CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWV884-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  5 05:27:38 PM UTC 2026

% Result   : Unsatisfiable 1.44s 2.54s
% Output   : CNFRefutation 6.43s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1122)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_card__insert_0,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert_0) ).

cnf(cls_Suc__eq__plus1_0,axiom,
    c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).

cnf(cls_card__Suc__Diff1_0,axiom,
    ( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3)) = c_Finite__Set_Ocard(X1,X3)
    | ~ c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__Diff1_0) ).

cnf(cls_conjecture_3,negated_conjecture,
    c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_Suc__mult__le__cancel1_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(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/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_lift__Suc__mono__le_0,axiom,
    ( c_lessequals(hAPP(X2,X3),hAPP(X2,X4),X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X4,tc_nat)
    | ~ c_lessequals(hAPP(X2,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X2,X1)),hAPP(X2,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X2,X1))),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__Suc__mono__le_0) ).

cnf(cls_mod__mult__self4_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).

cnf(cls_Suc__le__D__lemma_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X1,X3))))
    | ~ c_lessequals(c_Suc(X3),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__D__lemma_1) ).

cnf(cls_one__le__mult__iff_2,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).

cnf(cls_Suc__mult__le__cancel1_1,axiom,
    ( c_lessequals(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_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

cnf(cls_diff__Suc__diff__eq2_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).

cnf(cls_diff__Suc__diff__eq1_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).

cnf(cls_Suc__diff__diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

cnf(cls_one__le__mult__iff_0,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).

cnf(cls_one__le__mult__iff_1,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).

cnf(cls_zero__induct__lemma_0,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
    | hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1))))
    | ~ hBOOL(hAPP(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__induct__lemma_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).

cnf(cls_card__Suc__eq_5,axiom,
    ( c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
    | c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).

cnf(cls_inc__induct_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X1,X3))))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ c_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inc__induct_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_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/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).

cnf(cls_Suc__le__mono_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_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/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

cnf(cls_Suc__pred_0,axiom,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).

cnf(cls_diff__Suc__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).

cnf(cls_add__eq__if_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__if_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).

cnf(cls_Suc__diff__le_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat))
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).

cnf(cls_less__iff__Suc__add_1,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

cnf(cls_less__add__Suc1_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

cnf(cls_less__add__Suc2_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

cnf(cls_le__SucE_0,axiom,
    ( X1 = c_Suc(X2)
    | c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).

cnf(cls_Suc__le__D__lemma_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | c_lessequals(X3,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X1,X3),tc_nat)
    | ~ c_lessequals(c_Suc(X3),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__D__lemma_0) ).

cnf(cls_Suc__le__mono_1,axiom,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).

cnf(cls_le__less__Suc__eq_0,axiom,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

cnf(cls_not__less__eq__eq_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

cnf(cls_full__nat__induct_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,X3))
    | ~ c_lessequals(c_Suc(X3),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X1),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_full__nat__induct_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/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__iff__1_0) ).

cnf(cls_diff__Suc__Suc_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).

cnf(cls_add__Suc__shift_0,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).

cnf(cls_diff__Suc__eq__diff__pred_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).

cnf(cls_add__Suc_0,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).

cnf(cls_add__Suc__right_0,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

cnf(cls_Suc__le__D_0,axiom,
    ( X1 = c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X1))
    | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__D_0) ).

cnf(cls_mult__Suc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/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) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).

cnf(cls_Suc__leD_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).

cnf(cls_less__eq__Suc__le_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).

cnf(cls_Suc__le__eq_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_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/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

cnf(cls_less__Suc__eq__le_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_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/sandbox2/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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/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))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__iff__1_1) ).

cnf(cls_card__insert__if_1,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
    | c_in(X1,X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__if_1) ).

cnf(cls_card__Suc__eq_4,axiom,
    ( c_in(X1,X2,X3)
    | c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
    | c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__eq_4) ).

cnf(cls_le__Suc__eq_2,axiom,
    c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

cnf(cls_diff__less__Suc_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

cnf(cls_Suc__n__not__le__n_0,axiom,
    ~ c_lessequals(c_Suc(X1),X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

cnf(cls_Suc__diff__1_0,axiom,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).

cnf(cls_Suc__pred_H_0,axiom,
    ( X1 = c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).

cnf(cls_less__eq__Suc__le_0,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).

cnf(cls_Suc__leI_0,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).

cnf(cls_le__SucI_0,axiom,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).

cnf(cls_le__less__Suc__eq_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | ~ c_lessequals(X1,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).

cnf(cls_less__Suc__eq__le_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).

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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/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))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox2/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)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).

cnf(cls_card__eq__SucD_2,axiom,
    ( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,X3,X2),X2) = X3
    | c_Finite__Set_Ocard(X1,X2) != c_Suc(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__SucD_2) ).

cnf(cls_card__Suc__eq_2,axiom,
    ( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,X3,X2),X2) = X3
    | c_Finite__Set_Ocard(X1,X2) != c_Suc(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__eq_2) ).

cnf(cls_add__is__1_4,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).

cnf(cls_add__is__1_5,axiom,
    c_HOL_Oplus__class_Oplus(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/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).

cnf(cls_one__is__add_4,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).

cnf(cls_one__is__add_5,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox2/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) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).

cnf(cls_not__less__eq__eq_0,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

cnf(cls_card__eq__SucD_3,axiom,
    ( c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__SucD_3) ).

cnf(cls_card__Suc__eq_3,axiom,
    ( c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__eq_3) ).

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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/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)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).

cnf(cls_add__nonneg__eq__0__iff_2,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

cnf(cls_Suc__inject_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

cnf(cls_nat_Oinject_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mod__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/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).

cnf(cls_diff__Suc__1_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__1_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

cnf(cls_Suc__eq__plus1__left_0,axiom,
    c_Suc(X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

cnf(cls_Suc__n__not__n_0,axiom,
    c_Suc(X1) != X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

cnf(cls_n__not__Suc__n_0,axiom,
    X1 != c_Suc(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_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/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).

cnf(cls_image__subset__iff_2,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X5,X1,X3,X4)),X5,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_2) ).

cnf(cls_image__subsetI_1,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X5,X1,X3,X4)),X5,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subsetI_1) ).

cnf(cls_image__cong_1,axiom,
    ( c_Set_Oimage(X1,X2,X4,X5) = c_Set_Oimage(X3,X2,X4,X5)
    | hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X3,X4,X5)) != hAPP(X3,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X3,X4,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__cong_1) ).

cnf(cls_fun__upd__twist_0,axiom,
    ( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X7,X4,X5) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X6,X7,X4,X5),X2,X3,X4,X5)
    | X2 = X6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

cnf(cls_fun__upd__upd_0,axiom,
    c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2,X6,X4,X5) = c_Fun_Ofun__upd(X1,X2,X6,X4,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

cnf(cls_fun__upd__image_0,axiom,
    ( c_Set_Oimage(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5) = c_Set_Oinsert(X3,c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
    | ~ c_in(X2,X6,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).

cnf(cls_card__Diff2__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),c_Finite__Set_Ocard(X1,X3),tc_nat)
    | ~ c_in(X4,X1,X3)
    | ~ c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff2__less_0) ).

cnf(cls_inj__on__fun__updI_0,axiom,
    ( c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5)
    | c_in(X3,c_Set_Oimage(X1,X6,X4,X5),X5)
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).

cnf(cls_finite__subset__image_2,axiom,
    ( X1 = c_Set_Oimage(X2,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X3,X1,X2,X4,X5),X4,X5)
    | ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X1,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset__image_2) ).

cnf(cls_subset__image__iff_1,axiom,
    ( X1 = c_Set_Oimage(X2,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X4,X5)
    | ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_1) ).

cnf(cls_finite__subset__image_0,axiom,
    ( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X1,X2,X3,X4,X5),X1,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset__image_0) ).

cnf(cls_subset__image__iff_0,axiom,
    ( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X1,X2,X3,X4,X5),X1,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_0) ).

cnf(cls_finite__subset__image_1,axiom,
    ( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X1,X2,X3,X4,X5),X4)
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset__image_1) ).

cnf(cls_image__iff_0,axiom,
    ( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X1,X2,X3,X4,X5),X1,X4)
    | ~ c_in(X3,c_Set_Oimage(X2,X1,X4,X5),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_0) ).

cnf(cls_imageE_1,axiom,
    ( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X1,X2,X3,X4,X5),X1,X4)
    | ~ c_in(X2,c_Set_Oimage(X3,X1,X4,X5),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageE_1) ).

cnf(cls_inv__into__injective_0,axiom,
    ( X5 = X6
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5) != hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X6)
    | ~ c_in(X6,c_Set_Oimage(X2,X1,X3,X4),X4)
    | ~ c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).

cnf(cls_image__iff_1,axiom,
    ( X1 = hAPP(X2,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X3,X2,X1,X4,X5))
    | ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_1) ).

cnf(cls_imageE_0,axiom,
    ( X1 = hAPP(X2,c_ATP__Linkup_Osko__Set__XimageE__1__1(X3,X1,X2,X4,X5))
    | ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageE_0) ).

cnf(cls_inj__on__insert_1,axiom,
    ( ~ c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
    | ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

cnf(cls_image__subset__iff_1,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X5,X1,X3,X4),X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_1) ).

cnf(cls_image__subsetI_0,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X5,X1,X3,X4),X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subsetI_0) ).

cnf(cls_image__diff__subset_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

cnf(cls_image__Int__subset_0,axiom,
    c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

cnf(cls_fun__upd__image_1,axiom,
    ( c_Set_Oimage(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5) = c_Set_Oimage(X1,X6,X4,X5)
    | c_in(X2,X6,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).

cnf(cls_image__cong_0,axiom,
    ( c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X5,X2,X3,X4)
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4),X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__cong_0) ).

cnf(cls_weak__coinduct__image_0,axiom,
    ( c_in(hAPP(X1,X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),hAPP(X3,c_Set_Oimage(X1,X5,X6,X4)),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weak__coinduct__image_0) ).

cnf(cls_card__bij__eq_0,axiom,
    ( c_Finite__Set_Ocard(X1,X2) = c_Finite__Set_Ocard(X3,X4)
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(c_Set_Oimage(X5,X3,X4,X2),X1,tc_fun(X2,tc_bool))
    | ~ c_Fun_Oinj__on(X5,X3,X4,X2)
    | ~ c_lessequals(c_Set_Oimage(X6,X1,X2,X4),X3,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X6,X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).

cnf(cls_inj__on__insert_2,axiom,
    ( c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
    | c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

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(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X1,tc_nat),X2,tc_nat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mod_1) ).

cnf(cls_fun__upd__other_0,axiom,
    ( hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
    | X6 = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

cnf(cls_fun__upd__apply_1,axiom,
    ( hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
    | X6 = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).

cnf(cls_fun__upd__apply_0,axiom,
    hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

cnf(cls_fun__upd__same_0,axiom,
    hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

cnf(cls_inj__image__subset__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).

cnf(cls_inj__on__image__set__diff_0,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

cnf(cls_inj__on__image__Int_0,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).

cnf(cls_nat__le__add__iff1_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).

cnf(cls_nat__less__add__iff1_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).

cnf(cls_nat__le__add__iff2_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).

cnf(cls_nat__less__add__iff2_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).

cnf(cls_le__add__iff1_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).

cnf(cls_less__add__iff1_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).

cnf(cls_le__add__iff2_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).

cnf(cls_less__add__iff2_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).

cnf(cls_vimage__subsetI_0,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).

cnf(cls_image__set__diff_0,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__set__diff_0) ).

cnf(cls_image__Int_0,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int_0) ).

cnf(cls_inv__into__into_0,axiom,
    ( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5),X1,X3)
    | ~ c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__into_0) ).

cnf(cls_nat__le__add__iff1_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).

cnf(cls_nat__less__add__iff1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).

cnf(cls_nat__le__add__iff2_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).

cnf(cls_nat__less__add__iff2_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).

cnf(cls_fun__upd__idem__iff_0,axiom,
    ( hAPP(X1,X2) = X3
    | c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

cnf(cls_le__add__iff1_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).

cnf(cls_less__add__iff1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).

cnf(cls_le__add__iff2_0,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).

cnf(cls_less__add__iff2_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).

cnf(cls_f__inv__into__f_0,axiom,
    ( hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),X5)) = X5
    | ~ c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).

cnf(cls_image__inv__f__f_0,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),c_Set_Oimage(X2,X4,X1,X3),X3,X1) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).

cnf(cls_inv__image__comp_0,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),c_Set_Oimage(X2,X4,X1,X3),X3,X1) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).

cnf(cls_inv__into__image__cancel_0,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),c_Set_Oimage(X2,X5,X3,X4),X4,X3) = X5
    | ~ c_lessequals(X5,X1,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).

cnf(cls_vimage__code_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).

cnf(cls_inj__image__subset__iff_1,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).

cnf(cls_inj__on__inv__into_0,axiom,
    ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5,X4,X3)
    | ~ c_lessequals(X5,c_Set_Oimage(X2,X1,X3,X4),tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).

cnf(cls_endo__inj__surj_0,axiom,
    ( c_Set_Oimage(X1,X2,X3,X3) = X2
    | ~ c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X3),X2,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).

cnf(cls_image__vimage__subset_0,axiom,
    c_lessequals(c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4),X2,tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

cnf(cls_nat__diff__add__eq1_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).

cnf(cls_nat__diff__add__eq2_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).

cnf(cls_vimage__singleton__eq_0,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_in(X2,c_Set_Ovimage(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

cnf(cls_inf__period_I4_J_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Odvd(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X5,X6,X1),X1),X4,X1),X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).

cnf(cls_vimage__Diff_0,axiom,
    c_Set_Ovimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

cnf(cls_vimage__Int_0,axiom,
    c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

cnf(cls_psubset__insert__iff_9,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).

cnf(cls_inj__image__mem__iff_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).

cnf(cls_psubset__insert__iff_8,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X1,X4)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).

cnf(cls_card__inj__on__le_0,axiom,
    ( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X4),tc_nat)
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | ~ c_lessequals(c_Set_Oimage(X5,X1,X2,X4),X3,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X5,X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__inj__on__le_0) ).

cnf(cls_image__vimage__eq_0,axiom,
    c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).

cnf(cls_psubset__insert__iff_5,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X3,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).

cnf(cls_card__Diff1__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),c_Finite__Set_Ocard(X1,X3),tc_nat)
    | ~ c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff1__less_0) ).

cnf(cls_psubset__insert__iff_4,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X3,X4)
    | ~ c_in(X2,X1,X4)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).

cnf(cls_subset__insert__iff_4,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

cnf(cls_diff__single__insert_0,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X1,X4)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

cnf(cls_subset__insert__iff_3,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X1,X4)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

cnf(cls_card__Diff1__le_0,axiom,
    ( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),c_Finite__Set_Ocard(X1,X3),tc_nat)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff1__le_0) ).

cnf(cls_inj__image__eq__iff_0,axiom,
    ( X2 = X5
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).

cnf(cls_fun__upd__idem__iff_1,axiom,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).

cnf(cls_fun__upd__triv_0,axiom,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

cnf(cls_fun__upd__idem_0,axiom,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).

cnf(cls_inj__vimage__image__eq_0,axiom,
    ( c_Set_Ovimage(X1,c_Set_Oimage(X1,X2,X3,X4),X3,X4) = X2
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).

cnf(cls_finite__imageD_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Fun_Oinj__on(X3,X1,X2,X4)
    | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageD_0) ).

cnf(cls_image__mono_0,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).

cnf(cls_subset__image__iff_2,axiom,
    ( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

cnf(cls_vimage__mono_0,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),c_Set_Ovimage(X1,X5,X3,X4),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

cnf(cls_finite__surj__inj_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X2,X3,X3),tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).

cnf(cls_inf__period_I4_J_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Odvd(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X6,X1),X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).

cnf(cls_vimage__code_1,axiom,
    ( hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
    | ~ hBOOL(hAPP(X2,hAPP(X1,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_1) ).

cnf(cls_inj__image__mem__iff_1,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).

cnf(cls_nat__eq__add__iff2_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).

cnf(cls_nat__eq__add__iff1_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_1) ).

cnf(cls_card__image__le_0,axiom,
    ( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4),c_Finite__Set_Ocard(X2,X3),tc_nat)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__image__le_0) ).

cnf(cls_inv__f__f_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),hAPP(X2,X4)) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__f__f_0) ).

cnf(cls_inv__f__eq_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),hAPP(X1,X4)) = X4
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__f__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),c_HOL_Oplus__class_Oplus(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),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

cnf(cls_conjecture_6,negated_conjecture,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

cnf(cls_eq__card__imp__inj__on_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).

cnf(cls_psubset__insert__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | c_in(X2,X4,X3)
    | ~ c_in(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).

cnf(cls_eq__add__iff2_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X1),X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).

cnf(cls_eq__add__iff1_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).

cnf(cls_vimage__singleton__eq_1,axiom,
    c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3),X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

cnf(cls_image__subset__iff_0,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,X5,X6)
    | ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

cnf(cls_nat__diff__split_1,axiom,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X2,tc_nat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).

cnf(cls_nat__diff__split__asm_1,axiom,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X2,tc_nat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).

cnf(cls_mod__lemma_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X4,tc_nat),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/sandbox2/benchmark/theBenchmark.p',cls_mod__lemma_0) ).

cnf(cls_subset__insert__iff_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_in(X2,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

cnf(cls_inv__into__f__f_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5
    | ~ c_in(X5,X1,X3)
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).

cnf(cls_inv__into__f__eq_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X2,X4,X3,X5),hAPP(X4,X1)) = X1
    | ~ c_in(X1,X2,X3)
    | ~ c_Fun_Oinj__on(X4,X2,X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__f__eq_0) ).

cnf(cls_finite__vimageI_0,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Ovimage(X1,X2,X3,X4),X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).

cnf(cls_sum__squares__le__zero__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).

cnf(cls_sum__squares__le__zero__iff_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).

cnf(cls_not__sum__squares__lt__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

cnf(cls_nat__eq__add__iff1_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat) = X5
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_0) ).

cnf(cls_nat__eq__add__iff2_0,axiom,
    ( X3 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_0) ).

cnf(cls_vimageD_0,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageD_0) ).

cnf(cls_vimageE_0,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageE_0) ).

cnf(cls_finite__surj_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).

cnf(cls_inj__on__iff__eq__card_0,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff__eq__card_0) ).

cnf(cls_card__Diff__insert_0,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_in(X2,X3,X4)
    | ~ c_in(X2,X1,X4)
    | ~ c_Finite__Set_Ofinite(X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff__insert_0) ).

cnf(cls_image__insert_0,axiom,
    c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).

cnf(cls_card__image_0,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__image_0) ).

cnf(cls_insert__image_0,axiom,
    ( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
    | ~ c_in(X2,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).

cnf(cls_eq__add__iff1_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1) = X6
    | ~ class_Ring__and__Field_Oring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).

cnf(cls_eq__add__iff2_0,axiom,
    ( X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1)
    | ~ class_Ring__and__Field_Oring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).

cnf(cls_combine__common__factor_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1),X5,X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
    ( X3 = X5
    | X2 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox2/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)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).

cnf(cls_card__Diff__subset__Int_0,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3),tc_nat)
    | ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff__subset__Int_0) ).

cnf(cls_doubleton__eq__iff_0,axiom,
    ( X1 = X5
    | X1 = X4
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

cnf(cls_doubleton__eq__iff_1,axiom,
    ( X2 = X4
    | X1 = X4
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

cnf(cls_doubleton__eq__iff_2,axiom,
    ( X1 = X5
    | X2 = X5
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

cnf(cls_doubleton__eq__iff_3,axiom,
    ( X2 = X4
    | X2 = X5
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

cnf(cls_Diff__insert2_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

cnf(cls_left__add__mult__distrib_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).

cnf(cls_natgb_Oadd__mul__solve_0,axiom,
    ( X2 = X4
    | X1 = X3
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).

cnf(cls_natgb_Onoteq__reduce_0,axiom,
    ( X2 = X4
    | X1 = X3
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).

cnf(cls_inj__on__insert_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

cnf(cls_inj__on__diff_0,axiom,
    ( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

cnf(cls_card__Diff__singleton_0,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff__singleton_0) ).

cnf(cls_finite__Diff__insert_0,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

cnf(cls_subset__inj__on_0,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X5,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

cnf(cls_mod__diff__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).

cnf(cls_mod__add__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).

cnf(cls_insert__Diff_0,axiom,
    ( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
    | ~ c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

cnf(cls_sum__squares__le__zero__iff_2,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).

cnf(cls_insert__Diff__single_0,axiom,
    c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

cnf(cls_card__Diff__singleton__if_1,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Finite__Set_Ocard(X1,X3)
    | c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).

cnf(cls_rangeI_0,axiom,
    c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rangeI_0) ).

cnf(cls_vimageI_0,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI_0) ).

cnf(cls_vimageI2_0,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI2_0) ).

cnf(cls_vimage__eq_1,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

cnf(cls_mod__diff__cong_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X4,X1),X3,X1)
    | ~ class_Divides_Oring__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/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).

cnf(cls_mod__add__cong_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_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/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).

cnf(cls_imageI_0,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).

cnf(cls_image__eqI_0,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).

cnf(cls_image__iff_2,axiom,
    ( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).

cnf(cls_rev__image__eqI_0,axiom,
    ( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

cnf(cls_finite__Diff__insert_1,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

cnf(cls_mult__mono_H_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

cnf(cls_mult__mono_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).

cnf(cls_mult__less__le__imp__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

cnf(cls_mult__le__less__imp__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

cnf(cls_mult__strict__mono_H_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

cnf(cls_mult__strict__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

cnf(cls_le__diff__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).

cnf(cls_less__diff__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).

cnf(cls_Diff__mono_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

cnf(cls_Int__mono_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).

cnf(cls_Diff__insert_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

cnf(cls_Diff__Int2_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

cnf(cls_Diff__Int__distrib2_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

cnf(cls_Diff__Int__distrib_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

cnf(cls_inj__onD_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).

cnf(cls_inj__on__def_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

cnf(cls_inj__on__iff_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

cnf(cls_inj__on__contraD_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

cnf(cls_sum__squares__gt__zero__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox2/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),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

cnf(cls_sum__squares__ge__zero_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_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)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).

cnf(cls_subset__singletonD_0,axiom,
    ( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

cnf(cls_mult__le__cancel__left__pos_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(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/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

cnf(cls_mult__right__le__imp__le_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).

cnf(cls_mult__left__le__imp__le_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

cnf(cls_mult__right__less__imp__less_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).

cnf(cls_mult__left__less__imp__less_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

cnf(cls_mult__less__imp__less__right_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

cnf(cls_mult__less__imp__less__left_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

cnf(cls_mult__le__cancel__left__neg_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(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/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

cnf(cls_inf1E_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).

cnf(cls_inf1E_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_mult__le__cancel2_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).

cnf(cls_nat__mult__le__cancel1_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_0) ).

cnf(cls_mult__le__cancel1_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).

cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).

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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

cnf(cls_zmod__simps_I1_J_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I1_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/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).

cnf(cls_zmod__simps_I2_J_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).

cnf(cls_mod__diff__left__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).

cnf(cls_mod__add__left__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_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/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).

cnf(cls_mod__diff__right__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).

cnf(cls_mod__add__right__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__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/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__right__eq_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

cnf(cls_doubleton__eq__iff_4,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

cnf(cls_finite__imageI_0,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_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)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X5,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

cnf(cls_natgb_Oadd__mul__solve_1,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).

cnf(cls_natgb_Onoteq__reduce_1,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).

cnf(cls_injD_0,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_injD_0) ).

cnf(cls_le__diff__iff_1,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).

cnf(cls_less__diff__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).

cnf(cls_le__add__right__mono_0,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X5,X4,X1)
    | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X5,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom,
    ( X3 = X4
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).

cnf(cls_insert__inter__insert_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

cnf(cls_nat__diff__split_0,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).

cnf(cls_le__diff__conv2_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).

cnf(cls_le__diff__conv2_1,axiom,
    ( c_lessequals(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).

cnf(cls_psubset__insert__iff_7,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).

cnf(cls_add__le__cancel__right_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

cnf(cls_add__le__cancel__left_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_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(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox2/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(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

cnf(cls_Nat_Odiff__diff__eq_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).

cnf(cls_psubset__insert__iff_2,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_in(X4,X1,X3)
    | c_in(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).

cnf(cls_Int__insert__left_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

cnf(cls_Int__insert__right_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X2,X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

cnf(cls_double__diff_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X3
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).

cnf(cls_Int__greatest_0,axiom,
    ( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

cnf(cls_Int__subset__iff_2,axiom,
    ( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

cnf(cls_dvd__diffD1_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diffD1_0) ).

cnf(cls_dvd__diffD_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diffD_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).

cnf(cls_nat__add__left__cancel__le_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).

cnf(cls_nat__add__left__cancel__less_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).

cnf(cls_Int__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

cnf(cls_Int__assoc_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

cnf(cls_Int__left__commute_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

cnf(cls_empty__is__image_0,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X2,X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

cnf(cls_image__is__empty_0,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

cnf(cls_mult__mono1_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Omult__mono1(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).

cnf(cls_mult__left__mono_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Omult__mono(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

cnf(cls_mult__le__cancel__left__pos_1,axiom,
    ( c_lessequals(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_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).

cnf(cls_mult__right__mono_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Omult__mono(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

cnf(cls_mult__left__mono__neg_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X4,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).

cnf(cls_mult__le__cancel__left__neg_1,axiom,
    ( c_lessequals(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_lessequals(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).

cnf(cls_mult__right__mono__neg_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X4,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).

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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

cnf(cls_mult__right__le__one__le_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).

cnf(cls_mult__left__le__one__le_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).

cnf(cls_psubset__insert__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_in(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).

cnf(cls_Diff__insert__absorb_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2
    | c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

cnf(cls_le__add__diff_0,axiom,
    ( c_lessequals(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).

cnf(cls_add__mono_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).

cnf(cls_add__less__le__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

cnf(cls_add__le__less__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

cnf(cls_add__strict__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

cnf(cls_insert__Diff__if_1,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
    | c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

cnf(cls_sum__squares__eq__zero__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox2/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)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

cnf(cls_Int__subset__iff_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

cnf(cls_Int__subset__iff_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).

cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_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/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).

cnf(cls_add__inf__distrib__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).

cnf(cls_comm__semiring__class_Odistrib_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

cnf(cls_add__inf__distrib__left_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).

cnf(cls_class__semiring_Omul__d_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

cnf(cls_mod__mult__self2_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).

cnf(cls_mod__mult__self1_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).

cnf(cls_nat__mult__le__cancel1_1,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_1) ).

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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).

cnf(cls_mult__eq__if_1,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__if_1) ).

cnf(cls_inf1I_0,axiom,
    ( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(X1,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).

cnf(cls_add__le__mono_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X4,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).

cnf(cls_mult__le__mono_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X4,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).

cnf(cls_diff__less__mono2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

cnf(cls_diff__less__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).

cnf(cls_add__less__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_split__mod_0) ).

cnf(cls_subset__insert_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_in(X4,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).

cnf(cls_subset__insert__iff_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_in(X4,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

cnf(cls_singletonE_0,axiom,
    ( X1 = X2
    | ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_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/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).

cnf(cls_diff__mult__distrib_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).

cnf(cls_add__mult__distrib_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__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/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).

cnf(cls_diff__mult__distrib2_0,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).

cnf(cls_add__mult__distrib2_0,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).

cnf(cls_mod__mult__self3_0,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).

cnf(cls_psubset__insert__iff_3,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | c_in(X2,X3,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).

cnf(cls_card__Diff__subset_0,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(X2,X3),tc_nat)
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff__subset_0) ).

cnf(cls_insert__code_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).

cnf(cls_insert__mono_0,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).

cnf(cls_DiffE_1,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).

cnf(cls_le__imp__diff__is__add_1,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X1,tc_nat) = X2
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).

cnf(cls_le__diff__conv_1,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).

cnf(cls_less__diff__conv_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

cnf(cls_le__diff__conv_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).

cnf(cls_less__diff__conv_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).

cnf(cls_add__cancel__21_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

cnf(cls_diff__add__assoc2_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).

cnf(cls_add__diff__assoc2_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).

cnf(cls_diff__add__assoc_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).

cnf(cls_diff__diff__right_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).

cnf(cls_add__diff__assoc_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).

cnf(cls_insert__subset_2,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

cnf(cls_psubset__insert__iff_6,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).

cnf(cls_mult__le__0__iff_1,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).

cnf(cls_mult__le__0__iff_0,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).

cnf(cls_mult__le__0__iff_3,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).

cnf(cls_zero__le__mult__iff_0,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).

cnf(cls_zero__le__mult__iff_3,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).

cnf(cls_zero__le__mult__iff_2,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).

cnf(cls_zero__le__mult__iff_1,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).

cnf(cls_mult__le__0__iff_2,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).

cnf(cls_card__psubset_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(X2,X3),tc_nat)
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__psubset_0) ).

cnf(cls_DiffE_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).

cnf(cls_IntE_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).

cnf(cls_IntE_1,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).

cnf(cls_IntI_0,axiom,
    ( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).

cnf(cls_Int__iff_2,axiom,
    ( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).

cnf(cls_weak__coinduct_0,axiom,
    ( c_in(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_lessequals(X4,hAPP(X2,X4),tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weak__coinduct_0) ).

cnf(cls_insert__subset_1,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).

cnf(cls_mult__nonneg__nonpos2_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).

cnf(cls_mult__nonpos__nonneg_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

cnf(cls_split__mult__neg__le_1,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).

cnf(cls_mult__nonneg__nonpos_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).

cnf(cls_split__mult__neg__le_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).

cnf(cls_mult__le__0__iff_5,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).

cnf(cls_mult__le__0__iff_4,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

cnf(cls_add__nonpos__nonpos_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

cnf(cls_add__neg__nonpos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

cnf(cls_add__nonpos__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),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_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

cnf(cls_add__neg__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),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/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

cnf(cls_add__nonneg__nonneg_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

cnf(cls_mult__nonneg__nonneg_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

cnf(cls_split__mult__pos__le_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).

cnf(cls_zero__le__mult__iff_4,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).

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/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

cnf(cls_add__pos__nonneg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

cnf(cls_add__nonneg__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

cnf(cls_add__pos__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),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/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_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/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

cnf(cls_split__mult__pos__le_1,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).

cnf(cls_mult__nonpos__nonpos_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).

cnf(cls_zero__le__mult__iff_5,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

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),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

cnf(cls_le__cube_0,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__cube_0) ).

cnf(cls_add__left__mono_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

cnf(cls_add__le__cancel__left_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

cnf(cls_add__right__mono_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

cnf(cls_add__le__cancel__right_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).

cnf(cls_add__strict__left__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

cnf(cls_add__less__cancel__left_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

cnf(cls_add__strict__right__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

cnf(cls_add__less__cancel__right_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

cnf(cls_subset__insert_1,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).

cnf(cls_subset__insert__iff_2,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_1) ).

cnf(cls_add__increasing2_0,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

cnf(cls_add__increasing_0,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).

cnf(cls_add__strict__increasing_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

cnf(cls_add__strict__increasing2_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

cnf(cls_zero__induct__lemma_1,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__induct__lemma_1) ).

cnf(cls_pos__add__strict_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),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/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

cnf(cls_DiffI_0,axiom,
    ( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).

cnf(cls_Diff__iff_2,axiom,
    ( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

cnf(cls_insert__Diff1_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

cnf(cls_insert__subset_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).

cnf(cls_diff__le__mono2_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).

cnf(cls_diff__le__mono_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).

cnf(cls_nat__add__left__cancel__le_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).

cnf(cls_add__le__mono1_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).

cnf(cls_mult__le__mono2_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).

cnf(cls_mult__le__cancel1_2,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).

cnf(cls_mult__le__mono1_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).

cnf(cls_mult__le__cancel2_2,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).

cnf(cls_nat__add__left__cancel__less_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

cnf(cls_add__less__mono1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

cnf(cls_card__insert__le_0,axiom,
    ( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2),tc_nat)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__le_0) ).

cnf(cls_inf__greatest_0,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

cnf(cls_le__inf__iff_2,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

cnf(cls_le__infI_0,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).

cnf(cls_dvd__diff_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__ring__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/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).

cnf(cls_dvd__add_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),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/sandbox2/benchmark/theBenchmark.p',cls_dvd__add_0) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

cnf(cls_disjoint__iff__not__equal_0,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

cnf(cls_eq__diff__iff_0,axiom,
    ( X1 = X3
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).

cnf(cls_singleton__inject_0,axiom,
    ( X1 = X3
    | c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

cnf(cls_diff__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(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_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).

cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_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),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_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(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/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(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

cnf(cls_inf__sup__aci_I2_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

cnf(cls_inf__assoc_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

cnf(cls_class__semiring_Oadd__a_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

cnf(cls_inf__sup__aci_I3_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

cnf(cls_inf__left__commute_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

cnf(cls_add__cancel__21_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

cnf(cls_sum__squares__eq__zero__iff_2,axiom,
    ( c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_0) ).

cnf(cls_image__empty_0,axiom,
    c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).

cnf(cls_vimage__UNIV_0,axiom,
    c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).

cnf(cls_vimage__empty_0,axiom,
    c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

cnf(cls_empty__is__image_1,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

cnf(cls_le__iff__diff__le__0_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

cnf(cls_less__iff__diff__less__0_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

cnf(cls_dvd__diff__nat_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff__nat_0) ).

cnf(cls_insert__commute_0,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).

cnf(cls_subset__trans_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

cnf(cls_psubset__subset__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).

cnf(cls_subset__psubset__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).

cnf(cls_psubset__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__trans_0) ).

cnf(cls_le__eqI_1,axiom,
    ( c_lessequals(X3,X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X5,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).

cnf(cls_le__eqI_0,axiom,
    ( c_lessequals(X5,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).

cnf(cls_less__eqI_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).

cnf(cls_less__eqI_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X5,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).

cnf(cls_mult__le__cancel1_1,axiom,
    ( c_lessequals(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) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).

cnf(cls_mult__le__cancel2_1,axiom,
    ( c_lessequals(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) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).

cnf(cls_Int__insert__left_1,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool))
    | c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

cnf(cls_Int__insert__right_1,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).

cnf(cls_le__inf__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

cnf(cls_le__infE_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).

cnf(cls_le__inf__iff_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

cnf(cls_le__infE_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).

cnf(cls_of__nat__diff_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X1) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
    | ~ class_Ring__and__Field_Oring__1(X1)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).

cnf(cls_diff__cancel_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

cnf(cls_diff__cancel2_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

cnf(cls_diff__commute_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).

cnf(cls_diff__diff__left_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

cnf(cls_nat__add__assoc_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).

cnf(cls_nat__add__left__commute_0,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

cnf(cls_card__seteq_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(c_Finite__Set_Ocard(X2,X3),c_Finite__Set_Ocard(X1,X3),tc_nat)
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__seteq_0) ).

cnf(cls_insertE_0,axiom,
    ( c_in(X1,X2,X3)
    | X1 = X4
    | ~ c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

cnf(cls_Diff__idemp_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

cnf(cls_Int__left__absorb_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

cnf(cls_subset__insertI2_0,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_1) ).

cnf(cls_zero__less__diff_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

cnf(cls_less__add__eq__less_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

cnf(cls_add__leE_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).

cnf(cls_add__leE_1,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).

cnf(cls_add__lessD1_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox2/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,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__reduce_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).

cnf(cls_finite__Diff2_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

cnf(cls_inj__on__empty_0,axiom,
    c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_split__mod_5) ).

cnf(cls_add__nonneg__eq__0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

cnf(cls_add__nonneg__eq__0__iff_1,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

cnf(cls_less__fun__def_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_fun(X4,X1))
    | c_lessequals(X3,X2,tc_fun(X4,X1))
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X3,tc_fun(X4,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

cnf(cls_le__mod__geq_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).

cnf(cls_card__gt__0__iff_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__gt__0__iff_0) ).

cnf(cls_insert__code_2,axiom,
    ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).

cnf(cls_inc__induct_2,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X1,X3)))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ c_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inc__induct_2) ).

cnf(cls_finite__UNIV__card__ge__0_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1),tc_nat)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UNIV__card__ge__0_0) ).

cnf(cls_Max__mono_0,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMax(X2,X1),c_Finite__Set_Olinorder__class_OMax(X3,X1),X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__mono_0) ).

cnf(cls_Min__antimono_0,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X1),c_Finite__Set_Olinorder__class_OMin(X3,X1),X1)
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1)
    | ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__antimono_0) ).

cnf(cls_insert__ident_0,axiom,
    ( c_in(X1,X4,X3)
    | c_in(X1,X2,X3)
    | X2 = X4
    | c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

cnf(cls_even__less__0__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),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/sandbox2/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(c_HOL_Oplus__class_Oplus(X2,X2,X1),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/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_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),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

cnf(cls_atLeast__subset__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X3,X1),c_SetInterval_Oord__class_OatLeast(X2,X1),tc_fun(X1,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__subset__iff_0) ).

cnf(cls_singleton__iff_1,axiom,
    c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

cnf(cls_set__mp_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).

cnf(cls_subsetD_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).

cnf(cls_set__rev__mp_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

cnf(cls_subset__iff_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

cnf(cls_psubsetD_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubsetD_0) ).

cnf(cls_mod__if_1,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_1) ).

cnf(cls_less__fun__def_1,axiom,
    ( ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X3,tc_fun(X4,X1))
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_fun(X4,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_1) ).

cnf(cls_le__iff__diff__le__0_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

cnf(cls_less__iff__diff__less__0_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

cnf(cls_card__eq__UNIV__imp__eq__UNIV_0,axiom,
    ( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).

cnf(cls_Diff__disjoint_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_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/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__not__less_0) ).

cnf(cls_le__infI1_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).

cnf(cls_le__infI2_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).

cnf(cls_less__infI1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).

cnf(cls_less__infI2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_1) ).

cnf(cls_card__mono_0,axiom,
    ( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__mono_0) ).

cnf(cls_psubset__card__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__card__mono_0) ).

cnf(cls_add__gr__0_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox2/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),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).

cnf(cls_insertCI_0,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).

cnf(cls_insert__iff_2,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).

cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

cnf(cls_not__add__less1_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

cnf(cls_not__add__less2_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

cnf(cls_equalityI_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

cnf(cls_set__eq__subset_2,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

cnf(cls_mod__le__divisor_0,axiom,
    ( c_lessequals(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/sandbox2/benchmark/theBenchmark.p',cls_mod__le__divisor_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/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).

cnf(cls_card__insert__if_0,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__if_0) ).

cnf(cls_zero__less__diff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

cnf(cls_insert__code_1,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).

cnf(cls_Diff__triv_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

cnf(cls_le__add__diff__inverse2_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).

cnf(cls_diff__diff__cancel_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).

cnf(cls_le__add__diff__inverse_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).

cnf(cls_le__imp__diff__is__add_0,axiom,
    ( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).

cnf(cls_inc__induct_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X1,X3),X3,tc_nat)
    | ~ hBOOL(hAPP(X1,X3))
    | ~ c_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inc__induct_0) ).

cnf(cls_le__funD_0,axiom,
    ( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

cnf(cls_less__imp__diff__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

cnf(cls_termination__basic__simps_I3_J_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).

cnf(cls_trans__le__add1_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).

cnf(cls_termination__basic__simps_I4_J_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).

cnf(cls_trans__le__add2_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).

cnf(cls_dvd__reduce_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).

cnf(cls_trans__less__add1_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

cnf(cls_termination__basic__simps_I1_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

cnf(cls_trans__less__add2_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

cnf(cls_termination__basic__simps_I2_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

cnf(cls_xt1_I6_J_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

cnf(cls_order__trans_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_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/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).

cnf(cls_xt1_I8_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

cnf(cls_xt1_I7_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

cnf(cls_order__less__le__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

cnf(cls_order__le__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_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

cnf(cls_Min__singleton_0,axiom,
    ( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

cnf(cls_Max__singleton_0,axiom,
    ( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

cnf(cls_subset__empty_0,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).

cnf(cls_of__nat__add_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1) = c_HOL_Oplus__class_Oplus(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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).

cnf(cls_Diff__subset_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

cnf(cls_Int__lower1_0,axiom,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

cnf(cls_Int__lower2_0,axiom,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

cnf(cls_of__nat__le__iff_0,axiom,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

cnf(cls_dvd__imp__le_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__le_0) ).

cnf(cls_atLeast__subset__iff_1,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OatLeast(X2,X1),c_SetInterval_Oord__class_OatLeast(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__subset__iff_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).

cnf(cls_mod__add__self1_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).

cnf(cls_mod__add__self2_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).

cnf(cls_inf__sup__aci_I4_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

cnf(cls_inf__left__idem_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_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/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).

cnf(cls_le__trans_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).

cnf(cls_insert__absorb2_0,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

cnf(cls_bex__empty_0,axiom,
    ( ~ hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).

cnf(cls_gfp__upperbound_0,axiom,
    ( c_lessequals(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_lessequals(X2,hAPP(X3,X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gfp__upperbound_0) ).

cnf(cls_less__fun__def_0,axiom,
    ( c_lessequals(X2,X3,tc_fun(X4,X1))
    | ~ class_HOL_Oord(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_fun(X4,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_0) ).

cnf(cls_finite__Diff2_1,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).

cnf(cls_add__diff__inverse_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

cnf(cls_bot1E_0,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

cnf(cls_finite__insert_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).

cnf(cls_not__psubset__empty_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).

cnf(cls_less__le__not__le_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

cnf(cls_psubset__eq_2,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_2) ).

cnf(cls_subset__iff__psubset__eq_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).

cnf(cls_Int__absorb2_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

cnf(cls_Int__absorb1_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

cnf(cls_predicate1D_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X3,X2))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

cnf(cls_rev__predicate1D_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
    | ~ hBOOL(hAPP(X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

cnf(cls_psubset__eq_0,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_0) ).

cnf(cls_zero__less__two_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

cnf(cls_ball__empty_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).

cnf(cls_of__nat__le__iff_1,axiom,
    ( c_lessequals(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_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

cnf(cls_Min__le_0,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X1),X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_in(X3,X2,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__le_0) ).

cnf(cls_Max__ge_0,axiom,
    ( c_lessequals(X2,c_Finite__Set_Olinorder__class_OMax(X3,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_in(X2,X3,X1)
    | ~ c_Finite__Set_Ofinite(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__ge_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

cnf(cls_finite__Diff_0,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

cnf(cls_finite__Int_0,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).

cnf(cls_finite__Int_1,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).

cnf(cls_atLeast__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_in(X3,c_SetInterval_Oord__class_OatLeast(X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__iff_0) ).

cnf(cls_class__ringb_Oadd__cancel_0,axiom,
    ( X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

cnf(cls_subset__insertI_0,axiom,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
    ( c_in(X1,X2,X3)
    | c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

cnf(cls_order__eq__iff_2,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

cnf(cls_order__antisym_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).

cnf(cls_order__antisym__conv_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

cnf(cls_subset__empty_1,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).

cnf(cls_less__add__one_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).

cnf(cls_eq__eqI_1,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

cnf(cls_add__right__cancel_0,axiom,
    ( X2 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

cnf(cls_eq__eqI_0,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

cnf(cls_add__left__cancel_0,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

cnf(cls_add__imp__eq_0,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

cnf(cls_linorder__antisym__conv2_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

cnf(cls_linorder__not__less_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

cnf(cls_linorder__not__le_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

cnf(cls_less__le__not__le_1,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

cnf(cls_diffs0__imp__equal_0,axiom,
    ( X2 = X1
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

cnf(cls_zero__le__square_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

cnf(cls_atLeast__iff_1,axiom,
    ( c_in(X2,c_SetInterval_Oord__class_OatLeast(X3,X1),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__iff_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_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/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).

cnf(cls_le__antisym_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).

cnf(cls_add__diff__cancel_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

cnf(cls_diff__add__cancel_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

cnf(cls_inf__sup__ord_I1_J_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

cnf(cls_inf__le1_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).

cnf(cls_inf__sup__ord_I2_J_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

cnf(cls_inf__le2_0,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).

cnf(cls_nat__add__right__cancel_0,axiom,
    ( X1 = X3
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

cnf(cls_nat__add__left__cancel_0,axiom,
    ( X2 = X3
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

cnf(cls_natgb_Oadd__cancel_0,axiom,
    ( X2 = X3
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

cnf(cls_emptyE_0,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).

cnf(cls_empty__iff_0,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).

cnf(cls_ex__in__conv_0,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

cnf(cls_insertCI_1,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).

cnf(cls_insertI1_0,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).

cnf(cls_insert__iff_1,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).

cnf(cls_finite__subset_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).

cnf(cls_rev__finite__subset_0,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_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/sandbox2/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).

cnf(cls_diff__add__0_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

cnf(cls_diff__add__inverse_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

cnf(cls_diff__add__inverse2_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

cnf(cls_mod__less__eq__dividend_0,axiom,
    c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).

cnf(cls_diff__le__self_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).

cnf(cls_le__add1_0,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).

cnf(cls_le__iff__add_1,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).

cnf(cls_le__add2_0,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).

cnf(cls_le__square_0,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__square_0) ).

cnf(cls_empty__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

cnf(cls_Int__empty__left_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

cnf(cls_Diff__UNIV_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).

cnf(cls_Int__empty__right_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

cnf(cls_Int__commute_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).

cnf(cls_linorder__antisym__conv1_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

cnf(cls_linorder__antisym__conv2_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

cnf(cls_xt1_I11_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

cnf(cls_xt1_I12_J_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

cnf(cls_order__le__less_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).

cnf(cls_order__less__le_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).

cnf(cls_order__le__neq__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

cnf(cls_order__neq__le__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

cnf(cls_le__iff__inf_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

cnf(cls_le__iff__inf_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

cnf(cls_inf__absorb2_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

cnf(cls_order__le__less_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).

cnf(cls_order__less__imp__le_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

cnf(cls_finite__insert_1,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).

cnf(cls_card__gt__0__iff_1,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__gt__0__iff_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

cnf(cls_insert__absorb_0,axiom,
    ( c_Set_Oinsert(X1,X2,X3) = X2
    | ~ c_in(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

cnf(cls_diff__is__0__eq_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).

cnf(cls_nat__less__le_2,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).

cnf(cls_le__eq__less__or__eq_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).

cnf(cls_le__neq__implies__less_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).

cnf(cls_diff__is__0__eq_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).

cnf(cls_Min__in_0,axiom,
    ( c_in(c_Finite__Set_Olinorder__class_OMin(X2,X1),X2,X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__in_0) ).

cnf(cls_Max__in_0,axiom,
    ( c_in(c_Finite__Set_Olinorder__class_OMax(X2,X1),X2,X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__in_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/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).

cnf(cls_termination__basic__simps_I5_J_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

cnf(cls_nat__less__le_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).

cnf(cls_top1I_0,axiom,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).

cnf(cls_card__gt__0__iff_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat)
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__gt__0__iff_2) ).

cnf(cls_Int__UNIV__left_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).

cnf(cls_Diff__empty_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

cnf(cls_Int__UNIV__right_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).

cnf(cls_empty__subsetI_0,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

cnf(cls_subset__UNIV_0,axiom,
    c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

cnf(cls_empty__not__insert_0,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

cnf(cls_insert__not__empty_0,axiom,
    c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

cnf(cls_psubset__eq_1,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

cnf(cls_linorder__linear_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

cnf(cls_linorder__antisym__conv1_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X2,X1)
    | c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

cnf(cls_linorder__not__le_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

cnf(cls_not__leE_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).

cnf(cls_linorder__not__less_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

cnf(cls_mem__def_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

cnf(cls_inf__sup__aci_I1_J_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

cnf(cls_inf__commute_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).

cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

cnf(cls_class__semiring_Oadd__c_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

cnf(cls_not__one__le__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_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/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

cnf(cls_conjecture_5,negated_conjecture,
    ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_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/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_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/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

cnf(cls_class__ringb_Osubr0__iff_0,axiom,
    ( X2 = X3
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__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/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_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 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

cnf(cls_nat__le__linear_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

cnf(cls_UNIV__I_0,axiom,
    c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

cnf(cls_nat__add__commute_0,axiom,
    c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).

cnf(cls_inf__eq__top__eq1_0,axiom,
    ( X2 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).

cnf(cls_double__eq__0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

cnf(cls_inf__eq__top__eq2_0,axiom,
    ( X3 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).

cnf(cls_Diff__cancel_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

cnf(cls_mem__def_1,axiom,
    ( c_in(X1,X2,X3)
    | ~ hBOOL(hAPP(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

cnf(cls_right__minus__eq_0,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

cnf(cls_eq__iff__diff__eq__0_1,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

cnf(cls_full__nat__induct_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_full__nat__induct_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_0) ).

cnf(cls_zero__le__imp__of__nat_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).

cnf(cls_of__nat__0__le__iff_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).

cnf(cls_linorder__neq__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

cnf(cls_order__less__le_1,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).

cnf(cls_order__less__irrefl_0,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).

cnf(cls_le__0__eq_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).

cnf(cls_add__is__0_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).

cnf(cls_add__is__0_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).

cnf(cls_add__eq__self__zero_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != X1 ),
    file('/export/starexec/sandbox2/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 != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

cnf(cls_not__less0_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

cnf(cls_UNIV__not__empty_0,axiom,
    c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

cnf(cls_less__not__refl_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

cnf(cls_Int__absorb_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

cnf(cls_double__eq__0__iff_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

cnf(cls_equalityE_0,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

cnf(cls_subset__refl_0,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

cnf(cls_card__eq__0__iff_0,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).

cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
    ( X2 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

cnf(cls_zero__le__one_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

cnf(cls_finite__UNIV_0,axiom,
    ( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).

cnf(cls_class__ringb_Osubr0__iff_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).

cnf(cls_inf__bot__left_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_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/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_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/sandbox2/benchmark/theBenchmark.p',cls_mod__by__1_0) ).

cnf(cls_inf__bot__right_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_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/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

cnf(cls_inf__top__left_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__left_0) ).

cnf(cls_add__0__left_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).

cnf(cls_comm__monoid__add_Omult__1_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

cnf(cls_class__semiring_Oadd__0_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__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/sandbox2/benchmark/theBenchmark.p',cls_mult__1_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/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_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/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).

cnf(cls_diff__0__right_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

cnf(cls_inf__top__right_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(X1),X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__right_0) ).

cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_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/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

cnf(cls_card__empty_0,axiom,
    c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__empty_0) ).

cnf(cls_bot__least_0,axiom,
    ( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
    | ~ class_Orderings_Obot(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_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/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).

cnf(cls_top__greatest_0,axiom,
    ( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
    | ~ class_Orderings_Otop(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_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/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).

cnf(cls_finite_OemptyI_0,axiom,
    c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_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/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).

cnf(cls_right__minus__eq_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

cnf(cls_diff__self_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).

cnf(cls_eq__iff__diff__eq__0_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

cnf(cls_inf__idem_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_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/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).

cnf(cls_order__eq__iff_0,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

cnf(cls_order__eq__refl_0,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_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/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).

cnf(cls_add__is__0_2,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).

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/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).

cnf(cls_le__0__eq_1,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).

cnf(cls_diff__0__eq__0_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).

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/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).

cnf(cls_plus__nat_Oadd__0_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).

cnf(cls_minus__nat_Odiff__0_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

cnf(cls_Nat_Oadd__0__right_0,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).

cnf(cls_natgb_Oadd__r0__iff_1,axiom,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

cnf(cls_le0_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).

cnf(cls_diff__self__eq__0_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
    c_fequal(X1,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

cnf(cls_atLeast__eq__iff_0,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OatLeast(X2,X1) != c_SetInterval_Oord__class_OatLeast(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__eq__iff_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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

cnf(cls_le__refl_0,axiom,
    c_lessequals(X1,X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).

cnf(cls_eq__imp__le_0,axiom,
    c_lessequals(X1,X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

cnf(cls_dvd_Oeq__iff_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).

cnf(cls_conjecture_4,negated_conjecture,
    c_in(v_pn,v_U,tc_Com_Opname),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(clsarity_fun__Finite__Set_Ofinite_Ofinite,axiom,
    ( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

cnf(clsarity_fun__HOL_Oord,axiom,
    ( class_HOL_Oord(tc_fun(X1,X2))
    | ~ class_HOL_Oord(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

cnf(clsarity_fun__Orderings_Obot,axiom,
    ( class_Orderings_Obot(tc_fun(X1,X2))
    | ~ class_Orderings_Obot(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

cnf(clsarity_fun__Orderings_Otop,axiom,
    ( class_Orderings_Otop(tc_fun(X1,X2))
    | ~ class_Orderings_Otop(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

cnf(clsarity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

cnf(clsarity_fun__Lattices_Olattice,axiom,
    ( class_Lattices_Olattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
    ( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
    ( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Obounded__lattice(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

cnf(clsarity_fun__Orderings_Oorder,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

cnf(clsarity_fun__Orderings_Opreorder,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

cnf(cls_card__eq__0__iff_2,axiom,
    ( c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Finite__Set_Ofinite(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__0__iff_2) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

cnf(cls_finite_0,axiom,
    ( c_Finite__Set_Ofinite(X2,X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_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/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_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/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

cnf(clsarity_bool__HOL_Oord,axiom,
    class_HOL_Oord(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

cnf(clsarity_nat__HOL_Oord,axiom,
    class_HOL_Oord(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

cnf(clsarity_bool__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

cnf(clsarity_nat__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

cnf(clsarity_bool__Orderings_Otop,axiom,
    class_Orderings_Otop(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

cnf(clsarity_bool__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

cnf(clsarity_nat__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

cnf(clsarity_nat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

cnf(clsarity_nat__Ring__and__Field_Odvd,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).

cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

cnf(clsarity_bool__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

cnf(clsarity_nat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

cnf(clsarity_bool__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

cnf(clsarity_nat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

cnf(clsarity_nat__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).

cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

cnf(i_0_1121,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_card__insert_0 ).

cnf(i_0_1122,axiom,
    c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    cls_Suc__eq__plus1_0 ).

cnf(i_0_1123,axiom,
    ( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3)) = c_Finite__Set_Ocard(X1,X3)
    | ~ c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_card__Suc__Diff1_0 ).

cnf(i_0_1124,negated_conjecture,
    c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
    cls_conjecture_3 ).

cnf(i_0_1125,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(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__le__cancel1_0 ).

cnf(i_0_1126,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_1127,negated_conjecture,
    c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
    cls_conjecture_2 ).

cnf(i_0_1128,axiom,
    ( c_lessequals(hAPP(X2,X3),hAPP(X2,X4),X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X4,tc_nat)
    | ~ c_lessequals(hAPP(X2,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X2,X1)),hAPP(X2,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X2,X1))),X1) ),
    cls_lift__Suc__mono__le_0 ).

cnf(i_0_1129,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
    cls_mod__mult__self4_0 ).

cnf(i_0_1130,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X1,X3))))
    | ~ c_lessequals(c_Suc(X3),X2,tc_nat) ),
    cls_Suc__le__D__lemma_1 ).

cnf(i_0_1131,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    cls_one__le__mult__iff_2 ).

cnf(i_0_1132,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_1133,axiom,
    ( c_lessequals(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_lessequals(X2,X3,tc_nat) ),
    cls_Suc__mult__le__cancel1_1 ).

cnf(i_0_1134,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_1135,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_diff__Suc__diff__eq2_0 ).

cnf(i_0_1136,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_diff__Suc__diff__eq1_0 ).

cnf(i_0_1137,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_1138,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_1139,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
    cls_Suc__diff__diff_0 ).

cnf(i_0_1140,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    cls_one__le__mult__iff_0 ).

cnf(i_0_1141,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    cls_one__le__mult__iff_1 ).

cnf(i_0_1142,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
    | hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1))))
    | ~ hBOOL(hAPP(X1,X2)) ),
    cls_zero__induct__lemma_0 ).

cnf(i_0_1143,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_1144,axiom,
    ( c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
    | c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
    cls_card__Suc__eq_5 ).

cnf(i_0_1145,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X1,X3))))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ c_lessequals(X2,X3,tc_nat) ),
    cls_inc__induct_1 ).

cnf(i_0_1146,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_1147,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_1148,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    cls_Suc__le__mono_0 ).

cnf(i_0_1149,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_1150,axiom,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_Suc__pred_0 ).

cnf(i_0_1151,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_diff__Suc__less_0 ).

cnf(i_0_1152,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_1153,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_add__eq__if_1 ).

cnf(i_0_1154,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_1155,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat))
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_Suc__diff__le_0 ).

cnf(i_0_1156,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    cls_less__iff__Suc__add_1 ).

cnf(i_0_1157,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    cls_less__add__Suc1_0 ).

cnf(i_0_1158,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
    cls_less__add__Suc2_0 ).

cnf(i_0_1159,axiom,
    ( X1 = c_Suc(X2)
    | c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
    cls_le__SucE_0 ).

cnf(i_0_1160,axiom,
    ( hBOOL(hAPP(X1,X2))
    | c_lessequals(X3,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X1,X3),tc_nat)
    | ~ c_lessequals(c_Suc(X3),X2,tc_nat) ),
    cls_Suc__le__D__lemma_0 ).

cnf(i_0_1161,axiom,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_Suc__le__mono_1 ).

cnf(i_0_1162,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_1163,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_1164,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_1165,axiom,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_le__less__Suc__eq_0 ).

cnf(i_0_1166,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    cls_not__less__eq__eq_1 ).

cnf(i_0_1167,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_1168,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_1169,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,X3))
    | ~ c_lessequals(c_Suc(X3),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X1),tc_nat) ),
    cls_full__nat__induct_0 ).

cnf(i_0_1170,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_1171,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
    cls_diff__Suc__Suc_0 ).

cnf(i_0_1172,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
    cls_add__Suc__shift_0 ).

cnf(i_0_1173,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
    cls_diff__Suc__eq__diff__pred_0 ).

cnf(i_0_1174,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
    cls_add__Suc_0 ).

cnf(i_0_1175,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
    cls_add__Suc__right_0 ).

cnf(i_0_1176,axiom,
    ( X1 = c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X1))
    | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    cls_Suc__le__D_0 ).

cnf(i_0_1177,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    cls_mult__Suc_0 ).

cnf(i_0_1178,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    cls_mult__Suc__right_0 ).

cnf(i_0_1179,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_1180,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_1181,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_1182,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    cls_Suc__leD_0 ).

cnf(i_0_1183,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    cls_less__eq__Suc__le_1 ).

cnf(i_0_1184,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    cls_Suc__le__eq_0 ).

cnf(i_0_1185,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_1186,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    cls_less__Suc__eq__le_0 ).

cnf(i_0_1187,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_1188,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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    cls_one__is__add_1 ).

cnf(i_0_1189,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_1 ).

cnf(i_0_1190,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_1191,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
    | c_in(X1,X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_card__insert__if_1 ).

cnf(i_0_1192,axiom,
    ( c_in(X1,X2,X3)
    | c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
    | c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_card__Suc__eq_4 ).

cnf(i_0_1193,axiom,
    c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
    cls_le__Suc__eq_2 ).

cnf(i_0_1194,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_1195,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
    cls_diff__less__Suc_0 ).

cnf(i_0_1196,axiom,
    ~ c_lessequals(c_Suc(X1),X1,tc_nat),
    cls_Suc__n__not__le__n_0 ).

cnf(i_0_1197,axiom,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_Suc__diff__1_0 ).

cnf(i_0_1198,axiom,
    ( X1 = c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_Suc__pred_H_0 ).

cnf(i_0_1199,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_less__eq__Suc__le_0 ).

cnf(i_0_1200,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_Suc__leI_0 ).

cnf(i_0_1201,axiom,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__SucI_0 ).

cnf(i_0_1202,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | ~ c_lessequals(X1,X1,tc_nat) ),
    cls_le__less__Suc__eq_1 ).

cnf(i_0_1203,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_less__Suc__eq__le_1 ).

cnf(i_0_1204,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_1205,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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    cls_one__is__add_0 ).

cnf(i_0_1206,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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    cls_one__is__add_3 ).

cnf(i_0_1207,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_0 ).

cnf(i_0_1208,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_3 ).

cnf(i_0_1209,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_1210,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_1211,axiom,
    ( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,X3,X2),X2) = X3
    | c_Finite__Set_Ocard(X1,X2) != c_Suc(X3) ),
    cls_card__eq__SucD_2 ).

cnf(i_0_1212,axiom,
    ( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,X3,X2),X2) = X3
    | c_Finite__Set_Ocard(X1,X2) != c_Suc(X3) ),
    cls_card__Suc__eq_2 ).

cnf(i_0_1213,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_add__is__1_4 ).

cnf(i_0_1214,axiom,
    c_HOL_Oplus__class_Oplus(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_add__is__1_5 ).

cnf(i_0_1215,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_one__is__add_4 ).

cnf(i_0_1216,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    cls_one__is__add_5 ).

cnf(i_0_1217,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__Suc_0 ).

cnf(i_0_1218,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    cls_not__less__eq__eq_0 ).

cnf(i_0_1219,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_1220,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_1221,axiom,
    ( c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_card__eq__SucD_3 ).

cnf(i_0_1222,axiom,
    ( c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_card__Suc__eq_3 ).

cnf(i_0_1223,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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    cls_one__is__add_2 ).

cnf(i_0_1224,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_2 ).

cnf(i_0_1225,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__nonneg__eq__0__iff_2 ).

cnf(i_0_1226,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_Suc__inject_0 ).

cnf(i_0_1227,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_nat_Oinject_0 ).

cnf(i_0_1228,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_1229,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_1230,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_1231,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    cls_diff__Suc__1_0 ).

cnf(i_0_1232,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_1233,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_1234,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_lessI_0 ).

cnf(i_0_1235,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_less__Suc__eq_2 ).

cnf(i_0_1236,axiom,
    c_Suc(X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
    cls_Suc__eq__plus1__left_0 ).

cnf(i_0_1237,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_nat_Osimps_I3_J_0 ).

cnf(i_0_1238,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_Suc__neq__Zero_0 ).

cnf(i_0_1239,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_nat_Osimps_I2_J_0 ).

cnf(i_0_1240,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_Zero__neq__Suc_0 ).

cnf(i_0_1241,axiom,
    c_Suc(X1) != X1,
    cls_Suc__n__not__n_0 ).

cnf(i_0_1242,axiom,
    X1 != c_Suc(X1),
    cls_n__not__Suc__n_0 ).

cnf(i_0_1243,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_1244,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X5,X1,X3,X4)),X5,X4) ),
    cls_image__subset__iff_2,
    [final] ).

cnf(i_0_1245,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X5,X1,X3,X4)),X5,X4) ),
    cls_image__subsetI_1,
    [final] ).

cnf(i_0_1246,axiom,
    ( c_Set_Oimage(X1,X2,X4,X5) = c_Set_Oimage(X3,X2,X4,X5)
    | hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X3,X4,X5)) != hAPP(X3,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X3,X4,X5)) ),
    cls_image__cong_1,
    [final] ).

cnf(i_0_1247,axiom,
    ( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X7,X4,X5) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X6,X7,X4,X5),X2,X3,X4,X5)
    | X2 = X6 ),
    cls_fun__upd__twist_0,
    [final] ).

cnf(i_0_1248,axiom,
    c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2,X6,X4,X5) = c_Fun_Ofun__upd(X1,X2,X6,X4,X5),
    cls_fun__upd__upd_0,
    [final] ).

cnf(i_0_1249,axiom,
    ( c_Set_Oimage(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5) = c_Set_Oinsert(X3,c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
    | ~ c_in(X2,X6,X4) ),
    cls_fun__upd__image_0,
    [final] ).

cnf(i_0_1250,axiom,
    ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),c_Finite__Set_Ocard(X1,X3),tc_nat)
    | ~ c_in(X4,X1,X3)
    | ~ c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_card__Diff2__less_0,
    [final] ).

cnf(i_0_1251,axiom,
    ( c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5)
    | c_in(X3,c_Set_Oimage(X1,X6,X4,X5),X5)
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    cls_inj__on__fun__updI_0,
    [final] ).

cnf(i_0_1252,axiom,
    ( X1 = c_Set_Oimage(X2,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X3,X1,X2,X4,X5),X4,X5)
    | ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X1,X5) ),
    cls_finite__subset__image_2,
    [final] ).

cnf(i_0_1253,axiom,
    ( X1 = c_Set_Oimage(X2,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X4,X5)
    | ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool)) ),
    cls_subset__image__iff_1,
    [final] ).

cnf(i_0_1254,axiom,
    ( c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X1,X2,X3,X4,X5),X1,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    cls_finite__subset__image_0,
    [final] ).

cnf(i_0_1255,axiom,
    ( c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X1,X2,X3,X4,X5),X1,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool)) ),
    cls_subset__image__iff_0,
    [final] ).

cnf(i_0_1256,axiom,
    ( c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X1,X2,X3,X4,X5),X4)
    | ~ c_lessequals(X2,c_Set_Oimage(X3,X1,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X5) ),
    cls_finite__subset__image_1,
    [final] ).

cnf(i_0_1257,axiom,
    ( c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X1,X2,X3,X4,X5),X1,X4)
    | ~ c_in(X3,c_Set_Oimage(X2,X1,X4,X5),X5) ),
    cls_image__iff_0,
    [final] ).

cnf(i_0_1258,axiom,
    ( c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X1,X2,X3,X4,X5),X1,X4)
    | ~ c_in(X2,c_Set_Oimage(X3,X1,X4,X5),X5) ),
    cls_imageE_1,
    [final] ).

cnf(i_0_1259,axiom,
    ( X5 = X6
    | hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5) != hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X6)
    | ~ c_in(X6,c_Set_Oimage(X2,X1,X3,X4),X4)
    | ~ c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4) ),
    cls_inv__into__injective_0,
    [final] ).

cnf(i_0_1260,axiom,
    ( X1 = hAPP(X2,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X3,X2,X1,X4,X5))
    | ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
    cls_image__iff_1,
    [final] ).

cnf(i_0_1261,axiom,
    ( X1 = hAPP(X2,c_ATP__Linkup_Osko__Set__XimageE__1__1(X3,X1,X2,X4,X5))
    | ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
    cls_imageE_0,
    [final] ).

cnf(i_0_1262,axiom,
    ( ~ c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
    | ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) ),
    cls_inj__on__insert_1,
    [final] ).

cnf(i_0_1263,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X5,X1,X3,X4),X2,X3) ),
    cls_image__subset__iff_1,
    [final] ).

cnf(i_0_1264,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(X2,X5,X1,X3,X4),X2,X3) ),
    cls_image__subsetI_0,
    [final] ).

cnf(i_0_1265,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    cls_image__diff__subset_0,
    [final] ).

cnf(i_0_1266,axiom,
    c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
    cls_image__Int__subset_0,
    [final] ).

cnf(i_0_1267,axiom,
    ( c_Set_Oimage(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5) = c_Set_Oimage(X1,X6,X4,X5)
    | c_in(X2,X6,X4) ),
    cls_fun__upd__image_1,
    [final] ).

cnf(i_0_1268,axiom,
    ( c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X5,X2,X3,X4)
    | c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X2,X1,X5,X3,X4),X2,X3) ),
    cls_image__cong_0,
    [final] ).

cnf(i_0_1269,axiom,
    ( c_in(hAPP(X1,X2),c_Inductive_Ocomplete__lattice__class_Ogfp(X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),hAPP(X3,c_Set_Oimage(X1,X5,X6,X4)),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X5,X6) ),
    cls_weak__coinduct__image_0,
    [final] ).

cnf(i_0_1270,axiom,
    ( c_Finite__Set_Ocard(X1,X2) = c_Finite__Set_Ocard(X3,X4)
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | ~ c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(c_Set_Oimage(X5,X3,X4,X2),X1,tc_fun(X2,tc_bool))
    | ~ c_Fun_Oinj__on(X5,X3,X4,X2)
    | ~ c_lessequals(c_Set_Oimage(X6,X1,X2,X4),X3,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X6,X1,X2,X4) ),
    cls_card__bij__eq_0,
    [final] ).

cnf(i_0_1271,axiom,
    ( c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
    | c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X5),X5)
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5) ),
    cls_inj__on__insert_2,
    [final] ).

cnf(i_0_1272,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(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X1,tc_nat),X2,tc_nat))) ),
    cls_split__mod_1,
    [final] ).

cnf(i_0_1273,axiom,
    ( hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
    | X6 = X2 ),
    cls_fun__upd__other_0,
    [final] ).

cnf(i_0_1274,axiom,
    ( hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
    | X6 = X2 ),
    cls_fun__upd__apply_1,
    [final] ).

cnf(i_0_1275,axiom,
    hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
    cls_fun__upd__apply_0,
    [final] ).

cnf(i_0_1276,axiom,
    hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
    cls_fun__upd__same_0,
    [final] ).

cnf(i_0_1277,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    cls_inj__image__subset__iff_0,
    [final] ).

cnf(i_0_1278,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    cls_inj__on__image__set__diff_0,
    [final] ).

cnf(i_0_1279,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X3,X6,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X6,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
    cls_inj__on__image__Int_0,
    [final] ).

cnf(i_0_1280,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    cls_nat__le__add__iff1_1,
    [final] ).

cnf(i_0_1281,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    cls_nat__less__add__iff1_1,
    [final] ).

cnf(i_0_1282,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    cls_nat__le__add__iff2_1,
    [final] ).

cnf(i_0_1283,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    cls_nat__less__add__iff2_1,
    [final] ).

cnf(i_0_1284,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
    cls_le__add__iff1_1,
    [final] ).

cnf(i_0_1285,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
    cls_less__add__iff1_1,
    [final] ).

cnf(i_0_1286,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
    cls_le__add__iff2_1,
    [final] ).

cnf(i_0_1287,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
    cls_less__add__iff2_1,
    [final] ).

cnf(i_0_1288,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_vimage__subsetI_0,
    [final] ).

cnf(i_0_1289,axiom,
    ( c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_image__set__diff_0,
    [final] ).

cnf(i_0_1290,axiom,
    ( c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_image__Int_0,
    [final] ).

cnf(i_0_1291,axiom,
    ( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5),X1,X3)
    | ~ c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4) ),
    cls_inv__into__into_0,
    [final] ).

cnf(i_0_1292,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_nat__le__add__iff1_0,
    [final] ).

cnf(i_0_1293,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_nat__less__add__iff1_0,
    [final] ).

cnf(i_0_1294,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_nat__le__add__iff2_0,
    [final] ).

cnf(i_0_1295,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_nat__less__add__iff2_0,
    [final] ).

cnf(i_0_1296,axiom,
    ( hAPP(X1,X2) = X3
    | c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
    cls_fun__upd__idem__iff_0,
    [final] ).

cnf(i_0_1297,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
    cls_le__add__iff1_0,
    [final] ).

cnf(i_0_1298,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
    cls_less__add__iff1_0,
    [final] ).

cnf(i_0_1299,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
    cls_le__add__iff2_0,
    [final] ).

cnf(i_0_1300,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
    cls_less__add__iff2_0,
    [final] ).

cnf(i_0_1301,axiom,
    ( hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X3,X4),X5)) = X5
    | ~ c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4) ),
    cls_f__inv__into__f_0,
    [final] ).

cnf(i_0_1302,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),c_Set_Oimage(X2,X4,X1,X3),X3,X1) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    cls_image__inv__f__f_0,
    [final] ).

cnf(i_0_1303,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),c_Set_Oimage(X2,X4,X1,X3),X3,X1) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    cls_inv__image__comp_0,
    [final] ).

cnf(i_0_1304,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),c_Set_Oimage(X2,X5,X3,X4),X4,X3) = X5
    | ~ c_lessequals(X5,X1,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    cls_inv__into__image__cancel_0,
    [final] ).

cnf(i_0_1305,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    cls_vimage__code_0,
    [final] ).

cnf(i_0_1306,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__image__subset__iff_1,
    [final] ).

cnf(i_0_1307,axiom,
    ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5,X4,X3)
    | ~ c_lessequals(X5,c_Set_Oimage(X2,X1,X3,X4),tc_fun(X4,tc_bool)) ),
    cls_inj__on__inv__into_0,
    [final] ).

cnf(i_0_1308,axiom,
    ( c_Set_Oimage(X1,X2,X3,X3) = X2
    | ~ c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X3),X2,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_endo__inj__surj_0,
    [final] ).

cnf(i_0_1309,axiom,
    c_lessequals(c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4),X2,tc_fun(X4,tc_bool)),
    cls_image__vimage__subset_0,
    [final] ).

cnf(i_0_1310,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    cls_nat__diff__add__eq1_0,
    [final] ).

cnf(i_0_1311,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    cls_nat__diff__add__eq2_0,
    [final] ).

cnf(i_0_1312,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_in(X2,c_Set_Ovimage(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5) ),
    cls_vimage__singleton__eq_0,
    [final] ).

cnf(i_0_1313,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Odvd(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X5,X6,X1),X1),X4,X1),X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,X1) ),
    cls_inf__period_I4_J_1,
    [final] ).

cnf(i_0_1314,axiom,
    c_Set_Ovimage(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    cls_vimage__Diff_0,
    [final] ).

cnf(i_0_1315,axiom,
    c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
    cls_vimage__Int_0,
    [final] ).

cnf(i_0_1316,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_psubset__insert__iff_9,
    [final] ).

cnf(i_0_1317,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
    cls_inj__image__mem__iff_0,
    [final] ).

cnf(i_0_1318,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X1,X4)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_psubset__insert__iff_8,
    [final] ).

cnf(i_0_1319,axiom,
    ( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X4),tc_nat)
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | ~ c_lessequals(c_Set_Oimage(X5,X1,X2,X4),X3,tc_fun(X4,tc_bool))
    | ~ c_Fun_Oinj__on(X5,X1,X2,X4) ),
    cls_card__inj__on__le_0,
    [final] ).

cnf(i_0_1320,axiom,
    c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
    cls_image__vimage__eq_0,
    [final] ).

cnf(i_0_1321,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X3,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_psubset__insert__iff_5,
    [final] ).

cnf(i_0_1322,plain,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    inference(rw,[status(thm)],[i_0_1121,c_0_1122]),
    [final] ).

cnf(i_0_1323,axiom,
    ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),c_Finite__Set_Ocard(X1,X3),tc_nat)
    | ~ c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_card__Diff1__less_0,
    [final] ).

cnf(i_0_1324,plain,
    ( c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Finite__Set_Ocard(X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | ~ c_in(X2,X1,X3) ),
    inference(rw,[status(thm)],[i_0_1123,c_0_1122]),
    [final] ).

cnf(i_0_1325,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X3,X4)
    | ~ c_in(X2,X1,X4)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_psubset__insert__iff_4,
    [final] ).

cnf(i_0_1326,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert__iff_4,
    [final] ).

cnf(i_0_1327,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X1,X4)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_diff__single__insert_0,
    [final] ).

cnf(i_0_1328,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X1,X4)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert__iff_3,
    [final] ).

cnf(i_0_1329,axiom,
    ( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3),c_Finite__Set_Ocard(X1,X3),tc_nat)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_card__Diff1__le_0,
    [final] ).

cnf(i_0_1330,axiom,
    ( X2 = X5
    | c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__image__eq__iff_0,
    [final] ).

cnf(i_0_1331,axiom,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    cls_fun__upd__idem__iff_1,
    [final] ).

cnf(i_0_1332,axiom,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    cls_fun__upd__triv_0,
    [final] ).

cnf(i_0_1333,axiom,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    cls_fun__upd__idem_0,
    [final] ).

cnf(i_0_1334,axiom,
    ( c_Set_Ovimage(X1,c_Set_Oimage(X1,X2,X3,X4),X3,X4) = X2
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    cls_inj__vimage__image__eq_0,
    [final] ).

cnf(i_0_1335,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Fun_Oinj__on(X3,X1,X2,X4)
    | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
    cls_finite__imageD_0,
    [final] ).

cnf(i_0_1336,axiom,
    ( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
    cls_image__mono_0,
    [final] ).

cnf(i_0_1337,axiom,
    ( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_subset__image__iff_2,
    [final] ).

cnf(i_0_1338,axiom,
    ( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),c_Set_Ovimage(X1,X5,X3,X4),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X4,tc_bool)) ),
    cls_vimage__mono_0,
    [final] ).

cnf(i_0_1339,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X3)
    | ~ c_lessequals(X2,c_Set_Oimage(X1,X2,X3,X3),tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__surj__inj_0,
    [final] ).

cnf(i_0_1340,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Odvd(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X6,X1),X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X1) ),
    cls_inf__period_I4_J_0,
    [final] ).

cnf(i_0_1341,negated_conjecture,
    c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1124,c_0_1122]),
    [final] ).

cnf(i_0_1342,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1125,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1343,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1126,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1344,axiom,
    ( hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
    | ~ hBOOL(hAPP(X2,hAPP(X1,X5))) ),
    cls_vimage__code_1,
    [final] ).

cnf(i_0_1345,negated_conjecture,
    c_lessequals(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
    inference(rw,[status(thm)],[i_0_1127,c_0_1122]),
    [final] ).

cnf(i_0_1346,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_inj__image__mem__iff_1,
    [final] ).

cnf(i_0_1347,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_nat__eq__add__iff2_1,
    [final] ).

cnf(i_0_1348,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_nat__eq__add__iff1_1,
    [final] ).

cnf(i_0_1349,axiom,
    ( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4),c_Finite__Set_Ocard(X2,X3),tc_nat)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_card__image__le_0,
    [final] ).

cnf(i_0_1350,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),hAPP(X2,X4)) = X4
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
    cls_inv__f__f_0,
    [final] ).

cnf(i_0_1351,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,X2,X3),hAPP(X1,X4)) = X4
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
    cls_inv__f__eq_0,
    [final] ).

cnf(i_0_1352,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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),X1) ),
    cls_sum__squares__gt__zero__iff_0,
    [final] ).

cnf(i_0_1353,negated_conjecture,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    cls_conjecture_6,
    [final] ).

cnf(i_0_1354,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_eq__card__imp__inj__on_0,
    [final] ).

cnf(i_0_1355,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | c_in(X2,X4,X3)
    | ~ c_in(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
    cls_psubset__insert__iff_1,
    [final] ).

cnf(i_0_1356,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X1),X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    cls_eq__add__iff2_1,
    [final] ).

cnf(i_0_1357,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    cls_eq__add__iff1_1,
    [final] ).

cnf(i_0_1358,axiom,
    c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3),X4),
    cls_vimage__singleton__eq_1,
    [final] ).

cnf(i_0_1359,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,X5,X6)
    | ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),X3,tc_fun(X4,tc_bool)) ),
    cls_image__subset__iff_0,
    [final] ).

cnf(i_0_1360,axiom,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X2,tc_nat))) ),
    cls_nat__diff__split_1,
    [final] ).

cnf(i_0_1361,axiom,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X2,tc_nat))) ),
    cls_nat__diff__split__asm_1,
    [final] ).

cnf(i_0_1362,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X4,tc_nat),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_1363,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | ~ c_in(X2,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
    cls_subset__insert__iff_0,
    [final] ).

cnf(i_0_1364,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5
    | ~ c_in(X5,X1,X3)
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    cls_inv__into__f__f_0,
    [final] ).

cnf(i_0_1365,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X2,X4,X3,X5),hAPP(X4,X1)) = X1
    | ~ c_in(X1,X2,X3)
    | ~ c_Fun_Oinj__on(X4,X2,X3,X5) ),
    cls_inv__into__f__eq_0,
    [final] ).

cnf(i_0_1366,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Ovimage(X1,X2,X3,X4),X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    cls_finite__vimageI_0,
    [final] ).

cnf(i_0_1367,plain,
    ( c_lessequals(hAPP(X2,X3),hAPP(X2,X4),X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X4,tc_nat)
    | ~ c_lessequals(hAPP(X2,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X2,X1)),hAPP(X2,c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(X2,X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X1) ),
    inference(rw,[status(thm)],[i_0_1128,c_0_1122]),
    [final] ).

cnf(i_0_1368,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1129,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1369,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_sum__squares__le__zero__iff_0,
    [final] ).

cnf(i_0_1370,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_sum__squares__le__zero__iff_1,
    [final] ).

cnf(i_0_1371,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_not__sum__squares__lt__zero_0,
    [final] ).

cnf(i_0_1372,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat) = X5
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    cls_nat__eq__add__iff1_0,
    [final] ).

cnf(i_0_1373,axiom,
    ( X3 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    cls_nat__eq__add__iff2_0,
    [final] ).

cnf(i_0_1374,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
    cls_vimageD_0,
    [final] ).

cnf(i_0_1375,axiom,
    ( c_in(hAPP(X1,X2),X3,X4)
    | ~ c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
    cls_vimageE_0,
    [final] ).

cnf(i_0_1376,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,c_Set_Oimage(X3,X4,X5,X2),tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X4,X5) ),
    cls_finite__surj_0,
    [final] ).

cnf(i_0_1377,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_inj__on__iff__eq__card_0,
    [final] ).

cnf(i_0_1378,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_in(X2,X3,X4)
    | ~ c_in(X2,X1,X4)
    | ~ c_Finite__Set_Ofinite(X1,X4) ),
    cls_card__Diff__insert_0,
    [final] ).

cnf(i_0_1379,axiom,
    c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
    cls_image__insert_0,
    [final] ).

cnf(i_0_1380,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    cls_card__image_0,
    [final] ).

cnf(i_0_1381,axiom,
    ( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
    | ~ c_in(X2,X3,X4) ),
    cls_insert__image_0,
    [final] ).

cnf(i_0_1382,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1) = X6
    | ~ class_Ring__and__Field_Oring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
    cls_eq__add__iff1_0,
    [final] ).

cnf(i_0_1383,axiom,
    ( X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1)
    | ~ class_Ring__and__Field_Oring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
    cls_eq__add__iff2_0,
    [final] ).

cnf(i_0_1384,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1),X5,X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    cls_combine__common__factor_0,
    [final] ).

cnf(i_0_1385,axiom,
    ( X3 = X5
    | X2 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_class__ringb_Onoteq__reduce_0,
    [final] ).

cnf(i_0_1386,axiom,
    ( X3 = X5
    | X2 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_class__ringb_Oadd__mul__solve_0,
    [final] ).

cnf(i_0_1387,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ hBOOL(hAPP(X1,c_HOL_Oplus__class_Oplus(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X1,X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1130,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1388,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3),tc_nat)
    | ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3) ),
    cls_card__Diff__subset__Int_0,
    [final] ).

cnf(i_0_1389,axiom,
    ( X1 = X5
    | X1 = X4
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_0,
    [final] ).

cnf(i_0_1390,axiom,
    ( X2 = X4
    | X1 = X4
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_1,
    [final] ).

cnf(i_0_1391,axiom,
    ( X1 = X5
    | X2 = X5
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_2,
    [final] ).

cnf(i_0_1392,axiom,
    ( X2 = X4
    | X2 = X5
    | c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_doubleton__eq__iff_3,
    [final] ).

cnf(i_0_1393,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
    cls_Diff__insert2_0,
    [final] ).

cnf(i_0_1394,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
    cls_left__add__mult__distrib_0,
    [final] ).

cnf(i_0_1395,axiom,
    ( X2 = X4
    | X1 = X3
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    cls_natgb_Oadd__mul__solve_0,
    [final] ).

cnf(i_0_1396,axiom,
    ( X2 = X4
    | X1 = X3
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    cls_natgb_Onoteq__reduce_0,
    [final] ).

cnf(i_0_1397,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1131,c_0_1122]),c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1398,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1132,c_0_1122]),c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1399,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4) ),
    cls_inj__on__insert_0,
    [final] ).

cnf(i_0_1400,axiom,
    ( c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X4,X5) ),
    cls_inj__on__diff_0,
    [final] ).

cnf(i_0_1401,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1133,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1402,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),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_1134,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1403,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_card__Diff__singleton_0,
    [final] ).

cnf(i_0_1404,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)),X3) ),
    cls_finite__Diff__insert_0,
    [final] ).

cnf(i_0_1405,axiom,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X1,X5,X3,X4) ),
    cls_subset__inj__on_0,
    [final] ).

cnf(i_0_1406,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    cls_mod__diff__eq_0,
    [final] ).

cnf(i_0_1407,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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__add__eq_0,
    [final] ).

cnf(i_0_1408,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_1409,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1135,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1410,plain,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1136,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1411,axiom,
    ( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
    | ~ c_in(X1,X2,X3) ),
    cls_insert__Diff_0,
    [final] ).

cnf(i_0_1412,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_sum__squares__le__zero__iff_2,
    [final] ).

cnf(i_0_1413,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1137,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1414,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1138,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1415,axiom,
    c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
    cls_insert__Diff__single_0,
    [final] ).

cnf(i_0_1416,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Finite__Set_Ocard(X1,X3)
    | c_in(X2,X1,X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_card__Diff__singleton__if_1,
    [final] ).

cnf(i_0_1417,axiom,
    c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
    cls_rangeI_0,
    [final] ).

cnf(i_0_1418,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    cls_vimageI_0,
    [final] ).

cnf(i_0_1419,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    cls_vimageI2_0,
    [final] ).

cnf(i_0_1420,axiom,
    ( c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4)
    | ~ c_in(hAPP(X2,X1),X3,X5) ),
    cls_vimage__eq_1,
    [final] ).

cnf(i_0_1421,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X4,X1),X3,X1)
    | ~ class_Divides_Oring__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__diff__cong_0,
    [final] ).

cnf(i_0_1422,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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__add__cong_0,
    [final] ).

cnf(i_0_1423,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_1424,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4) ),
    cls_imageI_0,
    [final] ).

cnf(i_0_1425,axiom,
    ( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
    | ~ c_in(X2,X3,X4) ),
    cls_image__eqI_0,
    [final] ).

cnf(i_0_1426,axiom,
    ( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_in(X1,X2,X3) ),
    cls_image__iff_2,
    [final] ).

cnf(i_0_1427,axiom,
    ( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
    | ~ c_in(X1,X2,X3) ),
    cls_rev__image__eqI_0,
    [final] ).

cnf(i_0_1428,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_1429,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_1430,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),X4)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),X4) ),
    cls_finite__Diff__insert_1,
    [final] ).

cnf(i_0_1431,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1139,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1432,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_mult__mono_H_0,
    [final] ).

cnf(i_0_1433,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_mult__mono_0,
    [final] ).

cnf(i_0_1434,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_mult__less__le__imp__less_0,
    [final] ).

cnf(i_0_1435,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_mult__le__less__imp__less_0,
    [final] ).

cnf(i_0_1436,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_mult__strict__mono_H_0,
    [final] ).

cnf(i_0_1437,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_mult__strict__mono_0,
    [final] ).

cnf(i_0_1438,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    cls_le__diff__iff_0,
    [final] ).

cnf(i_0_1439,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    cls_less__diff__iff_0,
    [final] ).

cnf(i_0_1440,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Diff__mono_0,
    [final] ).

cnf(i_0_1441,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_Int__mono_0,
    [final] ).

cnf(i_0_1442,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
    cls_Diff__insert_0,
    [final] ).

cnf(i_0_1443,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
    cls_Diff__Int2_0,
    [final] ).

cnf(i_0_1444,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Diff__Int__distrib2_0,
    [final] ).

cnf(i_0_1445,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Diff__Int__distrib_0,
    [final] ).

cnf(i_0_1446,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5) ),
    cls_inj__onD_0,
    [final] ).

cnf(i_0_1447,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__def_0,
    [final] ).

cnf(i_0_1448,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__iff_0,
    [final] ).

cnf(i_0_1449,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_in(X3,X4,X5)
    | ~ c_in(X2,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
    cls_inj__on__contraD_0,
    [final] ).

cnf(i_0_1450,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),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_1451,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),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_1452,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_sum__squares__ge__zero_0,
    [final] ).

cnf(i_0_1453,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X4,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
    cls_nat__mod__eq__iff_1,
    [final] ).

cnf(i_0_1454,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1140,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1455,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1141,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1456,axiom,
    ( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
    cls_subset__singletonD_0,
    [final] ).

cnf(i_0_1457,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(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__le__cancel__left__pos_0,
    [final] ).

cnf(i_0_1458,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    cls_mult__right__le__imp__le_0,
    [final] ).

cnf(i_0_1459,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_mult__left__le__imp__le_0,
    [final] ).

cnf(i_0_1460,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    cls_mult__right__less__imp__less_0,
    [final] ).

cnf(i_0_1461,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_mult__left__less__imp__less_0,
    [final] ).

cnf(i_0_1462,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_1463,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    cls_mult__less__imp__less__right_0,
    [final] ).

cnf(i_0_1464,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_mult__less__imp__less__left_0,
    [final] ).

cnf(i_0_1465,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(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__le__cancel__left__neg_0,
    [final] ).

cnf(i_0_1466,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_1467,plain,
    ( hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
    | hBOOL(hAPP(X1,c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(rw,[status(thm)],[i_0_1142,c_0_1122]),
    [final] ).

cnf(i_0_1468,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
    cls_inf1E_0,
    [final] ).

cnf(i_0_1469,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
    cls_inf1E_1,
    [final] ).

cnf(i_0_1470,negated_conjecture,
    c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    cls_conjecture_1,
    [final] ).

cnf(i_0_1471,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    cls_mult__le__cancel2_0,
    [final] ).

cnf(i_0_1472,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(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__le__cancel1_0,
    [final] ).

cnf(i_0_1473,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    cls_mult__le__cancel1_0,
    [final] ).

cnf(i_0_1474,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_1475,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_1476,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_1477,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_1478,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_1479,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Onoteq__reduce_1,
    [final] ).

cnf(i_0_1480,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Oadd__mul__solve_1,
    [final] ).

cnf(i_0_1481,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_1482,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_1483,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_1484,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_1485,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I20_J_0,
    [final] ).

cnf(i_0_1486,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_1487,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_zmod__simps_I1_J_0,
    [final] ).

cnf(i_0_1488,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_1489,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_zmod__simps_I2_J_0,
    [final] ).

cnf(i_0_1490,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    cls_mod__diff__left__eq_0,
    [final] ).

cnf(i_0_1491,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__left__eq_0,
    [final] ).

cnf(i_0_1492,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_1493,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    cls_mod__diff__right__eq_0,
    [final] ).

cnf(i_0_1494,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__right__eq_0,
    [final] ).

cnf(i_0_1495,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_1496,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_1497,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_1498,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1143,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1499,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
    cls_doubleton__eq__iff_4,
    [final] ).

cnf(i_0_1500,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__imageI_0,
    [final] ).

cnf(i_0_1501,axiom,
    ( X4 = X5
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X5,X1),X1) ),
    cls_class__ringb_Oadd__scale__eq__noteq_0,
    [final] ).

cnf(i_0_1502,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    cls_natgb_Oadd__mul__solve_1,
    [final] ).

cnf(i_0_1503,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    cls_natgb_Onoteq__reduce_1,
    [final] ).

cnf(i_0_1504,axiom,
    ( X2 = X3
    | hAPP(X1,X2) != hAPP(X1,X3)
    | ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
    cls_injD_0,
    [final] ).

cnf(i_0_1505,plain,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    inference(rw,[status(thm)],[i_0_1144,c_0_1122]),
    [final] ).

cnf(i_0_1506,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X1,X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1145,c_0_1122]),
    [final] ).

cnf(i_0_1507,plain,
    ( X2 = X3
    | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) != c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1146,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1508,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_le__diff__iff_1,
    [final] ).

cnf(i_0_1509,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_less__diff__iff_1,
    [final] ).

cnf(i_0_1510,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X5,X4,X1)
    | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X5,X1),X1) ),
    cls_le__add__right__mono_0,
    [final] ).

cnf(i_0_1511,axiom,
    ( X3 = X4
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) ),
    cls_natgb_Oadd__scale__eq__noteq_0,
    [final] ).

cnf(i_0_1512,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3),
    cls_insert__inter__insert_0,
    [final] ).

cnf(i_0_1513,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))) ),
    cls_nat__diff__split_0,
    [final] ).

cnf(i_0_1514,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_1515,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_1516,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    cls_le__diff__conv2_0,
    [final] ).

cnf(i_0_1517,axiom,
    ( c_lessequals(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_le__diff__conv2_1,
    [final] ).

cnf(i_0_1518,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_psubset__insert__iff_7,
    [final] ).

cnf(i_0_1519,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
    cls_add__le__cancel__right_0,
    [final] ).

cnf(i_0_1520,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    cls_add__le__cancel__left_0,
    [final] ).

cnf(i_0_1521,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
    cls_add__less__cancel__right_0,
    [final] ).

cnf(i_0_1522,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    cls_add__less__cancel__left_0,
    [final] ).

cnf(i_0_1523,plain,
    ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1147,c_0_1122]),c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1524,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1148,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1525,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1149,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1526,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1150,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1527,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_Nat_Odiff__diff__eq_0,
    [final] ).

cnf(i_0_1528,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_in(X4,X1,X3)
    | c_in(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    cls_psubset__insert__iff_2,
    [final] ).

cnf(i_0_1529,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
    | ~ c_in(X1,X4,X3) ),
    cls_Int__insert__left_0,
    [final] ).

cnf(i_0_1530,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X2,X1,X4) ),
    cls_Int__insert__right_0,
    [final] ).

cnf(i_0_1531,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X3
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
    cls_double__diff_0,
    [final] ).

cnf(i_0_1532,axiom,
    ( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    cls_Int__greatest_0,
    [final] ).

cnf(i_0_1533,axiom,
    ( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    cls_Int__subset__iff_2,
    [final] ).

cnf(i_0_1534,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
    cls_dvd__diffD1_0,
    [final] ).

cnf(i_0_1535,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
    cls_dvd__diffD_0,
    [final] ).

cnf(i_0_1536,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_1537,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_1538,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_1539,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1151,c_0_1122]),
    [final] ).

cnf(i_0_1540,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    cls_nat__add__left__cancel__le_0,
    [final] ).

cnf(i_0_1541,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    cls_nat__add__left__cancel__less_0,
    [final] ).

cnf(i_0_1542,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_1543,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_1544,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),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_1152,c_0_1122]),
    [final] ).

cnf(i_0_1545,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Int__Diff_0,
    [final] ).

cnf(i_0_1546,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Int__assoc_0,
    [final] ).

cnf(i_0_1547,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Int__left__commute_0,
    [final] ).

cnf(i_0_1548,axiom,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X2,X3,X4,X1) ),
    cls_empty__is__image_0,
    [final] ).

cnf(i_0_1549,axiom,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
    cls_image__is__empty_0,
    [final] ).

cnf(i_0_1550,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Omult__mono1(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_mult__mono1_0,
    [final] ).

cnf(i_0_1551,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Omult__mono(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_mult__left__mono_0,
    [final] ).

cnf(i_0_1552,axiom,
    ( c_lessequals(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_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__le__cancel__left__pos_1,
    [final] ).

cnf(i_0_1553,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Omult__mono(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_mult__right__mono_0,
    [final] ).

cnf(i_0_1554,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_1555,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_1556,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_1557,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_1558,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_1559,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_1560,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X4,X3,X1) ),
    cls_mult__left__mono__neg_0,
    [final] ).

cnf(i_0_1561,axiom,
    ( c_lessequals(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_lessequals(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__cancel__left__neg_1,
    [final] ).

cnf(i_0_1562,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X4,X2,X1) ),
    cls_mult__right__mono__neg_0,
    [final] ).

cnf(i_0_1563,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_1564,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_1565,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_1566,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_1567,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_1568,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__right__le__one__le_0,
    [final] ).

cnf(i_0_1569,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_mult__left__le__one__le_0,
    [final] ).

cnf(i_0_1570,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_in(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    cls_psubset__insert__iff_0,
    [final] ).

cnf(i_0_1571,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2
    | c_in(X1,X2,X3) ),
    cls_Diff__insert__absorb_0,
    [final] ).

cnf(i_0_1572,axiom,
    ( c_lessequals(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_le__add__diff_0,
    [final] ).

cnf(i_0_1573,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_add__mono_0,
    [final] ).

cnf(i_0_1574,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_1575,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__less__le__mono_0,
    [final] ).

cnf(i_0_1576,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_add__le__less__mono_0,
    [final] ).

cnf(i_0_1577,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),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_1578,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
    | c_in(X1,X4,X3) ),
    cls_insert__Diff__if_1,
    [final] ).

cnf(i_0_1579,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_sum__squares__eq__zero__iff_0,
    [final] ).

cnf(i_0_1580,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_sum__squares__eq__zero__iff_1,
    [final] ).

cnf(i_0_1581,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Int__subset__iff_0,
    [final] ).

cnf(i_0_1582,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
    cls_Int__subset__iff_1,
    [final] ).

cnf(i_0_1583,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_1584,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I1_J_0,
    [final] ).

cnf(i_0_1585,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_1586,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
    cls_add__inf__distrib__right_0,
    [final] ).

cnf(i_0_1587,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,
    [final] ).

cnf(i_0_1588,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    cls_comm__semiring__class_Odistrib_0,
    [final] ).

cnf(i_0_1589,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I8_J_0,
    [final] ).

cnf(i_0_1590,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
    cls_add__inf__distrib__left_0,
    [final] ).

cnf(i_0_1591,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,
    [final] ).

cnf(i_0_1592,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__d_0,
    [final] ).

cnf(i_0_1593,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),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_1594,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),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_1595,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1153,c_0_1122]),
    [final] ).

cnf(i_0_1596,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__mult__le__cancel1_1,
    [final] ).

cnf(i_0_1597,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_1598,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_1599,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_1600,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_1601,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_1602,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_1603,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_mult__eq__if_1,
    [final] ).

cnf(i_0_1604,axiom,
    ( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(X1,X4)) ),
    cls_inf1I_0,
    [final] ).

cnf(i_0_1605,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X4,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_add__le__mono_0,
    [final] ).

cnf(i_0_1606,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X4,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_mult__le__mono_0,
    [final] ).

cnf(i_0_1607,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    cls_diff__less__mono2_0,
    [final] ).

cnf(i_0_1608,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_diff__less__mono_0,
    [final] ).

cnf(i_0_1609,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),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_1610,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_1611,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_1612,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_1613,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_in(X4,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    cls_subset__insert_0,
    [final] ).

cnf(i_0_1614,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_in(X4,X1,X3)
    | ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
    cls_subset__insert__iff_1,
    [final] ).

cnf(i_0_1615,axiom,
    ( X1 = X2
    | ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
    cls_singletonE_0,
    [final] ).

cnf(i_0_1616,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X2 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1154,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1617,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_1618,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    cls_diff__mult__distrib_0,
    [final] ).

cnf(i_0_1619,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    cls_add__mult__distrib_0,
    [final] ).

cnf(i_0_1620,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_1621,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    cls_diff__mult__distrib2_0,
    [final] ).

cnf(i_0_1622,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    cls_add__mult__distrib2_0,
    [final] ).

cnf(i_0_1623,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
    cls_mod__mult__self3_0,
    [final] ).

cnf(i_0_1624,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | c_in(X2,X3,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_psubset__insert__iff_3,
    [final] ).

cnf(i_0_1625,axiom,
    ( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(X2,X3),tc_nat)
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_card__Diff__subset_0,
    [final] ).

cnf(i_0_1626,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
    cls_insert__code_0,
    [final] ).

cnf(i_0_1627,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
    cls_insert__mono_0,
    [final] ).

cnf(i_0_1628,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
    cls_DiffE_1,
    [final] ).

cnf(i_0_1629,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1155,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1630,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X1,tc_nat) = X2
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    cls_le__imp__diff__is__add_1,
    [final] ).

cnf(i_0_1631,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    cls_le__diff__conv_1,
    [final] ).

cnf(i_0_1632,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
    cls_less__diff__conv_0,
    [final] ).

cnf(i_0_1633,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
    cls_le__diff__conv_0,
    [final] ).

cnf(i_0_1634,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
    cls_less__diff__conv_1,
    [final] ).

cnf(i_0_1635,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_1636,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_1637,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
    cls_add__cancel__21_0,
    [final] ).

cnf(i_0_1638,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    cls_diff__add__assoc2_0,
    [final] ).

cnf(i_0_1639,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_add__diff__assoc2_0,
    [final] ).

cnf(i_0_1640,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_diff__add__assoc_0,
    [final] ).

cnf(i_0_1641,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_diff__diff__right_0,
    [final] ).

cnf(i_0_1642,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_add__diff__assoc_0,
    [final] ).

cnf(i_0_1643,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    cls_insert__subset_2,
    [final] ).

cnf(i_0_1644,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_in(X2,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_psubset__insert__iff_6,
    [final] ).

cnf(i_0_1645,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__0__iff_1,
    [final] ).

cnf(i_0_1646,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__0__iff_0,
    [final] ).

cnf(i_0_1647,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__0__iff_3,
    [final] ).

cnf(i_0_1648,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    cls_zero__le__mult__iff_0,
    [final] ).

cnf(i_0_1649,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
    cls_zero__le__mult__iff_3,
    [final] ).

cnf(i_0_1650,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    cls_zero__le__mult__iff_2,
    [final] ).

cnf(i_0_1651,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
    cls_zero__le__mult__iff_1,
    [final] ).

cnf(i_0_1652,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__0__iff_2,
    [final] ).

cnf(i_0_1653,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X1,X3),c_Finite__Set_Ocard(X2,X3),tc_nat)
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_card__psubset_0,
    [final] ).

cnf(i_0_1654,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3) ),
    cls_DiffE_0,
    [final] ).

cnf(i_0_1655,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
    cls_IntE_0,
    [final] ).

cnf(i_0_1656,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) ),
    cls_IntE_1,
    [final] ).

cnf(i_0_1657,axiom,
    ( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    cls_IntI_0,
    [final] ).

cnf(i_0_1658,axiom,
    ( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    cls_Int__iff_2,
    [final] ).

cnf(i_0_1659,axiom,
    ( c_in(X1,c_Inductive_Ocomplete__lattice__class_Ogfp(X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_lessequals(X4,hAPP(X2,X4),tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    cls_weak__coinduct_0,
    [final] ).

cnf(i_0_1660,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1156,c_0_1122]),
    [final] ).

cnf(i_0_1661,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1157,c_0_1122]),
    [final] ).

cnf(i_0_1662,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1158,c_0_1122]),
    [final] ).

cnf(i_0_1663,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
    cls_insert__subset_1,
    [final] ).

cnf(i_0_1664,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1159,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1665,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_mult__nonneg__nonpos2_0,
    [final] ).

cnf(i_0_1666,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__nonpos__nonneg_0,
    [final] ).

cnf(i_0_1667,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_split__mult__neg__le_1,
    [final] ).

cnf(i_0_1668,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__nonneg__nonpos_0,
    [final] ).

cnf(i_0_1669,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_split__mult__neg__le_0,
    [final] ).

cnf(i_0_1670,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__0__iff_5,
    [final] ).

cnf(i_0_1671,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__le__0__iff_4,
    [final] ).

cnf(i_0_1672,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_1673,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_1674,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_1675,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__nonpos__nonpos_0,
    [final] ).

cnf(i_0_1676,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__neg__nonpos_0,
    [final] ).

cnf(i_0_1677,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),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_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__nonpos__neg_0,
    [final] ).

cnf(i_0_1678,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),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_1679,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__nonneg_0,
    [final] ).

cnf(i_0_1680,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__nonneg__nonneg_0,
    [final] ).

cnf(i_0_1681,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_split__mult__pos__le_0,
    [final] ).

cnf(i_0_1682,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_zero__le__mult__iff_4,
    [final] ).

cnf(i_0_1683,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_1684,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__pos__nonneg_0,
    [final] ).

cnf(i_0_1685,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__pos_0,
    [final] ).

cnf(i_0_1686,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),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_1687,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_1688,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_split__mult__pos__le_1,
    [final] ).

cnf(i_0_1689,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__nonpos__nonpos_0,
    [final] ).

cnf(i_0_1690,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_zero__le__mult__iff_5,
    [final] ).

cnf(i_0_1691,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_1692,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_lessequals(X3,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X1,X3),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1160,c_0_1122]),
    [final] ).

cnf(i_0_1693,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),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    cls_add__gr__0_0,
    [final] ).

cnf(i_0_1694,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
    cls_le__cube_0,
    [final] ).

cnf(i_0_1695,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_add__left__mono_0,
    [final] ).

cnf(i_0_1696,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_add__le__cancel__left_1,
    [final] ).

cnf(i_0_1697,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_add__right__mono_0,
    [final] ).

cnf(i_0_1698,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_add__le__cancel__right_1,
    [final] ).

cnf(i_0_1699,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_1700,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_1701,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),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_1702,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),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_1703,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),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_1704,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),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_1705,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert_1,
    [final] ).

cnf(i_0_1706,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4)
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insert__iff_2,
    [final] ).

cnf(i_0_1707,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_1708,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
    cls_add__increasing2_0,
    [final] ).

cnf(i_0_1709,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_add__increasing_0,
    [final] ).

cnf(i_0_1710,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_add__strict__increasing_0,
    [final] ).

cnf(i_0_1711,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_add__strict__increasing2_0,
    [final] ).

cnf(i_0_1712,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1161,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1713,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1162,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1714,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1163,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1715,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    cls_zero__induct__lemma_1,
    [final] ).

cnf(i_0_1716,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),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_1717,axiom,
    ( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    cls_DiffI_0,
    [final] ).

cnf(i_0_1718,axiom,
    ( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    cls_Diff__iff_2,
    [final] ).

cnf(i_0_1719,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    cls_insert__Diff1_0,
    [final] ).

cnf(i_0_1720,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
    cls_insert__subset_0,
    [final] ).

cnf(i_0_1721,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_diff__le__mono2_0,
    [final] ).

cnf(i_0_1722,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_diff__le__mono_0,
    [final] ).

cnf(i_0_1723,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    cls_nat__add__left__cancel__le_1,
    [final] ).

cnf(i_0_1724,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_add__le__mono1_0,
    [final] ).

cnf(i_0_1725,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    cls_mult__le__mono2_0,
    [final] ).

cnf(i_0_1726,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    cls_mult__le__cancel1_2,
    [final] ).

cnf(i_0_1727,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_mult__le__mono1_0,
    [final] ).

cnf(i_0_1728,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_mult__le__cancel2_2,
    [final] ).

cnf(i_0_1729,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_1730,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    cls_nat__add__left__cancel__less_1,
    [final] ).

cnf(i_0_1731,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_add__less__mono1_0,
    [final] ).

cnf(i_0_1732,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1164,c_0_1122]),c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1733,plain,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1165,c_0_1122]),
    [final] ).

cnf(i_0_1734,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I2_J_0,
    [final] ).

cnf(i_0_1735,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I3_J_0,
    [final] ).

cnf(i_0_1736,axiom,
    ( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2),tc_nat)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    cls_card__insert__le_0,
    [final] ).

cnf(i_0_1737,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_inf__greatest_0,
    [final] ).

cnf(i_0_1738,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__inf__iff_2,
    [final] ).

cnf(i_0_1739,axiom,
    ( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__infI_0,
    [final] ).

cnf(i_0_1740,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_1741,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_1742,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
    cls_dvd__diff_0,
    [final] ).

cnf(i_0_1743,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),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_1744,plain,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1166,c_0_1122]),
    [final] ).

cnf(i_0_1745,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1167,c_0_1122]),
    [final] ).

cnf(i_0_1746,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_1747,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_1748,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_1749,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_disjoint__iff__not__equal_0,
    [final] ).

cnf(i_0_1750,axiom,
    ( X1 = X3
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_eq__diff__iff_0,
    [final] ).

cnf(i_0_1751,axiom,
    ( X1 = X3
    | c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    cls_singleton__inject_0,
    [final] ).

cnf(i_0_1752,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(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_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_diff__less_0,
    [final] ).

cnf(i_0_1753,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
    cls_zero__le__double__add__iff__zero__le__single__add_0,
    [final] ).

cnf(i_0_1754,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),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
    cls_zero__less__double__add__iff__zero__less__single__add_0,
    [final] ).

cnf(i_0_1755,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__le__zero__iff__single__add__le__zero_0,
    [final] ).

cnf(i_0_1756,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(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_even__less__0__iff_0,
    [final] ).

cnf(i_0_1757,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(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__less__zero__iff__single__less__zero_0,
    [final] ).

cnf(i_0_1758,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),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_1168,c_0_1122]),
    [final] ).

cnf(i_0_1759,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I23_J_0,
    [final] ).

cnf(i_0_1760,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_1761,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I2_J_0,
    [final] ).

cnf(i_0_1762,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__assoc_0,
    [final] ).

cnf(i_0_1763,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
    [final] ).

cnf(i_0_1764,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__assoc_0,
    [final] ).

cnf(i_0_1765,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I21_J_0,
    [final] ).

cnf(i_0_1766,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_1767,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_1768,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I25_J_0,
    [final] ).

cnf(i_0_1769,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__a_0,
    [final] ).

cnf(i_0_1770,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_1771,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_1772,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I3_J_0,
    [final] ).

cnf(i_0_1773,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__left__commute_0,
    [final] ).

cnf(i_0_1774,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__left__commute_0,
    [final] ).

cnf(i_0_1775,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_add__cancel__21_1,
    [final] ).

cnf(i_0_1776,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I22_J_0,
    [final] ).

cnf(i_0_1777,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_1778,axiom,
    ( c_HOL_Oplus__class_Oplus(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) = 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_1779,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_1780,plain,
    ( hBOOL(hAPP(X1,X3))
    | hBOOL(hAPP(X1,X2))
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X1),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1169,c_0_1122]),
    [final] ).

cnf(i_0_1781,axiom,
    c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_image__empty_0,
    [final] ).

cnf(i_0_1782,axiom,
    c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
    cls_vimage__UNIV_0,
    [final] ).

cnf(i_0_1783,axiom,
    c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_vimage__empty_0,
    [final] ).

cnf(i_0_1784,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
    cls_empty__is__image_1,
    [final] ).

cnf(i_0_1785,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1170,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1786,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_le__iff__diff__le__0_1,
    [final] ).

cnf(i_0_1787,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_less__iff__diff__less__0_1,
    [final] ).

cnf(i_0_1788,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1171,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1789,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1172,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1790,plain,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
    inference(rw,[status(thm)],[i_0_1173,c_0_1122]),
    [final] ).

cnf(i_0_1791,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    cls_dvd__diff__nat_0,
    [final] ).

cnf(i_0_1792,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1174,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1793,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1175,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1794,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
    cls_insert__commute_0,
    [final] ).

cnf(i_0_1795,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_subset__trans_0,
    [final] ).

cnf(i_0_1796,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_psubset__subset__trans_0,
    [final] ).

cnf(i_0_1797,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_subset__psubset__trans_0,
    [final] ).

cnf(i_0_1798,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
    cls_psubset__trans_0,
    [final] ).

cnf(i_0_1799,axiom,
    ( c_lessequals(X3,X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X5,X4,X1) ),
    cls_le__eqI_1,
    [final] ).

cnf(i_0_1800,axiom,
    ( c_lessequals(X5,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_le__eqI_0,
    [final] ).

cnf(i_0_1801,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
    cls_less__eqI_1,
    [final] ).

cnf(i_0_1802,axiom,
    ( c_HOL_Oord__class_Oless(X4,X5,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_less__eqI_0,
    [final] ).

cnf(i_0_1803,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1176,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1804,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1177,c_0_1122]),
    [final] ).

cnf(i_0_1805,plain,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1178,c_0_1122]),
    [final] ).

cnf(i_0_1806,axiom,
    ( c_lessequals(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) ),
    cls_mult__le__cancel1_1,
    [final] ).

cnf(i_0_1807,axiom,
    ( c_lessequals(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) ),
    cls_mult__le__cancel2_1,
    [final] ).

cnf(i_0_1808,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool))
    | c_in(X1,X4,X3) ),
    cls_Int__insert__left_1,
    [final] ).

cnf(i_0_1809,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool))
    | c_in(X2,X1,X4) ),
    cls_Int__insert__right_1,
    [final] ).

cnf(i_0_1810,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_1811,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_1812,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    cls_le__inf__iff_0,
    [final] ).

cnf(i_0_1813,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
    cls_le__infE_0,
    [final] ).

cnf(i_0_1814,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    cls_le__inf__iff_1,
    [final] ).

cnf(i_0_1815,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
    cls_le__infE_1,
    [final] ).

cnf(i_0_1816,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X1) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
    | ~ class_Ring__and__Field_Oring__1(X1)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_of__nat__diff_0,
    [final] ).

cnf(i_0_1817,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
    cls_diff__cancel_0,
    [final] ).

cnf(i_0_1818,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
    cls_diff__cancel2_0,
    [final] ).

cnf(i_0_1819,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
    cls_diff__commute_0,
    [final] ).

cnf(i_0_1820,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    cls_diff__diff__left_0,
    [final] ).

cnf(i_0_1821,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    cls_nat__add__assoc_0,
    [final] ).

cnf(i_0_1822,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_1823,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
    cls_nat__add__left__commute_0,
    [final] ).

cnf(i_0_1824,axiom,
    ( X1 = X2
    | ~ c_lessequals(c_Finite__Set_Ocard(X2,X3),c_Finite__Set_Ocard(X1,X3),tc_nat)
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_card__seteq_0,
    [final] ).

cnf(i_0_1825,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1179,c_0_1122]),
    [final] ).

cnf(i_0_1826,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1180,c_0_1122]),
    [final] ).

cnf(i_0_1827,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1181,c_0_1122]),
    [final] ).

cnf(i_0_1828,axiom,
    ( c_in(X1,X2,X3)
    | X1 = X4
    | ~ c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
    cls_insertE_0,
    [final] ).

cnf(i_0_1829,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1182,c_0_1122]),
    [final] ).

cnf(i_0_1830,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1183,c_0_1122]),
    [final] ).

cnf(i_0_1831,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1184,c_0_1122]),
    [final] ).

cnf(i_0_1832,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1185,c_0_1122]),
    [final] ).

cnf(i_0_1833,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1186,c_0_1122]),
    [final] ).

cnf(i_0_1834,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_1835,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_1836,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_1837,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
    cls_Diff__idemp_0,
    [final] ).

cnf(i_0_1838,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
    cls_Int__left__absorb_0,
    [final] ).

cnf(i_0_1839,axiom,
    ( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    cls_subset__insertI2_0,
    [final] ).

cnf(i_0_1840,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_1841,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_1842,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    cls_zero__less__diff_0,
    [final] ).

cnf(i_0_1843,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1187,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1844,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    cls_less__add__eq__less_0,
    [final] ).

cnf(i_0_1845,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
    cls_add__leE_0,
    [final] ).

cnf(i_0_1846,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
    cls_add__leE_1,
    [final] ).

cnf(i_0_1847,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
    cls_add__lessD1_0,
    [final] ).

cnf(i_0_1848,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    cls_dvd__reduce_0,
    [final] ).

cnf(i_0_1849,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_1850,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_1851,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    cls_finite__Diff2_0,
    [final] ).

cnf(i_0_1852,axiom,
    c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
    cls_inj__on__empty_0,
    [final] ).

cnf(i_0_1853,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_1854,plain,
    ( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1188,c_0_1122]),c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1855,plain,
    ( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1189,c_0_1122]),c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1856,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__eq__0__iff_0,
    [final] ).

cnf(i_0_1857,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__eq__0__iff_1,
    [final] ).

cnf(i_0_1858,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_fun(X4,X1))
    | c_lessequals(X3,X2,tc_fun(X4,X1))
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X3,tc_fun(X4,X1)) ),
    cls_less__fun__def_2,
    [final] ).

cnf(i_0_1859,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_le__mod__geq_0,
    [final] ).

cnf(i_0_1860,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),tc_nat),
    cls_card__gt__0__iff_0,
    [final] ).

cnf(i_0_1861,axiom,
    ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    cls_insert__code_2,
    [final] ).

cnf(i_0_1862,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X1,X3)))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ c_lessequals(X2,X3,tc_nat) ),
    cls_inc__induct_2,
    [final] ).

cnf(i_0_1863,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1),tc_nat)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
    cls_finite__UNIV__card__ge__0_0,
    [final] ).

cnf(i_0_1864,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMax(X2,X1),c_Finite__Set_Olinorder__class_OMax(X3,X1),X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
    cls_Max__mono_0,
    [final] ).

cnf(i_0_1865,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X1),c_Finite__Set_Olinorder__class_OMin(X3,X1),X1)
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1)
    | ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
    cls_Min__antimono_0,
    [final] ).

cnf(i_0_1866,plain,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1190,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1867,axiom,
    ( c_in(X1,X4,X3)
    | c_in(X1,X2,X3)
    | X2 = X4
    | c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
    cls_insert__ident_0,
    [final] ).

cnf(i_0_1868,plain,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(X2,X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_in(X1,X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    inference(rw,[status(thm)],[i_0_1191,c_0_1122]),
    [final] ).

cnf(i_0_1869,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_1870,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_1871,plain,
    ( c_Finite__Set_Ocard(X2,X3) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(X2,X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_in(X1,X2,X3) ),
    inference(rw,[status(thm)],[i_0_1192,c_0_1122]),
    [final] ).

cnf(i_0_1872,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_1873,plain,
    c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1193,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1874,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_1875,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__le__zero__iff__single__add__le__zero_1,
    [final] ).

cnf(i_0_1876,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),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_1877,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),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_1878,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_zero__le__double__add__iff__zero__le__single__add_1,
    [final] ).

cnf(i_0_1879,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),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_1880,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1194,c_0_1122]),
    [final] ).

cnf(i_0_1881,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1195,c_0_1122]),
    [final] ).

cnf(i_0_1882,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(X3,X1),c_SetInterval_Oord__class_OatLeast(X2,X1),tc_fun(X1,tc_bool)) ),
    cls_atLeast__subset__iff_0,
    [final] ).

cnf(i_0_1883,axiom,
    c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
    cls_singleton__iff_1,
    [final] ).

cnf(i_0_1884,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    cls_set__mp_0,
    [final] ).

cnf(i_0_1885,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    cls_subsetD_0,
    [final] ).

cnf(i_0_1886,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    cls_set__rev__mp_0,
    [final] ).

cnf(i_0_1887,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
    cls_subset__iff_0,
    [final] ).

cnf(i_0_1888,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,tc_fun(X3,tc_bool)) ),
    cls_psubsetD_0,
    [final] ).

cnf(i_0_1889,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_mod__if_1,
    [final] ).

cnf(i_0_1890,axiom,
    ( ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X3,tc_fun(X4,X1))
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_fun(X4,X1)) ),
    cls_less__fun__def_1,
    [final] ).

cnf(i_0_1891,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__iff__diff__le__0_0,
    [final] ).

cnf(i_0_1892,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_less__iff__diff__less__0_0,
    [final] ).

cnf(i_0_1893,axiom,
    ( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
    cls_card__eq__UNIV__imp__eq__UNIV_0,
    [final] ).

cnf(i_0_1894,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_1895,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_Diff__disjoint_0,
    [final] ).

cnf(i_0_1896,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_1897,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(rw,[status(thm)],[i_0_1196,c_0_1122]),
    [final] ).

cnf(i_0_1898,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1197,c_0_1122]),
    [final] ).

cnf(i_0_1899,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(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_1198,c_0_1122]),
    [final] ).

cnf(i_0_1900,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__infI1_0,
    [final] ).

cnf(i_0_1901,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_le__infI2_0,
    [final] ).

cnf(i_0_1902,axiom,
    ( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_less__infI1_0,
    [final] ).

cnf(i_0_1903,axiom,
    ( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_less__infI2_0,
    [final] ).

cnf(i_0_1904,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_1905,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_1906,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_1907,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_1908,axiom,
    ( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    cls_card__mono_0,
    [final] ).

cnf(i_0_1909,axiom,
    ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    cls_psubset__card__mono_0,
    [final] ).

cnf(i_0_1910,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),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_1911,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),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_1912,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    cls_insertCI_0,
    [final] ).

cnf(i_0_1913,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    cls_insert__iff_2,
    [final] ).

cnf(i_0_1914,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I4_J_0,
    [final] ).

cnf(i_0_1915,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1199,c_0_1122]),
    [final] ).

cnf(i_0_1916,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1200,c_0_1122]),
    [final] ).

cnf(i_0_1917,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1201,c_0_1122]),
    [final] ).

cnf(i_0_1918,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ c_lessequals(X1,X1,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1202,c_0_1122]),
    [final] ).

cnf(i_0_1919,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1203,c_0_1122]),
    [final] ).

cnf(i_0_1920,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1204,c_0_1122]),
    [final] ).

cnf(i_0_1921,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    cls_not__add__less1_0,
    [final] ).

cnf(i_0_1922,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
    cls_not__add__less2_0,
    [final] ).

cnf(i_0_1923,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_equalityI_0,
    [final] ).

cnf(i_0_1924,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_set__eq__subset_2,
    [final] ).

cnf(i_0_1925,axiom,
    ( c_lessequals(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__le__divisor_0,
    [final] ).

cnf(i_0_1926,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_1927,axiom,
    ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Finite__Set_Ocard(X2,X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_card__insert__if_0,
    [final] ).

cnf(i_0_1928,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    cls_zero__less__diff_1,
    [final] ).

cnf(i_0_1929,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    cls_insert__code_1,
    [final] ).

cnf(i_0_1930,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_Diff__triv_0,
    [final] ).

cnf(i_0_1931,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_le__add__diff__inverse2_0,
    [final] ).

cnf(i_0_1932,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_diff__diff__cancel_0,
    [final] ).

cnf(i_0_1933,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__add__diff__inverse_0,
    [final] ).

cnf(i_0_1934,axiom,
    ( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__imp__diff__is__add_0,
    [final] ).

cnf(i_0_1935,axiom,
    ( hBOOL(hAPP(X1,X2))
    | c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(X1,X3),X3,tc_nat)
    | ~ hBOOL(hAPP(X1,X3))
    | ~ c_lessequals(X2,X3,tc_nat) ),
    cls_inc__induct_0,
    [final] ).

cnf(i_0_1936,axiom,
    ( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
    cls_le__funD_0,
    [final] ).

cnf(i_0_1937,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_less__imp__diff__less_0,
    [final] ).

cnf(i_0_1938,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_termination__basic__simps_I3_J_0,
    [final] ).

cnf(i_0_1939,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_trans__le__add1_0,
    [final] ).

cnf(i_0_1940,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_termination__basic__simps_I4_J_0,
    [final] ).

cnf(i_0_1941,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_trans__le__add2_0,
    [final] ).

cnf(i_0_1942,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    cls_dvd__reduce_1,
    [final] ).

cnf(i_0_1943,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_trans__less__add1_0,
    [final] ).

cnf(i_0_1944,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_termination__basic__simps_I1_J_0,
    [final] ).

cnf(i_0_1945,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_trans__less__add2_0,
    [final] ).

cnf(i_0_1946,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_termination__basic__simps_I2_J_0,
    [final] ).

cnf(i_0_1947,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1205,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1948,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1206,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1949,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(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_1207,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1950,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(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_1208,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1951,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(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_1209,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1952,plain,
    ( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(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_1210,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1953,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    cls_xt1_I6_J_0,
    [final] ).

cnf(i_0_1954,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_order__trans_0,
    [final] ).

cnf(i_0_1955,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_1956,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    cls_xt1_I8_J_0,
    [final] ).

cnf(i_0_1957,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    cls_xt1_I7_J_0,
    [final] ).

cnf(i_0_1958,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_1959,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_order__less__le__trans_0,
    [final] ).

cnf(i_0_1960,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_order__le__less__trans_0,
    [final] ).

cnf(i_0_1961,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_1962,axiom,
    ( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Min__singleton_0,
    [final] ).

cnf(i_0_1963,axiom,
    ( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Max__singleton_0,
    [final] ).

cnf(i_0_1964,plain,
    ( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,X3,X2),X2) = X3
    | c_Finite__Set_Ocard(X1,X2) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1211,c_0_1122]),
    [final] ).

cnf(i_0_1965,plain,
    ( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,X3,X2),X2) = X3
    | c_Finite__Set_Ocard(X1,X2) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1212,c_0_1122]),
    [final] ).

cnf(i_0_1966,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    cls_subset__empty_0,
    [final] ).

cnf(i_0_1967,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1) = c_HOL_Oplus__class_Oplus(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__add_0,
    [final] ).

cnf(i_0_1968,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_1969,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(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_1213,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1970,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(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_1214,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1971,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1215,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1972,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1216,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_1973,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    cls_Diff__subset_0,
    [final] ).

cnf(i_0_1974,axiom,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    cls_Int__lower1_0,
    [final] ).

cnf(i_0_1975,axiom,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    cls_Int__lower2_0,
    [final] ).

cnf(i_0_1976,axiom,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
    cls_of__nat__le__iff_0,
    [final] ).

cnf(i_0_1977,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_1978,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    cls_dvd__imp__le_0,
    [final] ).

cnf(i_0_1979,axiom,
    ( c_lessequals(c_SetInterval_Oord__class_OatLeast(X2,X1),c_SetInterval_Oord__class_OatLeast(X3,X1),tc_fun(X1,tc_bool))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_atLeast__subset__iff_1,
    [final] ).

cnf(i_0_1980,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_1981,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__self1_0,
    [final] ).

cnf(i_0_1982,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__self2_0,
    [final] ).

cnf(i_0_1983,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I4_J_0,
    [final] ).

cnf(i_0_1984,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__left__idem_0,
    [final] ).

cnf(i_0_1985,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_1986,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_le__trans_0,
    [final] ).

cnf(i_0_1987,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_1988,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(rw,[status(thm)],[i_0_1217,c_0_1122]),
    [final] ).

cnf(i_0_1989,plain,
    ( c_lessequals(X2,X1,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1218,c_0_1122]),
    [final] ).

cnf(i_0_1990,plain,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1219,c_0_1122]),
    [final] ).

cnf(i_0_1991,plain,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1220,c_0_1122]),
    [final] ).

cnf(i_0_1992,axiom,
    c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
    cls_insert__absorb2_0,
    [final] ).

cnf(i_0_1993,axiom,
    ( ~ hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    cls_bex__empty_0,
    [final] ).

cnf(i_0_1994,axiom,
    ( c_lessequals(X2,c_Inductive_Ocomplete__lattice__class_Ogfp(X3,X1),X1)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | ~ c_lessequals(X2,hAPP(X3,X2),X1) ),
    cls_gfp__upperbound_0,
    [final] ).

cnf(i_0_1995,axiom,
    ( c_lessequals(X2,X3,tc_fun(X4,X1))
    | ~ class_HOL_Oord(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_fun(X4,X1)) ),
    cls_less__fun__def_0,
    [final] ).

cnf(i_0_1996,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__Diff2_1,
    [final] ).

cnf(i_0_1997,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    cls_add__diff__inverse_0,
    [final] ).

cnf(i_0_1998,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    cls_bot1E_0,
    [final] ).

cnf(i_0_1999,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
    cls_finite__insert_0,
    [final] ).

cnf(i_0_2000,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    cls_not__psubset__empty_0,
    [final] ).

cnf(i_0_2001,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_less__le__not__le_2,
    [final] ).

cnf(i_0_2002,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_psubset__eq_2,
    [final] ).

cnf(i_0_2003,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_subset__iff__psubset__eq_0,
    [final] ).

cnf(i_0_2004,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
    | ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_Int__absorb2_0,
    [final] ).

cnf(i_0_2005,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X2
    | ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
    cls_Int__absorb1_0,
    [final] ).

cnf(i_0_2006,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X3,X2))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
    cls_predicate1D_0,
    [final] ).

cnf(i_0_2007,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
    | ~ hBOOL(hAPP(X3,X2)) ),
    cls_rev__predicate1D_0,
    [final] ).

cnf(i_0_2008,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_2009,axiom,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
    cls_psubset__eq_0,
    [final] ).

cnf(i_0_2010,plain,
    ( c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1221,c_0_1122]),
    [final] ).

cnf(i_0_2011,plain,
    ( c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1222,c_0_1122]),
    [final] ).

cnf(i_0_2012,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_zero__less__two_0,
    [final] ).

cnf(i_0_2013,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    cls_ball__empty_0,
    [final] ).

cnf(i_0_2014,axiom,
    ( c_lessequals(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_lessequals(X2,X3,tc_nat) ),
    cls_of__nat__le__iff_1,
    [final] ).

cnf(i_0_2015,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_2016,axiom,
    ( c_lessequals(c_Finite__Set_Olinorder__class_OMin(X2,X1),X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_in(X3,X2,X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_Min__le_0,
    [final] ).

cnf(i_0_2017,axiom,
    ( c_lessequals(X2,c_Finite__Set_Olinorder__class_OMax(X3,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_in(X2,X3,X1)
    | ~ c_Finite__Set_Ofinite(X3,X1) ),
    cls_Max__ge_0,
    [final] ).

cnf(i_0_2018,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_2019,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_finite__Diff_0,
    [final] ).

cnf(i_0_2020,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X1,X3) ),
    cls_finite__Int_0,
    [final] ).

cnf(i_0_2021,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__Int_1,
    [final] ).

cnf(i_0_2022,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_in(X3,c_SetInterval_Oord__class_OatLeast(X2,X1),X1) ),
    cls_atLeast__iff_0,
    [final] ).

cnf(i_0_2023,axiom,
    ( X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    cls_class__ringb_Oadd__cancel_0,
    [final] ).

cnf(i_0_2024,axiom,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    cls_subset__insertI_0,
    [final] ).

cnf(i_0_2025,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_1223,c_0_1122]),
    [final] ).

cnf(i_0_2026,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_1224,c_0_1122]),
    [final] ).

cnf(i_0_2027,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(cn,[status(thm)],[i_0_1225]),
    [final] ).

cnf(i_0_2028,axiom,
    ( c_in(X1,X2,X3)
    | c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_comm__monoid__add_Ononempty__iff_2,
    [final] ).

cnf(i_0_2029,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_2030,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__eq__iff_2,
    [final] ).

cnf(i_0_2031,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__antisym_0,
    [final] ).

cnf(i_0_2032,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_order__antisym__conv_0,
    [final] ).

cnf(i_0_2033,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
    cls_subset__empty_1,
    [final] ).

cnf(i_0_2034,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_less__add__one_0,
    [final] ).

cnf(i_0_2035,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
    cls_eq__eqI_1,
    [final] ).

cnf(i_0_2036,axiom,
    ( X2 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
    cls_add__right__cancel_0,
    [final] ).

cnf(i_0_2037,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
    cls_eq__eqI_0,
    [final] ).

cnf(i_0_2038,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    cls_add__left__cancel_0,
    [final] ).

cnf(i_0_2039,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    cls_add__imp__eq_0,
    [final] ).

cnf(i_0_2040,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__antisym__conv2_1,
    [final] ).

cnf(i_0_2041,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_linorder__not__less_1,
    [final] ).

cnf(i_0_2042,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_linorder__not__le_1,
    [final] ).

cnf(i_0_2043,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_2044,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_2045,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_less__le__not__le_1,
    [final] ).

cnf(i_0_2046,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_2047,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_2048,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1226,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_2049,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1227,c_0_1122]),c_0_1122]),
    [final] ).

cnf(i_0_2050,axiom,
    ( X2 = X1
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_diffs0__imp__equal_0,
    [final] ).

cnf(i_0_2051,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_zero__le__square_0,
    [final] ).

cnf(i_0_2052,axiom,
    ( c_in(X2,c_SetInterval_Oord__class_OatLeast(X3,X1),X1)
    | ~ class_HOL_Oord(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_atLeast__iff_1,
    [final] ).

cnf(i_0_2053,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_2054,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_2055,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_2056,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_2057,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_2058,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1228,c_0_1122]),
    [final] ).

cnf(i_0_2059,plain,
    c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rw,[status(thm)],[i_0_1229,c_0_1122]),
    [final] ).

cnf(i_0_2060,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__antisym_0,
    [final] ).

cnf(i_0_2061,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_2062,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_2063,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_2064,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_2065,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_2066,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_2067,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_2068,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_add__diff__cancel_0,
    [final] ).

cnf(i_0_2069,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_diff__add__cancel_0,
    [final] ).

cnf(i_0_2070,plain,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(rw,[status(thm)],[i_0_1230,c_0_1122]),
    [final] ).

cnf(i_0_2071,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I1_J_0,
    [final] ).

cnf(i_0_2072,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__le1_0,
    [final] ).

cnf(i_0_2073,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__ord_I2_J_0,
    [final] ).

cnf(i_0_2074,axiom,
    ( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__le2_0,
    [final] ).

cnf(i_0_2075,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_2076,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_2077,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_2078,axiom,
    ( X1 = X3
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    cls_nat__add__right__cancel_0,
    [final] ).

cnf(i_0_2079,axiom,
    ( X2 = X3
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) ),
    cls_nat__add__left__cancel_0,
    [final] ).

cnf(i_0_2080,axiom,
    ( X2 = X3
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) ),
    cls_natgb_Oadd__cancel_0,
    [final] ).

cnf(i_0_2081,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_emptyE_0,
    [final] ).

cnf(i_0_2082,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_empty__iff_0,
    [final] ).

cnf(i_0_2083,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_ex__in__conv_0,
    [final] ).

cnf(i_0_2084,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    inference(rw,[status(thm)],[i_0_1231,c_0_1122]),
    [final] ).

cnf(i_0_2085,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1232,c_0_1122]),
    [final] ).

cnf(i_0_2086,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1233,c_0_1122]),
    [final] ).

cnf(i_0_2087,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1234,c_0_1122]),
    [final] ).

cnf(i_0_2088,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1235,c_0_1122]),
    [final] ).

cnf(i_0_2089,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    cls_insertCI_1,
    [final] ).

cnf(i_0_2090,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    cls_insertI1_0,
    [final] ).

cnf(i_0_2091,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    cls_insert__iff_1,
    [final] ).

cnf(i_0_2092,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Finite__Set_Ofinite(X3,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
    cls_finite__subset_0,
    [final] ).

cnf(i_0_2093,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X2) ),
    cls_rev__finite__subset_0,
    [final] ).

cnf(i_0_2094,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_2095,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_diff__add__0_0,
    [final] ).

cnf(i_0_2096,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
    cls_diff__add__inverse_0,
    [final] ).

cnf(i_0_2097,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
    cls_diff__add__inverse2_0,
    [final] ).

cnf(i_0_2098,axiom,
    c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
    cls_mod__less__eq__dividend_0,
    [final] ).

cnf(i_0_2099,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
    cls_diff__le__self_0,
    [final] ).

cnf(i_0_2100,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    cls_le__add1_0,
    [final] ).

cnf(i_0_2101,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    cls_le__iff__add_1,
    [final] ).

cnf(i_0_2102,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    cls_le__add2_0,
    [final] ).

cnf(i_0_2103,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
    cls_le__square_0,
    [final] ).

cnf(i_0_2104,axiom,
    c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_empty__Diff_0,
    [final] ).

cnf(i_0_2105,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_Int__empty__left_0,
    [final] ).

cnf(i_0_2106,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Diff__UNIV_0,
    [final] ).

cnf(i_0_2107,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Int__empty__right_0,
    [final] ).

cnf(i_0_2108,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
    cls_Int__commute_0,
    [final] ).

cnf(i_0_2109,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_2110,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_2111,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_linorder__antisym__conv1_0,
    [final] ).

cnf(i_0_2112,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_linorder__antisym__conv2_0,
    [final] ).

cnf(i_0_2113,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_xt1_I11_J_0,
    [final] ).

cnf(i_0_2114,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_xt1_I12_J_0,
    [final] ).

cnf(i_0_2115,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__le__less_0,
    [final] ).

cnf(i_0_2116,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__less__le_2,
    [final] ).

cnf(i_0_2117,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__le__neq__trans_0,
    [final] ).

cnf(i_0_2118,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__neq__le__trans_0,
    [final] ).

cnf(i_0_2119,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
    cls_le__iff__inf_1,
    [final] ).

cnf(i_0_2120,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__iff__inf_0,
    [final] ).

cnf(i_0_2121,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_inf__absorb2_0,
    [final] ).

cnf(i_0_2122,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_order__le__less_1,
    [final] ).

cnf(i_0_2123,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_order__less__imp__le_0,
    [final] ).

cnf(i_0_2124,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
    | ~ c_Finite__Set_Ofinite(X2,X3) ),
    cls_finite__insert_1,
    [final] ).

cnf(i_0_2125,axiom,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat) ),
    cls_card__gt__0__iff_1,
    [final] ).

cnf(i_0_2126,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_2127,axiom,
    ( c_Set_Oinsert(X1,X2,X3) = X2
    | ~ c_in(X1,X2,X3) ),
    cls_insert__absorb_0,
    [final] ).

cnf(i_0_2128,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_diff__is__0__eq_0,
    [final] ).

cnf(i_0_2129,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_nat__less__le_2,
    [final] ).

cnf(i_0_2130,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__eq__less__or__eq_0,
    [final] ).

cnf(i_0_2131,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__neq__implies__less_0,
    [final] ).

cnf(i_0_2132,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_diff__is__0__eq_1,
    [final] ).

cnf(i_0_2133,axiom,
    ( c_in(c_Finite__Set_Olinorder__class_OMin(X2,X1),X2,X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_Min__in_0,
    [final] ).

cnf(i_0_2134,axiom,
    ( c_in(c_Finite__Set_Olinorder__class_OMax(X2,X1),X2,X1)
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Finite__Set_Ofinite(X2,X1) ),
    cls_Max__in_0,
    [final] ).

cnf(i_0_2135,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_2136,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_termination__basic__simps_I5_J_0,
    [final] ).

cnf(i_0_2137,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_nat__less__le_0,
    [final] ).

cnf(i_0_2138,axiom,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
    cls_top1I_0,
    [final] ).

cnf(i_0_2139,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(X1,X2),tc_nat)
    | X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    cls_card__gt__0__iff_2,
    [final] ).

cnf(i_0_2140,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
    cls_Int__UNIV__left_0,
    [final] ).

cnf(i_0_2141,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    cls_Diff__empty_0,
    [final] ).

cnf(i_0_2142,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    cls_Int__UNIV__right_0,
    [final] ).

cnf(i_0_2143,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
    cls_empty__subsetI_0,
    [final] ).

cnf(i_0_2144,axiom,
    c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    cls_subset__UNIV_0,
    [final] ).

cnf(i_0_2145,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
    cls_empty__not__insert_0,
    [final] ).

cnf(i_0_2146,axiom,
    c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    cls_insert__not__empty_0,
    [final] ).

cnf(i_0_2147,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
    cls_psubset__eq_1,
    [final] ).

cnf(i_0_2148,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_2149,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_2150,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_2151,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_2152,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_2153,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__linear_0,
    [final] ).

cnf(i_0_2154,axiom,
    ( c_HOL_Oord__class_Oless(X2,X2,X1)
    | c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__antisym__conv1_1,
    [final] ).

cnf(i_0_2155,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__not__le_0,
    [final] ).

cnf(i_0_2156,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_not__leE_0,
    [final] ).

cnf(i_0_2157,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__not__less_0,
    [final] ).

cnf(i_0_2158,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,X1,X3) ),
    cls_mem__def_0,
    [final] ).

cnf(i_0_2159,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I1_J_0,
    [final] ).

cnf(i_0_2160,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__commute_0,
    [final] ).

cnf(i_0_2161,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__commute_0,
    [final] ).

cnf(i_0_2162,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__c_0,
    [final] ).

cnf(i_0_2163,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I24_J_0,
    [final] ).

cnf(i_0_2164,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_2165,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_2166,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_not__one__le__zero_0,
    [final] ).

cnf(i_0_2167,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_2168,negated_conjecture,
    ~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
    cls_conjecture_5,
    [final] ).

cnf(i_0_2169,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_2170,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
    inference(rw,[status(thm)],[i_0_1236,c_0_1122]),
    [final] ).

cnf(i_0_2171,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_2172,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_2173,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_2174,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_2175,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_2176,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_2177,axiom,
    ( X2 = X3
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_class__ringb_Osubr0__iff_0,
    [final] ).

cnf(i_0_2178,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_2179,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
    cls_class__ringb_Oadd__r0__iff_0,
    [final] ).

cnf(i_0_2180,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    cls_nat__le__linear_0,
    [final] ).

cnf(i_0_2181,axiom,
    c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),
    cls_UNIV__I_0,
    [final] ).

cnf(i_0_2182,axiom,
    c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
    cls_nat__add__commute_0,
    [final] ).

cnf(i_0_2183,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_2184,axiom,
    ( X2 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    cls_inf__eq__top__eq1_0,
    [final] ).

cnf(i_0_2185,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_double__eq__0__iff_0,
    [final] ).

cnf(i_0_2186,axiom,
    ( X3 = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice(X1)
    | c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
    cls_inf__eq__top__eq2_0,
    [final] ).

cnf(i_0_2187,axiom,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_Diff__cancel_0,
    [final] ).

cnf(i_0_2188,axiom,
    ( c_in(X1,X2,X3)
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_mem__def_1,
    [final] ).

cnf(i_0_2189,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_right__minus__eq_0,
    [final] ).

cnf(i_0_2190,axiom,
    ( X2 = X3
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_eq__iff__diff__eq__0_1,
    [final] ).

cnf(i_0_2191,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(X1))) ),
    cls_full__nat__induct_1,
    [final] ).

cnf(i_0_2192,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_2193,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_zero__le__imp__of__nat_0,
    [final] ).

cnf(i_0_2194,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_of__nat__0__le__iff_0,
    [final] ).

cnf(i_0_2195,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__neq__iff_1,
    [final] ).

cnf(i_0_2196,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__le_1,
    [final] ).

cnf(i_0_2197,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__irrefl_0,
    [final] ).

cnf(i_0_2198,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_2199,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_2200,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_2201,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    cls_le__0__eq_0,
    [final] ).

cnf(i_0_2202,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rw,[status(thm)],[i_0_1237,c_0_1122]),
    [final] ).

cnf(i_0_2203,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rw,[status(thm)],[i_0_1238,c_0_1122]),
    [final] ).

cnf(i_0_2204,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1239,c_0_1122]),
    [final] ).

cnf(i_0_2205,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1240,c_0_1122]),
    [final] ).

cnf(i_0_2206,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_2207,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_add__is__0_0,
    [final] ).

cnf(i_0_2208,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_2209,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_add__is__0_1,
    [final] ).

cnf(i_0_2210,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_2211,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_2212,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(rw,[status(thm)],[i_0_1241,c_0_1122]),
    [final] ).

cnf(i_0_2213,plain,
    X1 != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1242,c_0_1122]),
    [final] ).

cnf(i_0_2214,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != X1 ),
    cls_add__eq__self__zero_0,
    [final] ).

cnf(i_0_2215,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    cls_natgb_Oadd__r0__iff_0,
    [final] ).

cnf(i_0_2216,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_not__less0_0,
    [final] ).

cnf(i_0_2217,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_2218,axiom,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0,
    [final] ).

cnf(i_0_2219,axiom,
    c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
    cls_UNIV__not__empty_0,
    [final] ).

cnf(i_0_2220,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_less__not__refl_0,
    [final] ).

cnf(i_0_2221,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_nat__less__le_1,
    [final] ).

cnf(i_0_2222,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
    cls_Int__absorb_0,
    [final] ).

cnf(i_0_2223,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_double__eq__0__iff_1,
    [final] ).

cnf(i_0_2224,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_equalityE_0,
    [final] ).

cnf(i_0_2225,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_subset__refl_0,
    [final] ).

cnf(i_0_2226,axiom,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Finite__Set_Ofinite(X1,X2) ),
    cls_card__eq__0__iff_0,
    [final] ).

cnf(i_0_2227,axiom,
    ( X2 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Oadd__r0__iff_1,
    [final] ).

cnf(i_0_2228,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_zero__le__one_0,
    [final] ).

cnf(i_0_2229,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_2230,axiom,
    ( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    cls_finite__UNIV_0,
    [final] ).

cnf(i_0_2231,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Osubr0__iff_1,
    [final] ).

cnf(i_0_2232,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_2233,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__bot__left_0,
    [final] ).

cnf(i_0_2234,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_2235,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_2236,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_2237,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_2238,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_2239,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Obot__class_Obot(X1)
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__bot__right_0,
    [final] ).

cnf(i_0_2240,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_2241,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_2242,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_2243,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__top__left_0,
    [final] ).

cnf(i_0_2244,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_add__0__left_0,
    [final] ).

cnf(i_0_2245,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__1_0,
    [final] ).

cnf(i_0_2246,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I5_J_0,
    [final] ).

cnf(i_0_2247,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__0_0,
    [final] ).

cnf(i_0_2248,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_2249,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_2250,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_2251,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_2252,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_2253,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_diff__0__right_0,
    [final] ).

cnf(i_0_2254,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(X1),X1) = X2
    | ~ class_Lattices_Obounded__lattice(X1) ),
    cls_inf__top__right_0,
    [final] ).

cnf(i_0_2255,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_monoid__add__class_Oadd__0__right_0,
    [final] ).

cnf(i_0_2256,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__1__right_0,
    [final] ).

cnf(i_0_2257,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I6_J_0,
    [final] ).

cnf(i_0_2258,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_2259,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_2260,axiom,
    c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_card__empty_0,
    [final] ).

cnf(i_0_2261,axiom,
    ( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
    | ~ class_Orderings_Obot(X1) ),
    cls_bot__least_0,
    [final] ).

cnf(i_0_2262,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_2263,axiom,
    ( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
    | ~ class_Orderings_Otop(X1) ),
    cls_top__greatest_0,
    [final] ).

cnf(i_0_2264,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_2265,axiom,
    c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
    cls_finite_OemptyI_0,
    [final] ).

cnf(i_0_2266,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_2267,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_right__minus__eq_1,
    [final] ).

cnf(i_0_2268,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_diff__self_0,
    [final] ).

cnf(i_0_2269,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_eq__iff__diff__eq__0_0,
    [final] ).

cnf(i_0_2270,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__idem_0,
    [final] ).

cnf(i_0_2271,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_2272,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_order__eq__iff_0,
    [final] ).

cnf(i_0_2273,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    cls_order__eq__refl_0,
    [final] ).

cnf(i_0_2274,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_2275,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_add__is__0_2,
    [final] ).

cnf(i_0_2276,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_2277,plain,
    c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_1243,c_0_1122]),
    [final] ).

cnf(i_0_2278,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_2279,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_2280,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_le__0__eq_1,
    [final] ).

cnf(i_0_2281,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_2282,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_diff__0__eq__0_0,
    [final] ).

cnf(i_0_2283,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_2284,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_2285,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    cls_plus__nat_Oadd__0_0,
    [final] ).

cnf(i_0_2286,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_2287,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    cls_minus__nat_Odiff__0_0,
    [final] ).

cnf(i_0_2288,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    cls_Nat_Oadd__0__right_0,
    [final] ).

cnf(i_0_2289,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_2290,axiom,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_natgb_Oadd__r0__iff_1,
    [final] ).

cnf(i_0_2291,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    cls_le0_0,
    [final] ).

cnf(i_0_2292,axiom,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_diff__self__eq__0_0,
    [final] ).

cnf(i_0_2293,axiom,
    c_fequal(X1,X1,X2),
    cls_ATP__Linkup_Oequal__imp__fequal_0,
    [final] ).

cnf(i_0_2294,axiom,
    ( X2 = X3
    | ~ class_Orderings_Olinorder(X1)
    | c_SetInterval_Oord__class_OatLeast(X2,X1) != c_SetInterval_Oord__class_OatLeast(X3,X1) ),
    cls_atLeast__eq__iff_0,
    [final] ).

cnf(i_0_2295,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_2296,axiom,
    c_lessequals(X1,X1,tc_nat),
    cls_le__refl_0,
    [final] ).

cnf(i_0_2297,axiom,
    c_lessequals(X1,X1,tc_nat),
    cls_eq__imp__le_0,
    [final] ).

cnf(i_0_2298,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
    cls_dvd_Oeq__iff_0,
    [final] ).

cnf(i_0_2299,negated_conjecture,
    c_in(v_pn,v_U,tc_Com_Opname),
    cls_conjecture_4,
    [final] ).

cnf(i_0_2300,axiom,
    ( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    clsarity_fun__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_2301,axiom,
    ( class_HOL_Oord(tc_fun(X1,X2))
    | ~ class_HOL_Oord(X2) ),
    clsarity_fun__HOL_Oord,
    [final] ).

cnf(i_0_2302,axiom,
    ( class_Orderings_Obot(tc_fun(X1,X2))
    | ~ class_Orderings_Obot(X2) ),
    clsarity_fun__Orderings_Obot,
    [final] ).

cnf(i_0_2303,axiom,
    ( class_Orderings_Otop(tc_fun(X1,X2))
    | ~ class_Orderings_Otop(X2) ),
    clsarity_fun__Orderings_Otop,
    [final] ).

cnf(i_0_2304,axiom,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
    clsarity_fun__Complete__Lattice_Ocomplete__lattice,
    [final] ).

cnf(i_0_2305,axiom,
    ( class_Lattices_Olattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olattice,
    [final] ).

cnf(i_0_2306,axiom,
    ( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_2307,axiom,
    ( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
    | ~ class_Lattices_Obounded__lattice(X2) ),
    clsarity_fun__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_2308,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_2309,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_2310,axiom,
    ( c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Finite__Set_Ofinite(X1,X2) ),
    cls_card__eq__0__iff_2,
    [final] ).

cnf(i_0_2311,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_2312,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_2313,axiom,
    ( c_Finite__Set_Ofinite(X2,X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    cls_finite_0,
    [final] ).

cnf(i_0_2314,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_2315,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_2316,negated_conjecture,
    c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
    cls_conjecture_0,
    [final] ).

cnf(i_0_2317,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring,
    [final] ).

cnf(i_0_2318,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__mult,
    [final] ).

cnf(i_0_2319,axiom,
    class_HOL_Oord(tc_bool),
    clsarity_bool__HOL_Oord,
    [final] ).

cnf(i_0_2320,axiom,
    class_HOL_Oord(tc_nat),
    clsarity_nat__HOL_Oord,
    [final] ).

cnf(i_0_2321,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    clsarity_bool__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_2322,axiom,
    class_Orderings_Obot(tc_bool),
    clsarity_bool__Orderings_Obot,
    [final] ).

cnf(i_0_2323,axiom,
    class_Orderings_Obot(tc_nat),
    clsarity_nat__Orderings_Obot,
    [final] ).

cnf(i_0_2324,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    clsarity_nat__Ring__and__Field_Omult__mono1,
    [final] ).

cnf(i_0_2325,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    clsarity_nat__Ring__and__Field_Omult__mono,
    [final] ).

cnf(i_0_2326,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,
    [final] ).

cnf(i_0_2327,axiom,
    class_Orderings_Otop(tc_bool),
    clsarity_bool__Orderings_Otop,
    [final] ).

cnf(i_0_2328,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    clsarity_bool__Complete__Lattice_Ocomplete__lattice,
    [final] ).

cnf(i_0_2329,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
    [final] ).

cnf(i_0_2330,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__add,
    [final] ).

cnf(i_0_2331,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    clsarity_nat__Ring__and__Field_Opordered__semiring,
    [final] ).

cnf(i_0_2332,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    clsarity_nat__Ring__and__Field_Omult__zero,
    [final] ).

cnf(i_0_2333,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    clsarity_nat__Ring__and__Field_Ono__zero__divisors,
    [final] ).

cnf(i_0_2334,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,
    [final] ).

cnf(i_0_2335,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semidom,
    [final] ).

cnf(i_0_2336,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
    [final] ).

cnf(i_0_2337,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
    [final] ).

cnf(i_0_2338,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,
    [final] ).

cnf(i_0_2339,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    clsarity_nat__Ring__and__Field_Osemiring,
    [final] ).

cnf(i_0_2340,axiom,
    class_Lattices_Olattice(tc_bool),
    clsarity_bool__Lattices_Olattice,
    [final] ).

cnf(i_0_2341,axiom,
    class_Lattices_Olattice(tc_nat),
    clsarity_nat__Lattices_Olattice,
    [final] ).

cnf(i_0_2342,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    clsarity_bool__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_2343,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    clsarity_nat__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_2344,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_2345,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semiring,
    [final] ).

cnf(i_0_2346,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    clsarity_nat__Nat_Osemiring__char__0,
    [final] ).

cnf(i_0_2347,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    clsarity_bool__Lattices_Obounded__lattice,
    [final] ).

cnf(i_0_2348,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semiring__strict,
    [final] ).

cnf(i_0_2349,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__mult,
    [final] ).

cnf(i_0_2350,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__mult,
    [final] ).

cnf(i_0_2351,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    clsarity_nat__Ring__and__Field_Odvd,
    [final] ).

cnf(i_0_2352,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    clsarity_nat__Ring__and__Field_Ozero__neq__one,
    [final] ).

cnf(i_0_2353,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Osemiring__1,
    [final] ).

cnf(i_0_2354,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    [final] ).

cnf(i_0_2355,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__add,
    [final] ).

cnf(i_0_2356,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__add,
    [final] ).

cnf(i_0_2357,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_2358,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_2359,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_2360,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_2361,axiom,
    class_Divides_Osemiring__div(tc_nat),
    clsarity_nat__Divides_Osemiring__div,
    [final] ).

cnf(i_0_2362,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
    [final] ).

cnf(i_0_2363,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
    [final] ).

cnf(i_0_2364,axiom,
    X1 = X1 ).

cnf(i_0_2365,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_2366,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_2367,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_2368,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_2369,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_2370,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_2371,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_2372,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).

cnf(i_0_2373,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).

cnf(i_0_2374,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).

cnf(i_0_2375,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).

cnf(i_0_2376,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).

cnf(i_0_2377,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_2378,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_2379,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_2380,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_2381,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_2382,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_2383,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_2384,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).

cnf(i_0_2385,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).

cnf(i_0_2386,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).

cnf(i_0_2387,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_2388,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_2389,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_2390,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_2391,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_2392,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_2393,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_2394,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_2395,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_2396,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_2397,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_2398,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_2399,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_2400,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_2401,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeast(X1,X3) = c_SetInterval_Oord__class_OatLeast(X2,X3) ) ).

cnf(i_0_2402,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeast(X3,X1) = c_SetInterval_Oord__class_OatLeast(X3,X2) ) ).

cnf(i_0_2403,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,X3,X4) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X2,X3,X4) ) ).

cnf(i_0_2404,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X3,X1,X4) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X3,X2,X4) ) ).

cnf(i_0_2405,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X3,X4,X1) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X3,X4,X2) ) ).

cnf(i_0_2406,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,X3,X4) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X2,X3,X4) ) ).

cnf(i_0_2407,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X3,X1,X4) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X3,X2,X4) ) ).

cnf(i_0_2408,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X3,X4,X1) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X3,X4,X2) ) ).

cnf(i_0_2409,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).

cnf(i_0_2410,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).

cnf(i_0_2411,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).

cnf(i_0_2412,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).

cnf(i_0_2413,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).

cnf(i_0_2414,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_2415,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_2416,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_2417,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_2418,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_2419,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_2420,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_2421,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_2422,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_2423,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Ocomm__ring(X2) ) ).

cnf(i_0_2424,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oordered__ring__strict(X2) ) ).

cnf(i_0_2425,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Oring(X2) ) ).

cnf(i_0_2426,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_2427,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring(X1)
    | class_Ring__and__Field_Osemiring(X2) ) ).

cnf(i_0_2428,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_2429,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_2430,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_2431,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_2432,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_2433,axiom,
    ( X1 != X2
    | ~ c_in(X1,X3,X4)
    | c_in(X2,X3,X4) ) ).

cnf(i_0_2434,axiom,
    ( X1 != X2
    | ~ c_in(X3,X1,X4)
    | c_in(X3,X2,X4) ) ).

cnf(i_0_2435,axiom,
    ( X1 != X2
    | ~ c_in(X3,X4,X1)
    | c_in(X3,X4,X2) ) ).

cnf(i_0_2436,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Ring__and__Field_Opordered__semiring(X2) ) ).

cnf(i_0_2437,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).

cnf(i_0_2438,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semiring(X1)
    | class_Ring__and__Field_Oordered__semiring(X2) ) ).

cnf(i_0_2439,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_2440,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_2441,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__mono1(X1)
    | class_Ring__and__Field_Omult__mono1(X2) ) ).

cnf(i_0_2442,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__mono(X1)
    | class_Ring__and__Field_Omult__mono(X2) ) ).

cnf(i_0_2443,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).

cnf(i_0_2444,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_2445,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).

cnf(i_0_2446,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_2447,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_2448,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_2449,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_2450,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
    | class_OrderedGroup_Olordered__ab__group__add__meet(X2) ) ).

cnf(i_0_2451,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_2452,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X2) ) ).

cnf(i_0_2453,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_2454,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).

cnf(i_0_2455,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_2456,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_2457,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_2458,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_2459,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_2460,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_2461,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X2) ) ).

cnf(i_0_2462,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_2463,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_2464,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X2) ) ).

cnf(i_0_2465,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Oring__1(X2) ) ).

cnf(i_0_2466,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_2467,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_2468,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_2469,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_2470,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
    | class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_2471,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_2472,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_2473,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_2474,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_2475,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_2476,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_2477,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_2478,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_2479,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | class_Ring__and__Field_Ono__zero__divisors(X2) ) ).

cnf(i_0_2480,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
    | class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_2481,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_2482,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_2483,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_2484,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_2485,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_2486,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | class_Ring__and__Field_Omult__zero(X2) ) ).

cnf(i_0_2487,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_2488,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_2489,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_2490,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_OrderedGroup_Omonoid__mult(X2) ) ).

cnf(i_0_2491,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_2492,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_2493,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_2494,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_2495,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Opordered__ring(X2) ) ).

cnf(i_0_2496,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_2497,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_2498,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_2499,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Odvd(X1)
    | class_Ring__and__Field_Odvd(X2) ) ).

cnf(i_0_2364_001,axiom,
    X1 = X1 ).

cnf(i_0_2365_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_2366_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_2367_004,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_2368_005,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_2369_006,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_2370_007,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_2371_008,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_2372_009,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).

cnf(i_0_2373_010,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).

cnf(i_0_2374_011,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).

cnf(i_0_2375_012,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).

cnf(i_0_2376_013,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).

cnf(i_0_2377_014,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_2378_015,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_2379_016,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_2380_017,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_2381_018,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_2382_019,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_2383_020,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_2384_021,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).

cnf(i_0_2385_022,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).

cnf(i_0_2386_023,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).

cnf(i_0_2387_024,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_2388_025,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_2389_026,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_2390_027,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_2391_028,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_2392_029,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_2393_030,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_2394_031,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_2395_032,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_2396_033,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_2397_034,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_2398_035,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_2399_036,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_2400_037,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_2401_038,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeast(X1,X3) = c_SetInterval_Oord__class_OatLeast(X2,X3) ) ).

cnf(i_0_2402_039,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeast(X3,X1) = c_SetInterval_Oord__class_OatLeast(X3,X2) ) ).

cnf(i_0_2403_040,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X1,X3,X4) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X2,X3,X4) ) ).

cnf(i_0_2404_041,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X3,X1,X4) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X3,X2,X4) ) ).

cnf(i_0_2405_042,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X3,X4,X1) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(X3,X4,X2) ) ).

cnf(i_0_2406_043,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X1,X3,X4) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X2,X3,X4) ) ).

cnf(i_0_2407_044,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X3,X1,X4) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X3,X2,X4) ) ).

cnf(i_0_2408_045,axiom,
    ( X1 != X2
    | c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X3,X4,X1) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(X3,X4,X2) ) ).

cnf(i_0_2409_046,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).

cnf(i_0_2410_047,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).

cnf(i_0_2411_048,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).

cnf(i_0_2412_049,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).

cnf(i_0_2413_050,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).

cnf(i_0_2414_051,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_2415_052,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_2416_053,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_2417_054,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_2418_055,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_2419_056,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_2420_057,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_2421_058,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_2422_059,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_2423_060,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Ocomm__ring(X2) ) ).

cnf(i_0_2424_061,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oordered__ring__strict(X2) ) ).

cnf(i_0_2425_062,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Oring(X2) ) ).

cnf(i_0_2426_063,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_2427_064,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring(X1)
    | class_Ring__and__Field_Osemiring(X2) ) ).

cnf(i_0_2428_065,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_2429_066,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_2430_067,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_2431_068,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_2432_069,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_2433_070,axiom,
    ( X1 != X2
    | ~ c_in(X1,X3,X4)
    | c_in(X2,X3,X4) ) ).

cnf(i_0_2434_071,axiom,
    ( X1 != X2
    | ~ c_in(X3,X1,X4)
    | c_in(X3,X2,X4) ) ).

cnf(i_0_2435_072,axiom,
    ( X1 != X2
    | ~ c_in(X3,X4,X1)
    | c_in(X3,X4,X2) ) ).

cnf(i_0_2436_073,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Ring__and__Field_Opordered__semiring(X2) ) ).

cnf(i_0_2437_074,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).

cnf(i_0_2438_075,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semiring(X1)
    | class_Ring__and__Field_Oordered__semiring(X2) ) ).

cnf(i_0_2439_076,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_2440_077,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_2441_078,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__mono1(X1)
    | class_Ring__and__Field_Omult__mono1(X2) ) ).

cnf(i_0_2442_079,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__mono(X1)
    | class_Ring__and__Field_Omult__mono(X2) ) ).

cnf(i_0_2443_080,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).

cnf(i_0_2444_081,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_2445_082,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).

cnf(i_0_2446_083,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_2447_084,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_2448_085,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_2449_086,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_2450_087,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
    | class_OrderedGroup_Olordered__ab__group__add__meet(X2) ) ).

cnf(i_0_2451_088,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_2452_089,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X2) ) ).

cnf(i_0_2453_090,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_2454_091,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).

cnf(i_0_2455_092,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_2456_093,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_2457_094,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_2458_095,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_2459_096,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_2460_097,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_2461_098,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X2) ) ).

cnf(i_0_2462_099,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_2463_100,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_2464_101,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X2) ) ).

cnf(i_0_2465_102,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Oring__1(X2) ) ).

cnf(i_0_2466_103,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_2467_104,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_2468_105,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_2469_106,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_2470_107,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
    | class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_2471_108,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_2472_109,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_2473_110,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_2474_111,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_2475_112,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_2476_113,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_2477_114,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_2478_115,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_2479_116,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | class_Ring__and__Field_Ono__zero__divisors(X2) ) ).

cnf(i_0_2480_117,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
    | class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_2481_118,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_2482_119,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_2483_120,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_2484_121,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_2485_122,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_2486_123,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | class_Ring__and__Field_Omult__zero(X2) ) ).

cnf(i_0_2487_124,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_2488_125,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_2489_126,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_2490_127,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_OrderedGroup_Omonoid__mult(X2) ) ).

cnf(i_0_2491_128,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_2492_129,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_2493_130,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_2494_131,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_2495_132,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Opordered__ring(X2) ) ).

cnf(i_0_2496_133,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_2497_134,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_2498_135,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_2499_136,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Odvd(X1)
    | class_Ring__and__Field_Odvd(X2) ) ).

cnf(i_0_2500,plain,
    c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,X4),
    inference(equality_inference,[],[1246]) ).

cnf(i_0_2501,plain,
    ( X1 = X1
    | ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5)
    | ~ c_in(X1,c_Set_Oimage(X2,X3,X4,X5),X5) ),
    inference(equality_inference,[],[1259]) ).

cnf(i_0_2502,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    inference(equality_inference,[],[1330]) ).

cnf(i_0_2503,plain,
    ( ~ c_lessequals(X1,X1,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),X2,tc_nat),X3,tc_nat) = X3 ),
    inference(equality_inference,[],[1372]) ).

cnf(i_0_2504,plain,
    ( ~ c_lessequals(X1,X1,tc_nat)
    | X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),X3,tc_nat),X2,tc_nat) ),
    inference(equality_inference,[],[1373]) ).

cnf(i_0_2505,plain,
    ( ~ class_Ring__and__Field_Oring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X2,X1),X3,X1),X4,X1) = X4 ),
    inference(equality_inference,[],[1382]) ).

cnf(i_0_2506,plain,
    ( ~ class_Ring__and__Field_Oring(X1)
    | X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X3,X1),X4,X1),X2,X1) ),
    inference(equality_inference,[],[1383]) ).

cnf(i_0_2507,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[1386]) ).

cnf(i_0_2508,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[1389]) ).

cnf(i_0_2509,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[1390]) ).

cnf(i_0_2510,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[1391]) ).

cnf(i_0_2511,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[1392]) ).

cnf(i_0_2512,plain,
    ( X1 = X1
    | X2 = X3 ),
    inference(equality_inference,[],[1396]) ).

cnf(i_0_2513,plain,
    ( ~ c_in(X1,X2,X3)
    | X1 = X1
    | ~ c_Fun_Oinj__on(X4,X2,X3,X5)
    | ~ c_in(X1,X2,X3) ),
    inference(equality_inference,[],[1449]) ).

cnf(i_0_2514,plain,
    c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat),
    inference(equality_inference,[],[1453]) ).

cnf(i_0_2515,plain,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | X3 = c_HOL_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[1501]) ).

cnf(i_0_2516,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
    inference(equality_inference,[],[1504]) ).

cnf(i_0_2517,plain,
    X1 = X1,
    inference(equality_inference,[],[1507]) ).

cnf(i_0_2518,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[1511]) ).

cnf(i_0_2519,plain,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
    inference(equality_inference,[],[1637]) ).

cnf(i_0_2520,plain,
    ( X1 = X1
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(equality_inference,[],[1750]) ).

cnf(i_0_2521,plain,
    X1 = X1,
    inference(equality_inference,[],[1751]) ).

cnf(i_0_2522,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(equality_inference,[],[1854]) ).

cnf(i_0_2523,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(equality_inference,[],[1855]) ).

cnf(i_0_2524,plain,
    ( X1 = X1
    | c_in(X2,X1,X3)
    | c_in(X2,X1,X3) ),
    inference(equality_inference,[],[1867]) ).

cnf(i_0_2525,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))
    | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
    inference(equality_inference,[],[1893]) ).

cnf(i_0_2526,plain,
    ( X1 = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(equality_inference,[],[1894]) ).

cnf(i_0_2527,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(equality_inference,[],[1947]) ).

cnf(i_0_2528,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(equality_inference,[],[1948]) ).

cnf(i_0_2529,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(equality_inference,[],[1949]) ).

cnf(i_0_2530,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(equality_inference,[],[1950]) ).

cnf(i_0_2531,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[2023]) ).

cnf(i_0_2532,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,[],[2025]) ).

cnf(i_0_2533,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,[],[2026]) ).

cnf(i_0_2534,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[2035]) ).

cnf(i_0_2535,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[2036]) ).

cnf(i_0_2536,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[2037]) ).

cnf(i_0_2537,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[2038]) ).

cnf(i_0_2538,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[2039]) ).

cnf(i_0_2539,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[2053]) ).

cnf(i_0_2540,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[2055]) ).

cnf(i_0_2541,plain,
    X1 = X1,
    inference(equality_inference,[],[2078]) ).

cnf(i_0_2542,plain,
    X1 = X1,
    inference(equality_inference,[],[2080]) ).

cnf(i_0_2543,plain,
    ( X1 = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(equality_inference,[],[2294]) ).

cnf(i_0_2544,plain,
    ( X1 = X1
    | ~ class_Nat_Osemiring__char__0(X2) ),
    inference(equality_inference,[],[2295]) ).

cnf(i_0_2545,plain,
    c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(v_G,t_a),
    inference(scs_inference,[],[i_0_1341,i_0_2365]) ).

cnf(i_0_2546,plain,
    c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4),tc_fun(X4,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1417,i_0_2365,i_0_1244]) ).

cnf(i_0_2547,plain,
    c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4),
    inference(rename_variables,[],[i_0_1417]) ).

cnf(i_0_2548,plain,
    ( ~ c_in(hAPP(X1,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(X2,X3,X1,X4,X5)),X3,X5)
    | c_lessequals(c_Set_Oimage(X1,X2,X4,X5),X3,tc_fun(X5,tc_bool)) ),
    inference(rename_variables,[],[i_0_1244]) ).

cnf(i_0_2549,plain,
    c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(v_U,v_G,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_fun(tc_Com_Opname,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1417,i_0_2365,i_0_1244,i_0_1255]) ).

cnf(i_0_2550,plain,
    ( ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(X3,X1,X2,X4,X5),X3,tc_fun(X4,tc_bool)) ),
    inference(rename_variables,[],[i_0_1255]) ).

cnf(i_0_2551,plain,
    ~ c_in(X1,c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X4),X4),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2083,i_0_1417,i_0_2365,i_0_1244,i_0_1255,i_0_1291]) ).

cnf(i_0_2552,plain,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    inference(rename_variables,[],[i_0_2083]) ).

cnf(i_0_2553,plain,
    ( c_in(hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,X3,X4),X5),X1,X3)
    | ~ c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4) ),
    inference(rename_variables,[],[i_0_1291]) ).

cnf(i_0_2554,plain,
    ~ hBOOL(hAPP(c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2083,i_0_1417,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305]) ).

cnf(i_0_2555,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(rename_variables,[],[i_0_1998]) ).

cnf(i_0_2556,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    inference(rename_variables,[],[i_0_1305]) ).

cnf(i_0_2557,plain,
    c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),v_G,t_a,tc_Com_Opname),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2083,i_0_1417,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307]) ).

cnf(i_0_2558,plain,
    ( ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5),X1,X5,X4) ),
    inference(rename_variables,[],[i_0_1307]) ).

cnf(i_0_2559,plain,
    c_lessequals(c_Set_Oimage(X1,v_G,t_a,X2),c_Set_Oimage(X1,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a,X2),tc_fun(X2,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2083,i_0_1417,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337]) ).

cnf(i_0_2560,plain,
    ( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool)) ),
    inference(rename_variables,[],[i_0_1337]) ).

cnf(i_0_2561,plain,
    c_lessequals(c_Set_Ovimage(X1,v_G,X2,t_a),c_Set_Ovimage(X1,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X2,t_a),tc_fun(X2,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2083,i_0_1417,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338]) ).

cnf(i_0_2562,plain,
    ( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool)) ),
    inference(rename_variables,[],[i_0_1338]) ).

cnf(i_0_2563,plain,
    hBOOL(hAPP(c_Set_Ovimage(X1,c_Set_Oinsert(hAPP(X1,X2),X3,X4),X5,X6),X2)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2083,i_0_1417,i_0_1929,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344]) ).

cnf(i_0_2564,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    inference(rename_variables,[],[i_0_1929]) ).

cnf(i_0_2565,plain,
    ( ~ hBOOL(hAPP(X1,hAPP(X2,X3)))
    | hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    inference(rename_variables,[],[i_0_1344]) ).

cnf(i_0_2566,plain,
    hBOOL(hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),X3,X4),X2)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2083,i_0_1417,i_0_1929,i_0_2564,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361]) ).

cnf(i_0_2567,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    inference(rename_variables,[],[i_0_1929]) ).

cnf(i_0_2568,plain,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X2,tc_nat)))
    | hBOOL(hAPP(X1,X3)) ),
    inference(rename_variables,[],[i_0_1361]) ).

cnf(i_0_2569,plain,
    c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),X3,X4),X5,X4),X5),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2091,i_0_2083,i_0_1417,i_0_1929,i_0_2564,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420]) ).

cnf(i_0_2570,plain,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    inference(rename_variables,[],[i_0_2091]) ).

cnf(i_0_2571,plain,
    ( ~ c_in(hAPP(X1,X2),X3,X4)
    | c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
    inference(rename_variables,[],[i_0_1420]) ).

cnf(i_0_2572,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X1,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2091,i_0_2182,i_0_2083,i_0_1417,i_0_1929,i_0_2564,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453]) ).

cnf(i_0_2573,plain,
    c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
    inference(rename_variables,[],[i_0_2182]) ).

cnf(i_0_2574,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat)
    | c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X4,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1453]) ).

cnf(i_0_2575,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2091,i_0_2182,i_0_2083,i_0_1417,i_0_1661,i_0_1929,i_0_2564,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525]) ).

cnf(i_0_2576,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_1661]) ).

cnf(i_0_2577,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1525]) ).

cnf(i_0_2578,plain,
    ~ c_HOL_Oord__class_Oless(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),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2221,i_0_2091,i_0_2182,i_0_2083,i_0_1417,i_0_1661,i_0_1929,i_0_2564,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537]) ).

cnf(i_0_2579,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2221]) ).

cnf(i_0_2580,plain,
    ( 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) ),
    inference(rename_variables,[],[i_0_1537]) ).

cnf(i_0_2581,plain,
    ~ c_HOL_Oord__class_Oless(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),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2221,i_0_2579,i_0_2091,i_0_2182,i_0_2083,i_0_1417,i_0_1661,i_0_1929,i_0_2564,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538]) ).

cnf(i_0_2582,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2221]) ).

cnf(i_0_2583,plain,
    ( 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) ),
    inference(rename_variables,[],[i_0_1538]) ).

cnf(i_0_2584,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2221,i_0_2579,i_0_2091,i_0_2182,i_0_2083,i_0_1973,i_0_1417,i_0_1661,i_0_1929,i_0_2564,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581]) ).

cnf(i_0_2585,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_1973]) ).

cnf(i_0_2586,plain,
    ( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
    inference(rename_variables,[],[i_0_1581]) ).

cnf(i_0_2587,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2221,i_0_2579,i_0_2091,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_1661,i_0_1929,i_0_2564,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582]) ).

cnf(i_0_2588,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_1973]) ).

cnf(i_0_2589,plain,
    ( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
    | c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
    inference(rename_variables,[],[i_0_1582]) ).

cnf(i_0_2590,plain,
    hBOOL(hAPP(c_Set_Oinsert(c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,X3),X1)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2221,i_0_2579,i_0_2091,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_1661,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612]) ).

cnf(i_0_2591,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    inference(rename_variables,[],[i_0_1929]) ).

cnf(i_0_2592,plain,
    ( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(rename_variables,[],[i_0_1612]) ).

cnf(i_0_2593,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),X1,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2221,i_0_2579,i_0_2297,i_0_2091,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_1661,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631]) ).

cnf(i_0_2594,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2297]) ).

cnf(i_0_2595,plain,
    ( ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1631]) ).

cnf(i_0_2596,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2221,i_0_2579,i_0_2297,i_0_2594,i_0_2091,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_1661,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633]) ).

cnf(i_0_2597,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2297]) ).

cnf(i_0_2598,plain,
    ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    inference(rename_variables,[],[i_0_1633]) ).

cnf(i_0_2599,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_2221,i_0_2579,i_0_2297,i_0_2594,i_0_2091,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634]) ).

cnf(i_0_2600,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2088]) ).

cnf(i_0_2601,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
    inference(rename_variables,[],[i_0_1634]) ).

cnf(i_0_2602,plain,
    ~ c_lessequals(c_Set_Oinsert(X1,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2221,i_0_2579,i_0_2297,i_0_2594,i_0_2091,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663]) ).

cnf(i_0_2603,plain,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_1663]) ).

cnf(i_0_2604,plain,
    c_in(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),X4),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2221,i_0_2579,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720]) ).

cnf(i_0_2605,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_2024]) ).

cnf(i_0_2606,plain,
    ( ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
    | c_in(X1,X4,X3) ),
    inference(rename_variables,[],[i_0_1720]) ).

cnf(i_0_2607,plain,
    ~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744]) ).

cnf(i_0_2608,plain,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1744]) ).

cnf(i_0_2609,plain,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1881,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745]) ).

cnf(i_0_2610,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1745]) ).

cnf(i_0_2611,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803]) ).

cnf(i_0_2612,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2205]) ).

cnf(i_0_2613,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1803]) ).

cnf(i_0_2614,plain,
    c_lessequals(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),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806]) ).

cnf(i_0_2615,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2221]) ).

cnf(i_0_2616,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(rename_variables,[],[i_0_1806]) ).

cnf(i_0_2617,plain,
    c_lessequals(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),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807]) ).

cnf(i_0_2618,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2221]) ).

cnf(i_0_2619,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
    inference(rename_variables,[],[i_0_1807]) ).

cnf(i_0_2620,plain,
    c_HOL_Oord__class_Oless(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831]) ).

cnf(i_0_2621,plain,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1831]) ).

cnf(i_0_2622,plain,
    c_lessequals(v_na,c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845]) ).

cnf(i_0_2623,plain,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | c_lessequals(X1,X3,tc_nat) ),
    inference(rename_variables,[],[i_0_1845]) ).

cnf(i_0_2624,plain,
    c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846]) ).

cnf(i_0_2625,plain,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | c_lessequals(X2,X3,tc_nat) ),
    inference(rename_variables,[],[i_0_1846]) ).

cnf(i_0_2626,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_2576,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847]) ).

cnf(i_0_2627,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_1661]) ).

cnf(i_0_2628,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(rename_variables,[],[i_0_1847]) ).

cnf(i_0_2629,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),X1,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_1661,i_0_2576,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919]) ).

cnf(i_0_2630,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    inference(rename_variables,[],[i_0_1921]) ).

cnf(i_0_2631,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1919]) ).

cnf(i_0_2632,plain,
    c_lessequals(c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_2600,i_0_1661,i_0_2576,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925]) ).

cnf(i_0_2633,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2088]) ).

cnf(i_0_2634,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1925]) ).

cnf(i_0_2635,plain,
    c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_1973,i_0_2585,i_0_1417,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926]) ).

cnf(i_0_2636,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2088]) ).

cnf(i_0_2637,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1926]) ).

cnf(i_0_2638,plain,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1,
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930]) ).

cnf(i_0_2639,plain,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1 ),
    inference(rename_variables,[],[i_0_1930]) ).

cnf(i_0_2640,plain,
    ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2203,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931]) ).

cnf(i_0_2641,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rename_variables,[],[i_0_2203]) ).

cnf(i_0_2642,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1931]) ).

cnf(i_0_2643,plain,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2203,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937]) ).

cnf(i_0_2644,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(rename_variables,[],[i_0_1937]) ).

cnf(i_0_2645,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_1897,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2203,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939]) ).

cnf(i_0_2646,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(rename_variables,[],[i_0_1897]) ).

cnf(i_0_2647,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1939]) ).

cnf(i_0_2648,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2203,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941]) ).

cnf(i_0_2649,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(rename_variables,[],[i_0_1897]) ).

cnf(i_0_2650,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    inference(rename_variables,[],[i_0_1941]) ).

cnf(i_0_2651,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),X1,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2203,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944]) ).

cnf(i_0_2652,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    inference(rename_variables,[],[i_0_1921]) ).

cnf(i_0_2653,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1944]) ).

cnf(i_0_2654,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2203,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946]) ).

cnf(i_0_2655,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    inference(rename_variables,[],[i_0_1921]) ).

cnf(i_0_2656,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(rename_variables,[],[i_0_1946]) ).

cnf(i_0_2657,plain,
    ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2203,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966]) ).

cnf(i_0_2658,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
    | ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    inference(rename_variables,[],[i_0_1966]) ).

cnf(i_0_2659,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2203,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991]) ).

cnf(i_0_2660,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
    inference(rename_variables,[],[i_0_1922]) ).

cnf(i_0_2661,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1991]) ).

cnf(i_0_2662,plain,
    ~ c_HOL_Oord__class_Oless(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2203,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009]) ).

cnf(i_0_2663,plain,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_2009]) ).

cnf(i_0_2664,plain,
    ~ class_OrderedGroup_Ogroup__add(tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069]) ).

cnf(i_0_2665,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rename_variables,[],[i_0_2203]) ).

cnf(i_0_2666,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    inference(rename_variables,[],[i_0_2069]) ).

cnf(i_0_2667,plain,
    c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2096,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128]) ).

cnf(i_0_2668,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
    inference(rename_variables,[],[i_0_2096]) ).

cnf(i_0_2669,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_2128]) ).

cnf(i_0_2670,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137]) ).

cnf(i_0_2671,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_2137]) ).

cnf(i_0_2672,plain,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158]) ).

cnf(i_0_2673,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_2158]) ).

cnf(i_0_2674,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180]) ).

cnf(i_0_2675,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_2180]) ).

cnf(i_0_2676,plain,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X4),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188]) ).

cnf(i_0_2677,plain,
    ( ~ hBOOL(hAPP(X1,X2))
    | c_in(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_2188]) ).

cnf(i_0_2678,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201]) ).

cnf(i_0_2679,plain,
    c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
    inference(rename_variables,[],[i_0_2098]) ).

cnf(i_0_2680,plain,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(rename_variables,[],[i_0_2201]) ).

cnf(i_0_2681,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) != X1,
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214]) ).

cnf(i_0_2682,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(rename_variables,[],[i_0_2212]) ).

cnf(i_0_2683,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
    inference(rename_variables,[],[i_0_2214]) ).

cnf(i_0_2684,plain,
    X1 != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215]) ).

cnf(i_0_2685,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(rename_variables,[],[i_0_2212]) ).

cnf(i_0_2686,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_2215]) ).

cnf(i_0_2687,plain,
    ~ c_fequal(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1),X4),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218]) ).

cnf(i_0_2688,plain,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    inference(rename_variables,[],[i_0_2218]) ).

cnf(i_0_2689,plain,
    ~ class_Orderings_Otop(tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263]) ).

cnf(i_0_2690,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(rename_variables,[],[i_0_1897]) ).

cnf(i_0_2691,plain,
    ( c_lessequals(X1,c_Orderings_Otop__class_Otop(X2),X2)
    | ~ class_Orderings_Otop(X2) ),
    inference(rename_variables,[],[i_0_2263]) ).

cnf(i_0_2692,plain,
    c_lessequals(X1,X1,tc_bool),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2357,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272]) ).

cnf(i_0_2693,plain,
    ( ~ class_Orderings_Oorder(X1)
    | c_lessequals(X2,X2,X1) ),
    inference(rename_variables,[],[i_0_2272]) ).

cnf(i_0_2694,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2357,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279]) ).

cnf(i_0_2695,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(rename_variables,[],[i_0_2279]) ).

cnf(i_0_2696,plain,
    c_Finite__Set_Ofinite(X1,tc_bool),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2357,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313]) ).

cnf(i_0_2697,plain,
    ( ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | c_Finite__Set_Ofinite(X2,X1) ),
    inference(rename_variables,[],[i_0_2313]) ).

cnf(i_0_2698,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),X2,tc_nat),X3,tc_nat) = X3,
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2357,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503]) ).

cnf(i_0_2699,plain,
    ( ~ c_lessequals(X1,X1,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),X2,tc_nat),X3,tc_nat) = X3 ),
    inference(rename_variables,[],[i_0_2503]) ).

cnf(i_0_2700,plain,
    X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),X3,tc_nat),X1,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2357,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504]) ).

cnf(i_0_2701,plain,
    ( ~ c_lessequals(X1,X1,tc_nat)
    | X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),X3,tc_nat),X2,tc_nat) ),
    inference(rename_variables,[],[i_0_2504]) ).

cnf(i_0_2702,plain,
    class_Ring__and__Field_Odvd(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2351,i_0_2357,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2290,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499]) ).

cnf(i_0_2703,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2704,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_Finite__Set_Ocard(v_G,t_a),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2351,i_0_2357,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366]) ).

cnf(i_0_2705,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(rename_variables,[],[i_0_2212]) ).

cnf(i_0_2706,plain,
    ~ c_lessequals(c_Set_Oinsert(X1,c_Set_Oinsert(X1,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2351,i_0_2357,i_0_1992,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420]) ).

cnf(i_0_2707,plain,
    c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
    inference(rename_variables,[],[i_0_1992]) ).

cnf(i_0_2708,plain,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Fun_Ofun__upd(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X1,hAPP(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),X1),X2,X3),tc_fun(t_a,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2351,i_0_2357,i_0_1992,i_0_1333,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421]) ).

cnf(i_0_2709,plain,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    inference(rename_variables,[],[i_0_1333]) ).

cnf(i_0_2710,plain,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),c_Fun_Ofun__upd(tc_fun(t_a,tc_bool),X1,hAPP(tc_fun(t_a,tc_bool),X1),X2,X3)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2351,i_0_2357,i_0_1992,i_0_1333,i_0_2709,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422]) ).

cnf(i_0_2711,plain,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    inference(rename_variables,[],[i_0_1333]) ).

cnf(i_0_2712,plain,
    class_Orderings_Oorder(c_HOL_Oplus__class_Oplus(tc_bool,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2351,i_0_2357,i_0_1992,i_0_1333,i_0_2709,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426]) ).

cnf(i_0_2713,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2714,plain,
    class_Ring__and__Field_Osemiring(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2339,i_0_2351,i_0_2357,i_0_1992,i_0_1333,i_0_2709,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427]) ).

cnf(i_0_2715,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2716,plain,
    class_Divides_Osemiring__div(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2339,i_0_2351,i_0_2357,i_0_2361,i_0_1992,i_0_1333,i_0_2709,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431]) ).

cnf(i_0_2717,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2718,plain,
    class_Ring__and__Field_Ocomm__semiring__1(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2339,i_0_2351,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432]) ).

cnf(i_0_2719,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2720,plain,
    ~ c_in(c_Fun_Ofun__upd(hAPP(v_mgt__call,v_pn),X1,hAPP(hAPP(v_mgt__call,v_pn),X1),X2,X3),v_G,t_a),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2339,i_0_2351,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433]) ).

cnf(i_0_2721,plain,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    inference(rename_variables,[],[i_0_1333]) ).

cnf(i_0_2722,plain,
    ~ c_in(hAPP(v_mgt__call,v_pn),c_Fun_Ofun__upd(v_G,X1,hAPP(v_G,X1),X2,X3),t_a),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2339,i_0_2351,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434]) ).

cnf(i_0_2723,plain,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    inference(rename_variables,[],[i_0_1333]) ).

cnf(i_0_2724,plain,
    ~ c_in(hAPP(v_mgt__call,v_pn),v_G,c_Fun_Ofun__upd(t_a,X1,hAPP(t_a,X1),X2,X3)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2339,i_0_2351,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435]) ).

cnf(i_0_2725,plain,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    inference(rename_variables,[],[i_0_1333]) ).

cnf(i_0_2726,plain,
    class_Ring__and__Field_Opordered__semiring(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2331,i_0_2339,i_0_2351,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436]) ).

cnf(i_0_2727,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2728,plain,
    class_Ring__and__Field_Oordered__semiring__strict(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2331,i_0_2339,i_0_2348,i_0_2351,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437]) ).

cnf(i_0_2729,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2730,plain,
    class_Ring__and__Field_Oordered__semiring(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2331,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438]) ).

cnf(i_0_2731,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2732,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2331,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440]) ).

cnf(i_0_2733,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2734,plain,
    class_Ring__and__Field_Omult__mono1(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2324,i_0_2331,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441]) ).

cnf(i_0_2735,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2736,plain,
    class_Ring__and__Field_Omult__mono(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2324,i_0_2325,i_0_2331,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442]) ).

cnf(i_0_2737,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2738,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2324,i_0_2325,i_0_2331,i_0_2334,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443]) ).

cnf(i_0_2739,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2740,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2331,i_0_2334,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445]) ).

cnf(i_0_2741,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2742,plain,
    ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_G,t_a),c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2331,i_0_2334,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446]) ).

cnf(i_0_2743,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2221]) ).

cnf(i_0_2744,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2331,i_0_2334,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447]) ).

cnf(i_0_2745,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2221]) ).

cnf(i_0_2746,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,c_Fun_Ofun__upd(tc_nat,X2,hAPP(tc_nat,X2),X3,X4)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2331,i_0_2334,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448]) ).

cnf(i_0_2747,plain,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    inference(rename_variables,[],[i_0_1333]) ).

cnf(i_0_2748,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449]) ).

cnf(i_0_2749,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2750,plain,
    class_Ring__and__Field_Ocomm__semiring(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452]) ).

cnf(i_0_2751,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2752,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2338,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454]) ).

cnf(i_0_2753,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2754,plain,
    class_OrderedGroup_Opordered__comm__monoid__add(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2338,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455]) ).

cnf(i_0_2755,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2756,plain,
    class_Ring__and__Field_Oordered__semidom(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2357,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456]) ).

cnf(i_0_2757,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2758,plain,
    class_OrderedGroup_Ocomm__monoid__add(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2356,i_0_2357,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457]) ).

cnf(i_0_2759,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2760,plain,
    class_Lattices_Olower__semilattice(c_HOL_Oplus__class_Oplus(tc_bool,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2342,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2356,i_0_2357,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458]) ).

cnf(i_0_2761,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2762,plain,
    class_Lattices_Olattice(c_HOL_Oplus__class_Oplus(tc_bool,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2356,i_0_2357,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462]) ).

cnf(i_0_2763,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2764,plain,
    class_OrderedGroup_Oab__semigroup__add(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463]) ).

cnf(i_0_2765,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2766,plain,
    class_OrderedGroup_Oab__semigroup__mult(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464]) ).

cnf(i_0_2767,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2768,plain,
    class_HOL_Oord(c_HOL_Oplus__class_Oplus(tc_bool,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466]) ).

cnf(i_0_2769,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2770,plain,
    class_Orderings_Olinorder(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467]) ).

cnf(i_0_2771,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2772,plain,
    class_Orderings_Opreorder(c_HOL_Oplus__class_Oplus(tc_bool,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2348,i_0_2351,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468]) ).

cnf(i_0_2773,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2774,plain,
    class_Ring__and__Field_Osemiring__1(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469]) ).

cnf(i_0_2775,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2776,plain,
    class_Complete__Lattice_Ocomplete__lattice(c_HOL_Oplus__class_Oplus(tc_bool,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475]) ).

cnf(i_0_2777,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2778,plain,
    class_OrderedGroup_Ocancel__semigroup__add(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2336,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476]) ).

cnf(i_0_2779,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2780,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2331,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477]) ).

cnf(i_0_2781,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2782,plain,
    class_Ring__and__Field_Ono__zero__divisors(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2331,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479]) ).

cnf(i_0_2783,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2784,plain,
    class_Lattices_Obounded__lattice(c_HOL_Oplus__class_Oplus(tc_bool,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2331,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2347,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481]) ).

cnf(i_0_2785,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2786,plain,
    ~ c_fequal(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3,X4),c_Set_Oinsert(X5,X6,X1),X7),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2331,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2347,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482]) ).

cnf(i_0_2787,plain,
    c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
    inference(rename_variables,[],[i_0_1333]) ).

cnf(i_0_2788,plain,
    class_Finite__Set_Ofinite_Ofinite(c_HOL_Oplus__class_Oplus(tc_bool,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2331,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2347,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485]) ).

cnf(i_0_2789,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2790,plain,
    class_Ring__and__Field_Omult__zero(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2347,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486]) ).

cnf(i_0_2791,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2792,plain,
    hAPP(c_Set_Oinsert(X1,X2,X3),X1) != hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2347,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487]) ).

cnf(i_0_2793,plain,
    class_OrderedGroup_Omonoid__add(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2347,i_0_2348,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488]) ).

cnf(i_0_2794,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2795,plain,
    class_OrderedGroup_Ocomm__monoid__mult(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2347,i_0_2348,i_0_2349,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489]) ).

cnf(i_0_2796,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2797,plain,
    class_OrderedGroup_Omonoid__mult(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490]) ).

cnf(i_0_2798,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2799,plain,
    class_Orderings_Obot(c_HOL_Oplus__class_Oplus(tc_bool,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491]) ).

cnf(i_0_2800,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2801,plain,
    tc_bool != tc_nat,
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492]) ).

cnf(i_0_2802,plain,
    class_Nat_Osemiring__char__0(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493]) ).

cnf(i_0_2803,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2804,plain,
    class_Ring__and__Field_Ozero__neq__one(c_HOL_Oplus__class_Oplus(tc_nat,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494]) ).

cnf(i_0_2805,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2290]) ).

cnf(i_0_2806,plain,
    c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X1,c_Set_Oimage(X2,X1,X3,tc_bool),X2,X3,tc_bool),X1,tc_fun(X3,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254]) ).

cnf(i_0_2807,plain,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    inference(rename_variables,[],[i_0_2225]) ).

cnf(i_0_2808,plain,
    ( ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(X3,X1,X2,X4,X5),X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X1,X5) ),
    inference(rename_variables,[],[i_0_1254]) ).

cnf(i_0_2809,plain,
    c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),X1,tc_nat),X2,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282]) ).

cnf(i_0_2810,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2102]) ).

cnf(i_0_2811,plain,
    ( ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1282]) ).

cnf(i_0_2812,plain,
    c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283]) ).

cnf(i_0_2813,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2086]) ).

cnf(i_0_2814,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1283]) ).

cnf(i_0_2815,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292]) ).

cnf(i_0_2816,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1292]) ).

cnf(i_0_2817,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),X1,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),X2,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293]) ).

cnf(i_0_2818,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
    inference(rename_variables,[],[i_0_1922]) ).

cnf(i_0_2819,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1293]) ).

cnf(i_0_2820,plain,
    c_lessequals(v_U,c_Set_Oinsert(v_pn,c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(v_U,c_Set_Oinsert(v_pn,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328]) ).

cnf(i_0_2821,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_2024]) ).

cnf(i_0_2822,plain,
    ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
    | c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool))
    | ~ c_in(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_1328]) ).

cnf(i_0_2823,plain,
    c_in(hAPP(X1,v_pn),c_Set_Oinsert(X2,c_Set_Oimage(X1,v_U,tc_Com_Opname,X3),X3),X3),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359]) ).

cnf(i_0_2824,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_2024]) ).

cnf(i_0_2825,plain,
    ( ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
    | c_in(hAPP(X1,X6),X5,X4)
    | ~ c_in(X6,X2,X3) ),
    inference(rename_variables,[],[i_0_1359]) ).

cnf(i_0_2826,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X1,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362]) ).

cnf(i_0_2827,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
    inference(rename_variables,[],[i_0_1922]) ).

cnf(i_0_2828,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2088]) ).

cnf(i_0_2829,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X4,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),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X4,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1362]) ).

cnf(i_0_2830,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372]) ).

cnf(i_0_2831,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rename_variables,[],[i_0_2203]) ).

cnf(i_0_2832,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1372]) ).

cnf(i_0_2833,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373]) ).

cnf(i_0_2834,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2205]) ).

cnf(i_0_2835,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1373]) ).

cnf(i_0_2836,plain,
    c_Finite__Set_Ofinite(v_G,t_a),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376]) ).

cnf(i_0_2837,plain,
    ( ~ c_lessequals(X1,c_Set_Oimage(X2,X3,X4,X5),tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X4)
    | c_Finite__Set_Ofinite(X1,X5) ),
    inference(rename_variables,[],[i_0_1376]) ).

cnf(i_0_2838,plain,
    c_Fun_Oinj__on(X1,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),X2,X4),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405]) ).

cnf(i_0_2839,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_1973]) ).

cnf(i_0_2840,plain,
    ( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_Fun_Oinj__on(X4,X2,X3,X5)
    | c_Fun_Oinj__on(X4,X1,X3,X5) ),
    inference(rename_variables,[],[i_0_1405]) ).

cnf(i_0_2841,plain,
    c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413]) ).

cnf(i_0_2842,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2088]) ).

cnf(i_0_2843,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    inference(rename_variables,[],[i_0_1413]) ).

cnf(i_0_2844,plain,
    c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516]) ).

cnf(i_0_2845,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2297]) ).

cnf(i_0_2846,plain,
    ( ~ c_lessequals(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1516]) ).

cnf(i_0_2847,plain,
    c_lessequals(v_na,c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517]) ).

cnf(i_0_2848,plain,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | c_lessequals(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(rename_variables,[],[i_0_1517]) ).

cnf(i_0_2849,plain,
    c_lessequals(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519]) ).

cnf(i_0_2850,plain,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | c_lessequals(X1,X4,X3) ),
    inference(rename_variables,[],[i_0_1519]) ).

cnf(i_0_2851,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),X3,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521]) ).

cnf(i_0_2852,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(rename_variables,[],[i_0_1521]) ).

cnf(i_0_2853,plain,
    ~ c_HOL_Oord__class_Oless(v_U,c_Set_Oinsert(v_pn,v_U,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570]) ).

cnf(i_0_2854,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
    inference(rename_variables,[],[i_0_2147]) ).

cnf(i_0_2855,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
    | ~ c_in(X4,X2,X3) ),
    inference(rename_variables,[],[i_0_1570]) ).

cnf(i_0_2856,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X2,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605]) ).

cnf(i_0_2857,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2297]) ).

cnf(i_0_2858,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X4,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    inference(rename_variables,[],[i_0_1605]) ).

cnf(i_0_2859,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat),X2,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609]) ).

cnf(i_0_2860,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(rename_variables,[],[i_0_1609]) ).

cnf(i_0_2861,plain,
    c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626]) ).

cnf(i_0_2862,plain,
    ( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
    | hBOOL(hAPP(X2,X4))
    | X1 = X4 ),
    inference(rename_variables,[],[i_0_1626]) ).

cnf(i_0_2863,plain,
    ~ c_in(hAPP(v_mgt__call,v_pn),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643]) ).

cnf(i_0_2864,plain,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ c_in(X1,X4,X3) ),
    inference(rename_variables,[],[i_0_1643]) ).

cnf(i_0_2865,plain,
    ~ c_HOL_Oord__class_Oless(c_Set_Oinsert(v_pn,v_U,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644]) ).

cnf(i_0_2866,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
    inference(rename_variables,[],[i_0_2147]) ).

cnf(i_0_2867,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_fun(X4,tc_bool))
    | ~ c_in(X2,X3,X4) ),
    inference(rename_variables,[],[i_0_1644]) ).

cnf(i_0_2868,plain,
    ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664]) ).

cnf(i_0_2869,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1664]) ).

cnf(i_0_2870,plain,
    c_lessequals(v_na,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),v_na),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692]) ).

cnf(i_0_2871,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(rename_variables,[],[i_0_1998]) ).

cnf(i_0_2872,plain,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | hBOOL(hAPP(X3,X2))
    | c_lessequals(X1,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(X3,X1),tc_nat) ),
    inference(rename_variables,[],[i_0_1692]) ).

cnf(i_0_2873,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693]) ).

cnf(i_0_2874,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2088]) ).

cnf(i_0_2875,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2221]) ).

cnf(i_0_2876,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(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) ),
    inference(rename_variables,[],[i_0_1693]) ).

cnf(i_0_2877,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703]) ).

cnf(i_0_2878,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(rename_variables,[],[i_0_1703]) ).

cnf(i_0_2879,plain,
    ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746]) ).

cnf(i_0_2880,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2088]) ).

cnf(i_0_2881,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(rename_variables,[],[i_0_2212]) ).

cnf(i_0_2882,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X2 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1746]) ).

cnf(i_0_2883,plain,
    ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747]) ).

cnf(i_0_2884,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2088]) ).

cnf(i_0_2885,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(rename_variables,[],[i_0_2212]) ).

cnf(i_0_2886,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X2 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1747]) ).

cnf(i_0_2887,plain,
    ~ c_in(v_pn,c_HOL_Ominus__class_Ominus(X1,v_U,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749]) ).

cnf(i_0_2888,plain,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_1895]) ).

cnf(i_0_2889,plain,
    ( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_in(X4,X2,X3)
    | ~ c_in(X4,X1,X3) ),
    inference(rename_variables,[],[i_0_1749]) ).

cnf(i_0_2890,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_2884,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749,i_0_1752]) ).

cnf(i_0_2891,plain,
    c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2088]) ).

cnf(i_0_2892,plain,
    ( ~ 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_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1752]) ).

cnf(i_0_2893,plain,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),v_G,tc_fun(t_a,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_2884,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749,i_0_1752,i_0_1795]) ).

cnf(i_0_2894,plain,
    ( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_1795]) ).

cnf(i_0_2895,plain,
    ~ c_HOL_Oord__class_Oless(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2147,i_0_2854,i_0_2866,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_2884,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749,i_0_1752,i_0_1795,i_0_1796]) ).

cnf(i_0_2896,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
    inference(rename_variables,[],[i_0_2147]) ).

cnf(i_0_2897,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X1,X4,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_1796]) ).

cnf(i_0_2898,plain,
    ~ c_HOL_Oord__class_Oless(c_Set_Oinsert(X1,c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2824,i_0_2147,i_0_2854,i_0_2866,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_2884,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749,i_0_1752,i_0_1795,i_0_1796,i_0_1797]) ).

cnf(i_0_2899,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_2024]) ).

cnf(i_0_2900,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
    | ~ c_HOL_Oord__class_Oless(X4,X2,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
    inference(rename_variables,[],[i_0_1797]) ).

cnf(i_0_2901,plain,
    c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2298,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2824,i_0_2147,i_0_2854,i_0_2866,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_2884,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749,i_0_1752,i_0_1795,i_0_1796,i_0_1797,i_0_1810]) ).

cnf(i_0_2902,plain,
    c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2298]) ).

cnf(i_0_2903,plain,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
    inference(rename_variables,[],[i_0_1810]) ).

cnf(i_0_2904,plain,
    c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2298,i_0_2902,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2824,i_0_2147,i_0_2854,i_0_2866,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_2884,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749,i_0_1752,i_0_1795,i_0_1796,i_0_1797,i_0_1810,i_0_1811]) ).

cnf(i_0_2905,plain,
    c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2298]) ).

cnf(i_0_2906,plain,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3) ),
    inference(rename_variables,[],[i_0_1811]) ).

cnf(i_0_2907,plain,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),X1,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2857,i_0_2298,i_0_2902,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2824,i_0_2147,i_0_2854,i_0_2866,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2343,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_2884,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749,i_0_1752,i_0_1795,i_0_1796,i_0_1797,i_0_1810,i_0_1811,i_0_1813]) ).

cnf(i_0_2908,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2297]) ).

cnf(i_0_2909,plain,
    ( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
    | ~ class_Lattices_Olower__semilattice(X4)
    | c_lessequals(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_1813]) ).

cnf(i_0_2910,plain,
    c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),X2,tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2857,i_0_2908,i_0_2298,i_0_2902,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2824,i_0_2147,i_0_2854,i_0_2866,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2343,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_2884,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749,i_0_1752,i_0_1795,i_0_1796,i_0_1797,i_0_1810,i_0_1811,i_0_1813,i_0_1815]) ).

cnf(i_0_2911,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_2297]) ).

cnf(i_0_2912,plain,
    ( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
    | ~ class_Lattices_Olower__semilattice(X4)
    | c_lessequals(X1,X3,X4) ),
    inference(rename_variables,[],[i_0_1815]) ).

cnf(i_0_2913,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2857,i_0_2908,i_0_2298,i_0_2902,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2824,i_0_2147,i_0_2854,i_0_2866,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2217,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2343,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_2884,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749,i_0_1752,i_0_1795,i_0_1796,i_0_1797,i_0_1810,i_0_1811,i_0_1813,i_0_1815,i_0_1827]) ).

cnf(i_0_2914,plain,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_2217]) ).

cnf(i_0_2915,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1 ),
    inference(rename_variables,[],[i_0_1827]) ).

cnf(i_0_2916,plain,
    $false,
    inference(scs_inference,[],[i_0_1341,i_0_1470,i_0_1353,i_0_2299,i_0_2316,i_0_2168,i_0_1345,i_0_2221,i_0_2579,i_0_2582,i_0_2615,i_0_2618,i_0_2743,i_0_2745,i_0_2297,i_0_2594,i_0_2597,i_0_2845,i_0_2857,i_0_2908,i_0_2298,i_0_2902,i_0_2091,i_0_2024,i_0_2605,i_0_2821,i_0_2824,i_0_2147,i_0_2854,i_0_2866,i_0_2225,i_0_1852,i_0_2182,i_0_2083,i_0_1921,i_0_2630,i_0_2652,i_0_1922,i_0_2660,i_0_2818,i_0_2098,i_0_2102,i_0_1973,i_0_2585,i_0_2588,i_0_2217,i_0_2317,i_0_2318,i_0_2319,i_0_2321,i_0_2322,i_0_2324,i_0_2325,i_0_2326,i_0_2327,i_0_2328,i_0_2329,i_0_2330,i_0_2331,i_0_2332,i_0_2333,i_0_2334,i_0_2335,i_0_2336,i_0_2337,i_0_2338,i_0_2339,i_0_2340,i_0_2342,i_0_2343,i_0_2344,i_0_2345,i_0_2346,i_0_2347,i_0_2348,i_0_2349,i_0_2350,i_0_2351,i_0_2352,i_0_2353,i_0_2354,i_0_2355,i_0_2356,i_0_2357,i_0_2359,i_0_2361,i_0_2362,i_0_2363,i_0_1992,i_0_1333,i_0_2709,i_0_2711,i_0_2721,i_0_2723,i_0_2725,i_0_2747,i_0_1417,i_0_1895,i_0_2145,i_0_2146,i_0_1897,i_0_2646,i_0_2649,i_0_2088,i_0_2600,i_0_2633,i_0_2636,i_0_2828,i_0_2842,i_0_2874,i_0_2880,i_0_2884,i_0_1661,i_0_2576,i_0_2627,i_0_2096,i_0_2212,i_0_2682,i_0_2685,i_0_2705,i_0_2881,i_0_2213,i_0_2290,i_0_2703,i_0_2713,i_0_2715,i_0_2717,i_0_2719,i_0_2727,i_0_2729,i_0_2731,i_0_2733,i_0_2735,i_0_2737,i_0_2739,i_0_2741,i_0_2749,i_0_2751,i_0_2753,i_0_2755,i_0_2757,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2767,i_0_2769,i_0_2771,i_0_2773,i_0_2775,i_0_2777,i_0_2779,i_0_2781,i_0_2783,i_0_2785,i_0_2789,i_0_2791,i_0_2794,i_0_2796,i_0_2798,i_0_2800,i_0_2803,i_0_1881,i_0_2086,i_0_2203,i_0_2641,i_0_2665,i_0_2205,i_0_2612,i_0_1929,i_0_2564,i_0_2567,i_0_2591,i_0_1998,i_0_2555,i_0_2365,i_0_1244,i_0_1255,i_0_1291,i_0_1305,i_0_1307,i_0_1337,i_0_1338,i_0_1344,i_0_1361,i_0_1420,i_0_1453,i_0_1525,i_0_1537,i_0_1538,i_0_1581,i_0_1582,i_0_1612,i_0_1631,i_0_1633,i_0_1634,i_0_1663,i_0_1720,i_0_1744,i_0_1745,i_0_1803,i_0_1806,i_0_1807,i_0_1831,i_0_1845,i_0_1846,i_0_1847,i_0_1919,i_0_1925,i_0_1926,i_0_1930,i_0_1931,i_0_1937,i_0_1939,i_0_1941,i_0_1944,i_0_1946,i_0_1966,i_0_1991,i_0_2009,i_0_2069,i_0_2128,i_0_2137,i_0_2158,i_0_2180,i_0_2188,i_0_2201,i_0_2214,i_0_2215,i_0_2218,i_0_2263,i_0_2272,i_0_2279,i_0_2313,i_0_2503,i_0_2504,i_0_2499,i_0_2366,i_0_2420,i_0_2421,i_0_2422,i_0_2426,i_0_2427,i_0_2431,i_0_2432,i_0_2433,i_0_2434,i_0_2435,i_0_2436,i_0_2437,i_0_2438,i_0_2440,i_0_2441,i_0_2442,i_0_2443,i_0_2445,i_0_2446,i_0_2447,i_0_2448,i_0_2449,i_0_2452,i_0_2454,i_0_2455,i_0_2456,i_0_2457,i_0_2458,i_0_2462,i_0_2463,i_0_2464,i_0_2466,i_0_2467,i_0_2468,i_0_2469,i_0_2475,i_0_2476,i_0_2477,i_0_2479,i_0_2481,i_0_2482,i_0_2485,i_0_2486,i_0_2487,i_0_2488,i_0_2489,i_0_2490,i_0_2491,i_0_2492,i_0_2493,i_0_2494,i_0_1254,i_0_1282,i_0_1283,i_0_1292,i_0_1293,i_0_1328,i_0_1359,i_0_1362,i_0_1372,i_0_1373,i_0_1376,i_0_1405,i_0_1413,i_0_1516,i_0_1517,i_0_1519,i_0_1521,i_0_1570,i_0_1605,i_0_1609,i_0_1626,i_0_1643,i_0_1644,i_0_1664,i_0_1692,i_0_1693,i_0_1703,i_0_1746,i_0_1747,i_0_1749,i_0_1752,i_0_1795,i_0_1796,i_0_1797,i_0_1810,i_0_1811,i_0_1813,i_0_1815,i_0_1827,i_0_1828]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem    : SWV884-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.07  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.25  % Computer : n018.cluster.edu
% 0.07/0.25  % Model    : x86_64 x86_64
% 0.07/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25  % Memory   : 8042.1875MB
% 0.07/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25  % CPULimit   : 300
% 0.07/0.25  % WCLimit    : 300
% 0.07/0.25  % DateTime   : Tue May  5 06:07:01 EDT 2026
% 0.07/0.25  % CPUTime    : 
% 0.07/0.26  % start to proof: theBenchmark
% 1.44/2.54  % Version  : CSE_E---1.7
% 1.44/2.54  % Problem  : theBenchmark.p
% 1.44/2.54  % SZS status Unsatisfiable for theBenchmark.p
% 1.44/2.54  % SZS output start CNFRefutation
% See solution above
% 6.43/7.58  % Total time : 2.273s
%------------------------------------------------------------------------------