304,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__self_0,
    [final] ).

cnf(i_0_1305,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
    cls_dB_Osimps_I8_J_0,
    [final] ).

cnf(i_0_1306,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
    cls_dB_Osimps_I5_J_0,
    [final] ).

cnf(i_0_1307,axiom,
    c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    cls_dB_Osimps_I9_J_0,
    [final] ).

cnf(i_0_1308,axiom,
    c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    cls_dB_Osimps_I4_J_0,
    [final] ).

cnf(i_0_1309,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X2,X1) = X2
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
    cls_mult__idem_0,
    [final] ).

cnf(i_0_1310,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_dvd__refl_0,
    [final] ).

cnf(i_0_1311,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    cls_nat__mult__eq__1__iff_2,
    [final] ).

cnf(i_0_1312,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    cls_nat__1__eq__mult__iff_2,
    [final] ).

cnf(i_0_1313,axiom,
    c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
    cls_listsp_ONil_0,
    [final] ).

cnf(i_0_1314,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_gr0I_0,
    [final] ).

cnf(i_0_1315,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    cls_nat__dvd__1__iff__1_1,
    [final] ).

cnf(i_0_1316,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_mult__is__0_1,
    [final] ).

cnf(i_0_1317,axiom,
    c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    cls_power__eq__if_0,
    [final] ).

cnf(i_0_1318,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_mult__is__0_2,
    [final] ).

cnf(i_0_1319,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_add__is__0_2,
    [final] ).

cnf(i_0_1320,plain,
    c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[i_0_738,c_0_637]),
    [final] ).

cnf(i_0_1321,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
    cls_nat__mult__1_0,
    [final] ).

cnf(i_0_1322,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    cls_nat__mult__1__right_0,
    [final] ).

cnf(i_0_1323,axiom,
    c_fequal(X1,X1,X2),
    cls_ATP__Linkup_Oequal__imp__fequal_0,
    [final] ).

cnf(i_0_1324,axiom,
    ( X2 = X3
    | ~ class_Nat_Osemiring__char__0(X1)
    | c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
    cls_of__nat__eq__iff_0,
    [final] ).

cnf(i_0_1325,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
    cls_plus__nat_Oadd__0_0,
    [final] ).

cnf(i_0_1326,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
    cls_dvd_Oeq__iff_0,
    [final] ).

cnf(i_0_1327,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
    cls_Nat_Oadd__0__right_0,
    [final] ).

cnf(i_0_1328,axiom,
    X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_natgb_Oadd__r0__iff_1,
    [final] ).

cnf(i_0_1329,axiom,
    ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    cls_abs_0,
    [final] ).

cnf(i_0_1330,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_1331,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_1332,axiom,
    ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
    cls_beta__cases_I1_J_0,
    [final] ).

cnf(i_0_1333,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__1_0,
    [final] ).

cnf(i_0_1334,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__0_0,
    [final] ).

cnf(i_0_1335,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    cls_conjecture_2,
    [final] ).

cnf(i_0_1336,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_dB_Osize_I4_J_0,
    [final] ).

cnf(i_0_1337,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
    cls_zero__neq__one_0,
    [final] ).

cnf(i_0_1338,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_one__neq__zero_0,
    [final] ).

cnf(i_0_1339,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    cls_dB_Osimps_I3_J_0,
    [final] ).

cnf(i_0_1340,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    cls_dB_Osimps_I1_J_0,
    [final] ).

cnf(i_0_1341,axiom,
    c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
    cls_dB_Osimps_I7_J_0,
    [final] ).

cnf(i_0_1342,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    cls_dB_Osimps_I6_J_0,
    [final] ).

cnf(i_0_1343,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_dB_Osize_I1_J_0,
    [final] ).

cnf(i_0_1344,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring,
    [final] ).

cnf(i_0_1345,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__mult,
    [final] ).

cnf(i_0_1346,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    [final] ).

cnf(i_0_1347,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Osemigroup__add,
    [final] ).

cnf(i_0_1348,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    clsarity_nat__Ring__and__Field_Osemiring__0,
    [final] ).

cnf(i_0_1349,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__add,
    [final] ).

cnf(i_0_1350,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1351,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_1352,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    clsarity_nat__Nat_Osemiring__char__0,
    [final] ).

cnf(i_0_1353,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    clsarity_nat__Ring__and__Field_Omult__zero,
    [final] ).

cnf(i_0_1354,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    clsarity_nat__Ring__and__Field_Ono__zero__divisors,
    [final] ).

cnf(i_0_1355,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    clsarity_nat__Ring__and__Field_Ozero__neq__one,
    [final] ).

cnf(i_0_1356,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,
    [final] ).

cnf(i_0_1357,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semiring__strict,
    [final] ).

cnf(i_0_1358,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
    [final] ).

cnf(i_0_1359,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1360,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__mult,
    [final] ).

cnf(i_0_1361,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    clsarity_nat__Ring__and__Field_Odvd,
    [final] ).

cnf(i_0_1362,axiom,
    class_Power_Opower(tc_nat),
    clsarity_nat__Power_Opower,
    [final] ).

cnf(i_0_1363,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_1364,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_1365,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__add,
    [final] ).

cnf(i_0_1366,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__add,
    [final] ).

cnf(i_0_1367,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
    [final] ).

cnf(i_0_1368,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__mult,
    [final] ).

cnf(i_0_1369,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Osemiring__1,
    [final] ).

cnf(i_0_1370,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semidom,
    [final] ).

cnf(i_0_1371,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    clsarity_nat__Ring__and__Field_Osemiring,
    [final] ).

cnf(i_0_1372,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
    [final] ).

cnf(i_0_1373,axiom,
    class_Divides_Osemiring__div(tc_nat),
    clsarity_nat__Divides_Osemiring__div,
    [final] ).

cnf(i_0_1374,axiom,
    X1 = X1 ).

cnf(i_0_1375,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1376,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1377,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1378,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1379,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1380,axiom,
    ( X1 != X2
    | c_Type_Oshift(X1,X3,X4,X5) = c_Type_Oshift(X2,X3,X4,X5) ) ).

cnf(i_0_1381,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X1,X4,X5) = c_Type_Oshift(X3,X2,X4,X5) ) ).

cnf(i_0_1382,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X4,X1,X5) = c_Type_Oshift(X3,X4,X2,X5) ) ).

cnf(i_0_1383,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X4,X5,X1) = c_Type_Oshift(X3,X4,X5,X2) ) ).

cnf(i_0_1384,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_1385,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_1386,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_1387,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).

cnf(i_0_1388,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).

cnf(i_0_1389,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).

cnf(i_0_1390,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).

cnf(i_0_1391,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).

cnf(i_0_1392,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).

cnf(i_0_1393,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_1394,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_1395,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_1396,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).

cnf(i_0_1397,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).

cnf(i_0_1398,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).

cnf(i_0_1399,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1400,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1401,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1402,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1403,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1404,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__size(X1) = c_Lambda_OdB_OdB__size(X2) ) ).

cnf(i_0_1405,axiom,
    ( X1 != X2
    | c_Lambda_Osubstn(X1,X3,X4) = c_Lambda_Osubstn(X2,X3,X4) ) ).

cnf(i_0_1406,axiom,
    ( X1 != X2
    | c_Lambda_Osubstn(X3,X1,X4) = c_Lambda_Osubstn(X3,X2,X4) ) ).

cnf(i_0_1407,axiom,
    ( X1 != X2
    | c_Lambda_Osubstn(X3,X4,X1) = c_Lambda_Osubstn(X3,X4,X2) ) ).

cnf(i_0_1408,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_1409,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_1410,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_1411,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_1412,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_1413,axiom,
    ( X1 != X2
    | c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_1414,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X1,X4,X5) = c_List_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_1415,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X4,X1,X5) = c_List_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_1416,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X4,X5,X1) = c_List_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_1417,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1418,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oordered__ring__strict(X2) ) ).

cnf(i_0_1419,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring(X1)
    | class_Ring__and__Field_Osemiring(X2) ) ).

cnf(i_0_1420,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_1421,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_1422,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1423,axiom,
    ( X1 != X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X4) ) ).

cnf(i_0_1424,axiom,
    ( X1 != X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,X4)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4) ) ).

cnf(i_0_1425,axiom,
    ( X1 != X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2) ) ).

cnf(i_0_1426,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_1427,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X2) ) ).

cnf(i_0_1428,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1429,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).

cnf(i_0_1430,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X1,X3,X4)
    | c_Type_Otypings(X2,X3,X4) ) ).

cnf(i_0_1431,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X1,X4)
    | c_Type_Otypings(X3,X2,X4) ) ).

cnf(i_0_1432,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X4,X1)
    | c_Type_Otypings(X3,X4,X2) ) ).

cnf(i_0_1433,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).

cnf(i_0_1434,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1435,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_1436,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_OrderedGroup_Omonoid__mult(X2) ) ).

cnf(i_0_1437,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1438,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_1439,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1440,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_1441,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X2) ) ).

cnf(i_0_1442,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1443,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X1,X3,X4)
    | c_Type_Otyping(X2,X3,X4) ) ).

cnf(i_0_1444,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X1,X4)
    | c_Type_Otyping(X3,X2,X4) ) ).

cnf(i_0_1445,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X4,X1)
    | c_Type_Otyping(X3,X4,X2) ) ).

cnf(i_0_1446,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_1447,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_1448,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_1449,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1450,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1451,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
    | class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_1452,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1453,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_Ring__and__Field_Osemiring__0(X2) ) ).

cnf(i_0_1454,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1455,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1456,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X1,X3,X4)
    | c_List_Olistsp(X2,X3,X4) ) ).

cnf(i_0_1457,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X1,X4)
    | c_List_Olistsp(X3,X2,X4) ) ).

cnf(i_0_1458,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X4,X1)
    | c_List_Olistsp(X3,X4,X2) ) ).

cnf(i_0_1459,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Odvd(X1)
    | class_Ring__and__Field_Odvd(X2) ) ).

cnf(i_0_1460,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_1461,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | class_Ring__and__Field_Ono__zero__divisors(X2) ) ).

cnf(i_0_1462,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | class_Ring__and__Field_Omult__zero(X2) ) ).

cnf(i_0_1463,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
    | class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_1464,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
    | class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_1465,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_1466,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_1467,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_1468,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_1469,axiom,
    ( X1 != X2
    | ~ c_Lambda_Obeta(X1,X3)
    | c_Lambda_Obeta(X2,X3) ) ).

cnf(i_0_1470,axiom,
    ( X1 != X2
    | ~ c_Lambda_Obeta(X3,X1)
    | c_Lambda_Obeta(X3,X2) ) ).

cnf(i_0_1471,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_1472,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_1473,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_1474,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Osemigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X2) ) ).

cnf(i_0_1475,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_1476,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_1374_001,axiom,
    X1 = X1 ).

cnf(i_0_1375_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1376_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1377_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1378_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1379_006,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1380_007,axiom,
    ( X1 != X2
    | c_Type_Oshift(X1,X3,X4,X5) = c_Type_Oshift(X2,X3,X4,X5) ) ).

cnf(i_0_1381_008,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X1,X4,X5) = c_Type_Oshift(X3,X2,X4,X5) ) ).

cnf(i_0_1382_009,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X4,X1,X5) = c_Type_Oshift(X3,X4,X2,X5) ) ).

cnf(i_0_1383_010,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X4,X5,X1) = c_Type_Oshift(X3,X4,X5,X2) ) ).

cnf(i_0_1384_011,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_1385_012,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_1386_013,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_1387_014,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).

cnf(i_0_1388_015,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).

cnf(i_0_1389_016,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).

cnf(i_0_1390_017,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).

cnf(i_0_1391_018,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).

cnf(i_0_1392_019,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).

cnf(i_0_1393_020,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_1394_021,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_1395_022,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_1396_023,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).

cnf(i_0_1397_024,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).

cnf(i_0_1398_025,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).

cnf(i_0_1399_026,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1400_027,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1401_028,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1402_029,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1403_030,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1404_031,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__size(X1) = c_Lambda_OdB_OdB__size(X2) ) ).

cnf(i_0_1405_032,axiom,
    ( X1 != X2
    | c_Lambda_Osubstn(X1,X3,X4) = c_Lambda_Osubstn(X2,X3,X4) ) ).

cnf(i_0_1406_033,axiom,
    ( X1 != X2
    | c_Lambda_Osubstn(X3,X1,X4) = c_Lambda_Osubstn(X3,X2,X4) ) ).

cnf(i_0_1407_034,axiom,
    ( X1 != X2
    | c_Lambda_Osubstn(X3,X4,X1) = c_Lambda_Osubstn(X3,X4,X2) ) ).

cnf(i_0_1408_035,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_1409_036,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_1410_037,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_1411_038,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_1412_039,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_1413_040,axiom,
    ( X1 != X2
    | c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_1414_041,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X1,X4,X5) = c_List_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_1415_042,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X4,X1,X5) = c_List_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_1416_043,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X4,X5,X1) = c_List_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_1417_044,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1418_045,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oordered__ring__strict(X2) ) ).

cnf(i_0_1419_046,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring(X1)
    | class_Ring__and__Field_Osemiring(X2) ) ).

cnf(i_0_1420_047,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_1421_048,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_1422_049,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1423_050,axiom,
    ( X1 != X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X4) ) ).

cnf(i_0_1424_051,axiom,
    ( X1 != X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,X4)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4) ) ).

cnf(i_0_1425_052,axiom,
    ( X1 != X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2) ) ).

cnf(i_0_1426_053,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_1427_054,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X2) ) ).

cnf(i_0_1428_055,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1429_056,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).

cnf(i_0_1430_057,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X1,X3,X4)
    | c_Type_Otypings(X2,X3,X4) ) ).

cnf(i_0_1431_058,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X1,X4)
    | c_Type_Otypings(X3,X2,X4) ) ).

cnf(i_0_1432_059,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X4,X1)
    | c_Type_Otypings(X3,X4,X2) ) ).

cnf(i_0_1433_060,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).

cnf(i_0_1434_061,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1435_062,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_1436_063,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_OrderedGroup_Omonoid__mult(X2) ) ).

cnf(i_0_1437_064,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1438_065,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_1439_066,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1440_067,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_1441_068,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X2) ) ).

cnf(i_0_1442_069,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1443_070,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X1,X3,X4)
    | c_Type_Otyping(X2,X3,X4) ) ).

cnf(i_0_1444_071,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X1,X4)
    | c_Type_Otyping(X3,X2,X4) ) ).

cnf(i_0_1445_072,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X4,X1)
    | c_Type_Otyping(X3,X4,X2) ) ).

cnf(i_0_1446_073,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_1447_074,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_1448_075,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_1449_076,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1450_077,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1451_078,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
    | class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_1452_079,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1453_080,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_Ring__and__Field_Osemiring__0(X2) ) ).

cnf(i_0_1454_081,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1455_082,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1456_083,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X1,X3,X4)
    | c_List_Olistsp(X2,X3,X4) ) ).

cnf(i_0_1457_084,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X1,X4)
    | c_List_Olistsp(X3,X2,X4) ) ).

cnf(i_0_1458_085,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X4,X1)
    | c_List_Olistsp(X3,X4,X2) ) ).

cnf(i_0_1459_086,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Odvd(X1)
    | class_Ring__and__Field_Odvd(X2) ) ).

cnf(i_0_1460_087,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_1461_088,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | class_Ring__and__Field_Ono__zero__divisors(X2) ) ).

cnf(i_0_1462_089,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | class_Ring__and__Field_Omult__zero(X2) ) ).

cnf(i_0_1463_090,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
    | class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_1464_091,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
    | class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_1465_092,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_1466_093,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_1467_094,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_1468_095,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_1469_096,axiom,
    ( X1 != X2
    | ~ c_Lambda_Obeta(X1,X3)
    | c_Lambda_Obeta(X2,X3) ) ).

cnf(i_0_1470_097,axiom,
    ( X1 != X2
    | ~ c_Lambda_Obeta(X3,X1)
    | c_Lambda_Obeta(X3,X2) ) ).

cnf(i_0_1471_098,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_1472_099,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_1473_100,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_1474_101,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Osemigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X2) ) ).

cnf(i_0_1475_102,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_1476_103,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_1477,plain,
    X1 = X1,
    inference(equality_inference,[],[752]) ).

cnf(i_0_1478,plain,
    X1 = X1,
    inference(equality_inference,[],[753]) ).

cnf(i_0_1479,plain,
    X1 = X1,
    inference(equality_inference,[],[754]) ).

cnf(i_0_1480,plain,
    X1 = X1,
    inference(equality_inference,[],[755]) ).

cnf(i_0_1481,plain,
    X1 = X1,
    inference(equality_inference,[],[758]) ).

cnf(i_0_1482,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[793]) ).

cnf(i_0_1483,plain,
    ( X1 = X1
    | X2 = X3 ),
    inference(equality_inference,[],[796]) ).

cnf(i_0_1484,plain,
    c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat),
    inference(equality_inference,[],[842]) ).

cnf(i_0_1485,plain,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | X3 = c_HOL_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[872]) ).

cnf(i_0_1486,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[891]) ).

cnf(i_0_1487,plain,
    X1 = X1,
    inference(equality_inference,[],[892]) ).

cnf(i_0_1488,plain,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
    inference(equality_inference,[],[957]) ).

cnf(i_0_1489,plain,
    ( X1 = X1
    | ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),X3,X2) ),
    inference(equality_inference,[],[1056]) ).

cnf(i_0_1490,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[1061]) ).

cnf(i_0_1491,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[1062]) ).

cnf(i_0_1492,plain,
    ( X1 = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(equality_inference,[],[1074]) ).

cnf(i_0_1493,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[1110]) ).

cnf(i_0_1494,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[1111]) ).

cnf(i_0_1495,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[1112]) ).

cnf(i_0_1496,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[1113]) ).

cnf(i_0_1497,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[1134]) ).

cnf(i_0_1498,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1147]) ).

cnf(i_0_1499,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1148]) ).

cnf(i_0_1500,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[1149]) ).

cnf(i_0_1501,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[1150]) ).

cnf(i_0_1502,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[1152]) ).

cnf(i_0_1503,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[1167]) ).

cnf(i_0_1504,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[1168]) ).

cnf(i_0_1505,plain,
    X1 = X1,
    inference(equality_inference,[],[1186]) ).

cnf(i_0_1506,plain,
    X1 = X1,
    inference(equality_inference,[],[1188]) ).

cnf(i_0_1507,plain,
    X1 = X1,
    inference(equality_inference,[],[1208]) ).

cnf(i_0_1508,plain,
    X1 = X1,
    inference(equality_inference,[],[1209]) ).

cnf(i_0_1509,plain,
    ( X1 = X1
    | ~ class_Nat_Osemiring__char__0(X2) ),
    inference(equality_inference,[],[1324]) ).

cnf(i_0_1510,plain,
    X1 = X1,
    inference(equality_inference,[],[1339]) ).

cnf(i_0_1511,plain,
    X1 = X1,
    inference(equality_inference,[],[1340]) ).

cnf(i_0_1512,plain,
    $false,
    inference(scs_inference,[],[i_0_739,i_0_956,i_0_740,i_0_743]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LCL759-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12  % 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
% 0.15/0.33  % Computer : n005.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Mon May  4 23:06:00 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 1.81/2.67  % Version  : CSE_E---1.7
% 1.81/2.67  % Problem  : theBenchmark.p
% 1.81/2.67  % SZS status Unsatisfiable for theBenchmark.p
% 1.81/2.67  % SZS output start CNFRefutation
% See solution above
% 1.86/2.73  % Total time : 2.326s
%------------------------------------------------------------------------------