CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWV882-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n015.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 1.06s 1.67s
% Output   : CNFRefutation 1.61s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_628)

% 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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_lift__Suc__mono__le_0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_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/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_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/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_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/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

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

cnf(cls_less__add__Suc2_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_le__SucE_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

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

cnf(cls_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

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

cnf(cls_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

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

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

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

cnf(cls_Suc__leD_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

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

cnf(cls_add__is__1_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).

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

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

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

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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).

cnf(cls_of__nat__Suc_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X1) = 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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).

cnf(cls_add__is__1_2,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

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

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

cnf(cls_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

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

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

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

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

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

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

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

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

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

cnf(cls_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_1) ).

cnf(cls_assms_I3_J_1,axiom,
    ( hBOOL(hAPP(hAPP(v_P,X1),c_Set_Oinsert(v_mgt(X2),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | ~ hBOOL(hAPP(hAPP(v_P,X1),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(X1,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | ~ v_wt(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I3_J_1) ).

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/sandbox/benchmark/theBenchmark.p',cls_card__Diff2__less_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/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_2) ).

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/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_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/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_1) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_0) ).

cnf(cls_conjecture_7,negated_conjecture,
    ( hBOOL(hAPP(hAPP(v_P,X1),c_Set_Oinsert(v_mgt(X2),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | c_Finite__Set_Ocard(X1,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),v_na,tc_nat)
    | ~ c_lessequals(X1,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
    | ~ v_wt(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).

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/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_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/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct__image_0) ).

cnf(cls_assms_I2_J_0,axiom,
    ( hBOOL(hAPP(hAPP(v_P,X1),c_Set_Oinsert(hAPP(v_mgt__call,X2),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,X2),X1,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(X2),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I2_J_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

cnf(cls_finite__subset__induct_4,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Set_Oinsert(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X3,X1,X4),c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X3,X1,X4),X4)))
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
    | ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_4) ).

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/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

cnf(cls_setsum__diff1_H_0,axiom,
    ( c_Finite__Set_Osetsum(X2,X3,X4,X1) = c_HOL_Oplus__class_Oplus(hAPP(X2,X5),c_Finite__Set_Osetsum(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_in(X5,X3,X4)
    | ~ c_Finite__Set_Ofinite(X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_H_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/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).

cnf(cls_setsum__diff_0,axiom,
    ( c_Finite__Set_Osetsum(X2,c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X5,tc_bool)),X5,X1) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X2,X3,X5,X1),c_Finite__Set_Osetsum(X2,X4,X5,X1),X1)
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | ~ c_lessequals(X4,X3,tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_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/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

cnf(cls_setsum__diff1__ring_0,axiom,
    ( c_Finite__Set_Osetsum(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X5,X1) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X2,X3,X5,X1),hAPP(X2,X4),X1)
    | ~ class_Ring__and__Field_Oring(X1)
    | ~ c_in(X4,X3,X5)
    | ~ c_Finite__Set_Ofinite(X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).

cnf(cls_setsum__diff1_0,axiom,
    ( c_Finite__Set_Osetsum(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X5,X1) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X2,X3,X5,X1),hAPP(X2,X4),X1)
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | ~ c_in(X4,X3,X5)
    | ~ c_Finite__Set_Ofinite(X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_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/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_card__inj__on__le_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__le_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).

cnf(cls_setsum__diff1_1,axiom,
    ( c_Finite__Set_Osetsum(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X5,X1) = c_Finite__Set_Osetsum(X2,X3,X5,X1)
    | c_in(X4,X3,X5)
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | ~ c_Finite__Set_Ofinite(X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).

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/sandbox/benchmark/theBenchmark.p',cls_vimage__code_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/sandbox/benchmark/theBenchmark.p',cls_card__image__le_0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).

cnf(cls_assms_I3_J_0,axiom,
    ( hBOOL(hAPP(hAPP(v_P,X1),c_Set_Oinsert(v_mgt(X2),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | c_in(v_sko__local__Xassms__3__1(X1,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
    | ~ v_wt(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I3_J_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/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

cnf(cls_setsum__insert_0,axiom,
    ( c_Finite__Set_Osetsum(X2,c_Set_Oinsert(X3,X4,X5),X5,X1) = c_HOL_Oplus__class_Oplus(hAPP(X2,X3),c_Finite__Set_Osetsum(X2,X4,X5,X1),X1)
    | c_in(X3,X4,X5)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_Finite__Set_Ofinite(X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__insert_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

cnf(cls_conjecture_6,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

cnf(cls_finite__subset__induct_2,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X3,X1,X4),c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X3,X1,X4),X4)
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
    | ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_2) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_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/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_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/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).

cnf(cls_finite__subset__induct_3,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X3,X1,X4)))
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
    | ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_3) ).

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/sandbox/benchmark/theBenchmark.p',cls_Diff__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/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_finite__subset__induct_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | c_in(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X3,X1,X4),X3,X4)
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
    | ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_1) ).

cnf(cls_image__constant_0,axiom,
    ( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
    | ~ c_in(X5,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

cnf(cls_finite__subset__induct_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X3,X1,X4),X4)
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
    | ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_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/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).

cnf(cls_image__constant__conv_1,axiom,
    ( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

cnf(cls_add__less__cancel__left_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).

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/sandbox/benchmark/theBenchmark.p',cls_double__diff_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

cnf(cls_vimage__const_1,axiom,
    ( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_in(X1,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).

cnf(cls_image__constant__conv_0,axiom,
    c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_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/sandbox/benchmark/theBenchmark.p',cls_add__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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_singletonE_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

cnf(cls_setsum__0_0,axiom,
    ( c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,X2),X3,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__0_0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_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/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_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/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

cnf(cls_ab__semigroup__mult_Omult__ac_I1_J_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__ac_I1_J_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_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/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_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/sandbox/benchmark/theBenchmark.p',cls_image__empty_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_nat__add__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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

cnf(cls_setsum__empty_0,axiom,
    ( c_Finite__Set_Osetsum(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__empty_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_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/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

cnf(cls_setsum__infinite_0,axiom,
    ( c_Finite__Set_Osetsum(X2,X3,X4,X1) = c_HOL_Ozero__class_Ozero(X1)
    | c_Finite__Set_Ofinite(X3,X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__infinite_0) ).

cnf(cls_setsum__def_1,axiom,
    ( c_Finite__Set_Osetsum(X2,X3,X4,X1) = c_HOL_Ozero__class_Ozero(X1)
    | c_Finite__Set_Ofinite(X3,X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__def_1) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
    ( c_HOL_Oord__class_Oless(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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

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/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

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/sandbox/benchmark/theBenchmark.p',cls_subset__iff_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/sandbox/benchmark/theBenchmark.p',cls_set__rev__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/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_set__mp_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/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

cnf(cls_ab__semigroup__mult_Omult__left__commute_0,axiom,
    ( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__left__commute_0) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).

cnf(cls_add__gr__0_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),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/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).

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

cnf(cls_insertCI_0,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_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/sandbox/benchmark/theBenchmark.p',cls_order__trans_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/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_order__less__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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_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/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_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/sandbox/benchmark/theBenchmark.p',cls_le__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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

cnf(cls_ab__semigroup__mult_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))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ononempty__iff_2) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_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/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_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/sandbox/benchmark/theBenchmark.p',cls_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).

cnf(cls_assms_I1_J_0,axiom,
    ( hBOOL(hAPP(hAPP(v_P,X1),X2))
    | ~ c_lessequals(X2,X1,tc_fun(t_a,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I1_J_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

cnf(cls_add__imp__eq_0,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

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

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

cnf(cls_insertI1_0,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

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/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_le__add2_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/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_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/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Max__in_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_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/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_2) ).

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/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_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/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

cnf(cls_COMBK__def_0,axiom,
    hAPP(c_COMBK(X1,X2,X3),X4) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

cnf(cls_assms_I4_J_0,axiom,
    ( v_wt(c_Option_Othe(c_Com_Obody(X1),tc_Com_Ocom))
    | ~ c_in(X1,v_U,tc_Com_Opname) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I4_J_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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

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

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

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

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

cnf(cls_linorder__linear_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mem__def_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_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/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_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/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_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/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

cnf(cls_ab__semigroup__mult_Omult__commute_0,axiom,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__commute_0) ).

cnf(cls_mem__def_1,axiom,
    ( c_in(X1,X2,X3)
    | ~ hBOOL(hAPP(X2,X1)) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

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

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_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/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

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

cnf(cls_natgb_Oadd__r0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

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

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

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

cnf(cls_subset__refl_0,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

cnf(cls_equalityE_0,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

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

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/sandbox/benchmark/theBenchmark.p',cls_add__0__left_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_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/sandbox/benchmark/theBenchmark.p',cls_diff__0__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/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_bot__least_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/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

cnf(cls_order__eq__refl_0,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

cnf(cls_order__eq__iff_0,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_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/sandbox/benchmark/theBenchmark.p',cls_add__is__0_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_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/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

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

cnf(cls_eq__imp__le_0,axiom,
    c_lessequals(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

cnf(cls_le__refl_0,axiom,
    c_lessequals(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

cnf(cls_conjecture_4,negated_conjecture,
    c_in(v_pn,v_U,tc_Com_Opname),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

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

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

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/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

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

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

cnf(cls_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).

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

cnf(cls_finite_0,axiom,
    ( c_Finite__Set_Ofinite(X2,X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).

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

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

cnf(cls_conjecture_0,negated_conjecture,
    c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

cnf(clsarity_bool__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

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

cnf(clsarity_bool__HOL_Oord,axiom,
    class_HOL_Oord(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

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

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

cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(i_0_627,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_628,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_629,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_630,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_631,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_632,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_633,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_634,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_635,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_636,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_637,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_638,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_639,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_640,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_641,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_642,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_643,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_644,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_645,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_646,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_647,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_648,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_649,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_650,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_651,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    cls_not__less__eq__eq_1 ).

cnf(i_0_652,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_653,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_654,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_655,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_656,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_657,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_658,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_659,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_660,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_661,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_662,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    cls_Suc__leD_0 ).

cnf(i_0_663,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_664,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_665,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_666,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_667,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_668,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_669,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_670,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_671,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_672,axiom,
    c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
    cls_le__Suc__eq_2 ).

cnf(i_0_673,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_674,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_675,axiom,
    ~ c_lessequals(c_Suc(X1),X1,tc_nat),
    cls_Suc__n__not__le__n_0 ).

cnf(i_0_676,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_677,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_678,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_679,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_680,axiom,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__SucI_0 ).

cnf(i_0_681,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_682,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_683,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_684,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_685,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_686,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_687,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_688,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_689,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_690,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_691,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_692,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_693,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    cls_not__less__eq__eq_0 ).

cnf(i_0_694,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_695,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_696,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_697,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_698,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_699,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_Suc__inject_0 ).

cnf(i_0_700,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_nat_Oinject_0 ).

cnf(i_0_701,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_702,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_703,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_704,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_705,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_lessI_0 ).

cnf(i_0_706,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_less__Suc__eq_2 ).

cnf(i_0_707,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_708,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_nat_Osimps_I3_J_0 ).

cnf(i_0_709,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_Suc__neq__Zero_0 ).

cnf(i_0_710,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_nat_Osimps_I2_J_0 ).

cnf(i_0_711,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_Zero__neq__Suc_0 ).

cnf(i_0_712,axiom,
    c_Suc(X1) != X1,
    cls_Suc__n__not__n_0 ).

cnf(i_0_713,axiom,
    X1 != c_Suc(X1),
    cls_n__not__Suc__n_0 ).

cnf(i_0_714,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_715,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_716,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_717,axiom,
    ( hBOOL(hAPP(hAPP(v_P,X1),c_Set_Oinsert(v_mgt(X2),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | ~ hBOOL(hAPP(hAPP(v_P,X1),c_Set_Oinsert(hAPP(v_mgt__call,v_sko__local__Xassms__3__1(X1,v_P,v_U,v_mgt__call)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | ~ v_wt(X2) ),
    cls_assms_I3_J_1,
    [final] ).

cnf(i_0_718,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_719,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_720,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_721,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_722,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_723,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_724,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_725,negated_conjecture,
    ( hBOOL(hAPP(hAPP(v_P,X1),c_Set_Oinsert(v_mgt(X2),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | c_Finite__Set_Ocard(X1,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),v_na,tc_nat)
    | ~ c_lessequals(X1,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
    | ~ v_wt(X2) ),
    cls_conjecture_7,
    [final] ).

cnf(i_0_726,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_727,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_728,axiom,
    ( hBOOL(hAPP(hAPP(v_P,X1),c_Set_Oinsert(hAPP(v_mgt__call,X2),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(hAPP(v_mgt__call,X2),X1,t_a)),c_Set_Oinsert(v_mgt(c_Option_Othe(c_Com_Obody(X2),tc_Com_Ocom)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
    cls_assms_I2_J_0,
    [final] ).

cnf(i_0_729,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_730,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_731,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Set_Oinsert(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X3,X1,X4),c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X3,X1,X4),X4)))
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
    | ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    cls_finite__subset__induct_4,
    [final] ).

cnf(i_0_732,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_733,axiom,
    ( c_Finite__Set_Osetsum(X2,X3,X4,X1) = c_HOL_Oplus__class_Oplus(hAPP(X2,X5),c_Finite__Set_Osetsum(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_in(X5,X3,X4)
    | ~ c_Finite__Set_Ofinite(X3,X4) ),
    cls_setsum__diff1_H_0,
    [final] ).

cnf(i_0_734,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_735,axiom,
    ( c_Finite__Set_Osetsum(X2,c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X5,tc_bool)),X5,X1) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X2,X3,X5,X1),c_Finite__Set_Osetsum(X2,X4,X5,X1),X1)
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | ~ c_lessequals(X4,X3,tc_fun(X5,tc_bool))
    | ~ c_Finite__Set_Ofinite(X3,X5) ),
    cls_setsum__diff_0,
    [final] ).

cnf(i_0_736,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_737,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_738,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_739,axiom,
    ( c_Finite__Set_Osetsum(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X5,X1) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X2,X3,X5,X1),hAPP(X2,X4),X1)
    | ~ class_Ring__and__Field_Oring(X1)
    | ~ c_in(X4,X3,X5)
    | ~ c_Finite__Set_Ofinite(X3,X5) ),
    cls_setsum__diff1__ring_0,
    [final] ).

cnf(i_0_740,axiom,
    ( c_Finite__Set_Osetsum(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X5,X1) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X2,X3,X5,X1),hAPP(X2,X4),X1)
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | ~ c_in(X4,X3,X5)
    | ~ c_Finite__Set_Ofinite(X3,X5) ),
    cls_setsum__diff1_0,
    [final] ).

cnf(i_0_741,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_742,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_743,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_744,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_745,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_746,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_627,c_0_628]),
    [final] ).

cnf(i_0_747,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_748,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_629,c_0_628]),
    [final] ).

cnf(i_0_749,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_750,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_751,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_752,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_753,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_754,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_755,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_756,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_757,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_758,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_759,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_630,c_0_628]),
    [final] ).

cnf(i_0_760,axiom,
    ( c_Finite__Set_Osetsum(X2,c_HOL_Ominus__class_Ominus(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_fun(X5,tc_bool)),X5,X1) = c_Finite__Set_Osetsum(X2,X3,X5,X1)
    | c_in(X4,X3,X5)
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | ~ c_Finite__Set_Ofinite(X3,X5) ),
    cls_setsum__diff1_1,
    [final] ).

cnf(i_0_761,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_762,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_631,c_0_628]),
    [final] ).

cnf(i_0_763,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_764,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_765,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_766,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_767,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_768,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_769,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_770,axiom,
    ( hBOOL(hAPP(hAPP(v_P,X1),c_Set_Oinsert(v_mgt(X2),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | c_in(v_sko__local__Xassms__3__1(X1,v_P,v_U,v_mgt__call),v_U,tc_Com_Opname)
    | ~ v_wt(X2) ),
    cls_assms_I3_J_0,
    [final] ).

cnf(i_0_771,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_772,axiom,
    ( c_Finite__Set_Osetsum(X2,c_Set_Oinsert(X3,X4,X5),X5,X1) = c_HOL_Oplus__class_Oplus(hAPP(X2,X3),c_Finite__Set_Osetsum(X2,X4,X5,X1),X1)
    | c_in(X3,X4,X5)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_Finite__Set_Ofinite(X4,X5) ),
    cls_setsum__insert_0,
    [final] ).

cnf(i_0_773,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_632,c_0_628]),
    [final] ).

cnf(i_0_774,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_775,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_776,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_777,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_778,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_779,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_780,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_781,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_782,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
    cls_conjecture_6,
    [final] ).

cnf(i_0_783,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_784,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_785,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_786,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_787,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_788,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X3,X1,X4),c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X3,X1,X4),X4)
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
    | ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    cls_finite__subset__induct_2,
    [final] ).

cnf(i_0_789,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_790,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_791,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_792,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_793,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_794,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_633,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_795,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_634,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_796,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_797,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_798,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_799,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_800,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_801,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_802,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_803,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_804,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_805,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_806,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_807,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_635,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_808,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_809,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_810,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X3,X1,X4)))
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
    | ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    cls_finite__subset__induct_3,
    [final] ).

cnf(i_0_811,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_812,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_813,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_814,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_815,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_816,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_817,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_818,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_819,axiom,
    ( hBOOL(hAPP(X1,X2))
    | c_in(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1(X3,X1,X4),X3,X4)
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
    | ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    cls_finite__subset__induct_1,
    [final] ).

cnf(i_0_820,axiom,
    ( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
    | ~ c_in(X5,X4,X3) ),
    cls_image__constant_0,
    [final] ).

cnf(i_0_821,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_822,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_823,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_824,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_636,c_0_628]),
    [final] ).

cnf(i_0_825,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_826,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_827,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_828,axiom,
    ( hBOOL(hAPP(X1,X2))
    | c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2(X3,X1,X4),X4)
    | ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
    | ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
    | ~ c_Finite__Set_Ofinite(X2,X4) ),
    cls_finite__subset__induct_0,
    [final] ).

cnf(i_0_829,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_830,axiom,
    ( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
    cls_image__constant__conv_1,
    [final] ).

cnf(i_0_831,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_832,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_833,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_834,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_835,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_836,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_837,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_838,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_637,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_839,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_638,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_840,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_639,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_841,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_842,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_843,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_844,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_640,c_0_628]),
    [final] ).

cnf(i_0_845,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_846,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_847,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_848,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_849,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_850,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_851,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_852,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_853,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_854,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_855,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_856,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_857,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_641,c_0_628]),
    [final] ).

cnf(i_0_858,axiom,
    ( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | c_in(X1,X4,X2) ),
    cls_vimage__const_1,
    [final] ).

cnf(i_0_859,axiom,
    c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    cls_image__constant__conv_0,
    [final] ).

cnf(i_0_860,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_861,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_862,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_863,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_864,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_865,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_866,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_867,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_868,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_869,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
    cls_insert__code_0,
    [final] ).

cnf(i_0_870,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_871,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_872,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_642,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_873,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_874,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_875,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_876,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_877,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_878,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_879,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_880,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_881,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_882,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_883,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_884,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_885,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_886,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_887,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_888,axiom,
    ( c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,X2),X3,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_setsum__0_0,
    [final] ).

cnf(i_0_889,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_890,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_643,c_0_628]),
    [final] ).

cnf(i_0_891,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_644,c_0_628]),
    [final] ).

cnf(i_0_892,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_645,c_0_628]),
    [final] ).

cnf(i_0_893,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_894,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_646,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_895,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_896,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_897,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_898,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_899,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_900,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_901,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_902,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_903,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_904,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_905,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_906,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_907,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_908,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_909,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_910,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_911,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_912,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_913,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_914,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_915,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_916,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_917,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_918,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_647,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_919,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_648,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_920,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_649,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_921,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_922,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_923,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_924,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_925,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_926,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_927,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_928,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_929,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_930,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_931,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_932,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_650,c_0_628]),
    [final] ).

cnf(i_0_933,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_934,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_651,c_0_628]),
    [final] ).

cnf(i_0_935,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_652,c_0_628]),
    [final] ).

cnf(i_0_936,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_937,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_938,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    cls_ab__semigroup__mult_Omult__ac_I1_J_0,
    [final] ).

cnf(i_0_939,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_940,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_941,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_942,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_943,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_944,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_945,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_653,c_0_628]),
    [final] ).

cnf(i_0_946,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_947,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_948,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_949,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_950,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_951,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_952,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_953,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_954,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_955,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_956,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_957,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_958,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_959,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_960,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_654,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_961,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_655,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_962,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_656,c_0_628]),
    [final] ).

cnf(i_0_963,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_657,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_964,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_658,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_965,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_966,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_967,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_968,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_969,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_970,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_971,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_972,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_973,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_974,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_975,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_976,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_977,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_978,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_979,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_980,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_981,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_982,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_659,c_0_628]),
    [final] ).

cnf(i_0_983,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_660,c_0_628]),
    [final] ).

cnf(i_0_984,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_661,c_0_628]),
    [final] ).

cnf(i_0_985,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_986,axiom,
    ( c_Finite__Set_Osetsum(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_setsum__empty_0,
    [final] ).

cnf(i_0_987,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_662,c_0_628]),
    [final] ).

cnf(i_0_988,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_663,c_0_628]),
    [final] ).

cnf(i_0_989,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_664,c_0_628]),
    [final] ).

cnf(i_0_990,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_665,c_0_628]),
    [final] ).

cnf(i_0_991,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_666,c_0_628]),
    [final] ).

cnf(i_0_992,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_993,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_994,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_995,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_667,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_996,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_997,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_998,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_999,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_1000,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_1001,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_1002,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_668,c_0_628]),c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1003,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_669,c_0_628]),c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1004,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_1005,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_1006,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_1007,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_1008,axiom,
    ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
    | ~ hBOOL(hAPP(X2,X4)) ),
    cls_insert__code_2,
    [final] ).

cnf(i_0_1009,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_1010,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_1011,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_1012,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_670,c_0_628]),
    [final] ).

cnf(i_0_1013,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_671,c_0_628]),
    [final] ).

cnf(i_0_1014,axiom,
    ( c_Finite__Set_Osetsum(X2,X3,X4,X1) = c_HOL_Ozero__class_Ozero(X1)
    | c_Finite__Set_Ofinite(X3,X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_setsum__infinite_0,
    [final] ).

cnf(i_0_1015,axiom,
    ( c_Finite__Set_Osetsum(X2,X3,X4,X1) = c_HOL_Ozero__class_Ozero(X1)
    | c_Finite__Set_Ofinite(X3,X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_setsum__def_1,
    [final] ).

cnf(i_0_1016,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_672,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1017,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_1018,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_1019,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_1020,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_1021,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_1022,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_673,c_0_628]),
    [final] ).

cnf(i_0_1023,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_674,c_0_628]),
    [final] ).

cnf(i_0_1024,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_1025,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_1026,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_1027,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_1028,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_1029,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_1030,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_1031,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_1032,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_1033,axiom,
    ( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
    cls_ab__semigroup__mult_Omult__left__commute_0,
    [final] ).

cnf(i_0_1034,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_675,c_0_628]),
    [final] ).

cnf(i_0_1035,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_676,c_0_628]),
    [final] ).

cnf(i_0_1036,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_677,c_0_628]),
    [final] ).

cnf(i_0_1037,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_1038,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_1039,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_1040,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_1041,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    cls_insert__iff_2,
    [final] ).

cnf(i_0_1042,axiom,
    ( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    cls_insertCI_0,
    [final] ).

cnf(i_0_1043,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_678,c_0_628]),
    [final] ).

cnf(i_0_1044,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_679,c_0_628]),
    [final] ).

cnf(i_0_1045,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_680,c_0_628]),
    [final] ).

cnf(i_0_1046,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_681,c_0_628]),
    [final] ).

cnf(i_0_1047,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_682,c_0_628]),
    [final] ).

cnf(i_0_1048,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_683,c_0_628]),
    [final] ).

cnf(i_0_1049,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_1050,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_1051,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_1052,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_1053,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_1054,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_1055,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    cls_insert__code_1,
    [final] ).

cnf(i_0_1056,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_1057,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_1058,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_1059,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_1060,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_1061,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_1062,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_1063,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_1064,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_1065,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_1066,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_1067,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_1068,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_1069,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_1070,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_684,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1071,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_685,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1072,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_686,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1073,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_687,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1074,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_1075,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_1076,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_1077,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_1078,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_1079,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_1080,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_1081,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_1082,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_1083,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_1084,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_1085,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_1086,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_688,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1087,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_689,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1088,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_690,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1089,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_691,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1090,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_1091,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_1092,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_1093,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_1094,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_692,c_0_628]),
    [final] ).

cnf(i_0_1095,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_693,c_0_628]),
    [final] ).

cnf(i_0_1096,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_694,c_0_628]),
    [final] ).

cnf(i_0_1097,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_695,c_0_628]),
    [final] ).

cnf(i_0_1098,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_1099,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_1100,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_1101,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_1102,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_1103,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_1104,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    cls_bot1E_0,
    [final] ).

cnf(i_0_1105,axiom,
    ( c_in(X1,X2,X3)
    | c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
    | ~ c_OrderedGroup_Oab__semigroup__mult(X4,X5) ),
    cls_ab__semigroup__mult_Ononempty__iff_2,
    [final] ).

cnf(i_0_1106,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_1107,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_1108,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_1109,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_1110,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_1111,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_1112,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_1113,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_1114,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_1115,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_1116,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_1117,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_1118,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_1119,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_1120,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_1121,axiom,
    ( hBOOL(hAPP(hAPP(v_P,X1),X2))
    | ~ c_lessequals(X2,X1,tc_fun(t_a,tc_bool)) ),
    cls_assms_I1_J_0,
    [final] ).

cnf(i_0_1122,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_1123,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_1124,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_1125,axiom,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    cls_subset__insertI_0,
    [final] ).

cnf(i_0_1126,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_696,c_0_628]),
    [final] ).

cnf(i_0_1127,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_697,c_0_628]),
    [final] ).

cnf(i_0_1128,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_698]),
    [final] ).

cnf(i_0_1129,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_1130,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_1131,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_1132,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_1133,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_1134,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_1135,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_1136,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_1137,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_1138,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_1139,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_1140,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_1141,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_1142,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_1143,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_1144,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_1145,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_1146,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_1147,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_1148,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_1149,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_699,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1150,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_700,c_0_628]),c_0_628]),
    [final] ).

cnf(i_0_1151,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_1152,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_701,c_0_628]),
    [final] ).

cnf(i_0_1153,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__antisym_0,
    [final] ).

cnf(i_0_1154,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_1155,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_1156,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_1157,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_1158,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_1159,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_emptyE_0,
    [final] ).

cnf(i_0_1160,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_empty__iff_0,
    [final] ).

cnf(i_0_1161,axiom,
    ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    cls_ex__in__conv_0,
    [final] ).

cnf(i_0_1162,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_702,c_0_628]),
    [final] ).

cnf(i_0_1163,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_703,c_0_628]),
    [final] ).

cnf(i_0_1164,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_704,c_0_628]),
    [final] ).

cnf(i_0_1165,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_705,c_0_628]),
    [final] ).

cnf(i_0_1166,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_706,c_0_628]),
    [final] ).

cnf(i_0_1167,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    cls_insertCI_1,
    [final] ).

cnf(i_0_1168,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    cls_insertI1_0,
    [final] ).

cnf(i_0_1169,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    cls_insert__iff_1,
    [final] ).

cnf(i_0_1170,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_1171,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_1172,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_1173,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_1174,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_1175,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
    cls_diff__le__self_0,
    [final] ).

cnf(i_0_1176,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    cls_le__add1_0,
    [final] ).

cnf(i_0_1177,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    cls_le__iff__add_1,
    [final] ).

cnf(i_0_1178,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    cls_le__add2_0,
    [final] ).

cnf(i_0_1179,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_1180,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_1181,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_1182,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_1183,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_1184,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_1185,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_1186,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_1187,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_1188,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_1189,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_1190,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_1191,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_1192,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_1193,axiom,
    ( c_Set_Oinsert(X1,X2,X3) = X2
    | ~ c_in(X1,X2,X3) ),
    cls_insert__absorb_0,
    [final] ).

cnf(i_0_1194,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_1195,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_1196,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_1197,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_1198,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_1199,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_1200,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_1201,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_1202,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_1203,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_1204,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_1205,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_1206,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_1207,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_1208,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
    cls_psubset__eq_1,
    [final] ).

cnf(i_0_1209,axiom,
    hAPP(c_COMBK(X1,X2,X3),X4) = X1,
    cls_COMBK__def_0,
    [final] ).

cnf(i_0_1210,axiom,
    ( v_wt(c_Option_Othe(c_Com_Obody(X1),tc_Com_Ocom))
    | ~ c_in(X1,v_U,tc_Com_Opname) ),
    cls_assms_I4_J_0,
    [final] ).

cnf(i_0_1211,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_1212,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_1213,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_1214,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_1215,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_1216,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__linear_0,
    [final] ).

cnf(i_0_1217,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_1218,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_1219,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_1220,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_1221,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,X1,X3) ),
    cls_mem__def_0,
    [final] ).

cnf(i_0_1222,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_1223,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_1224,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_1225,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_1226,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_1227,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_707,c_0_628]),
    [final] ).

cnf(i_0_1228,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_1229,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_1230,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_1231,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_1232,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    cls_nat__le__linear_0,
    [final] ).

cnf(i_0_1233,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_1234,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_1235,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_1236,axiom,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
    cls_ab__semigroup__mult_Omult__commute_0,
    [final] ).

cnf(i_0_1237,axiom,
    ( c_in(X1,X2,X3)
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_mem__def_1,
    [final] ).

cnf(i_0_1238,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_1239,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_1240,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_1241,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_1242,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__neq__iff_1,
    [final] ).

cnf(i_0_1243,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__irrefl_0,
    [final] ).

cnf(i_0_1244,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__le_1,
    [final] ).

cnf(i_0_1245,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_1246,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_1247,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_708,c_0_628]),
    [final] ).

cnf(i_0_1248,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_709,c_0_628]),
    [final] ).

cnf(i_0_1249,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_710,c_0_628]),
    [final] ).

cnf(i_0_1250,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_711,c_0_628]),
    [final] ).

cnf(i_0_1251,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_1252,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_1253,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(rw,[status(thm)],[i_0_712,c_0_628]),
    [final] ).

cnf(i_0_1254,plain,
    X1 != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_713,c_0_628]),
    [final] ).

cnf(i_0_1255,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_1256,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_1257,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_not__less0_0,
    [final] ).

cnf(i_0_1258,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_1259,axiom,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0,
    [final] ).

cnf(i_0_1260,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_less__not__refl_0,
    [final] ).

cnf(i_0_1261,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_nat__less__le_1,
    [final] ).

cnf(i_0_1262,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_1263,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_subset__refl_0,
    [final] ).

cnf(i_0_1264,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_equalityE_0,
    [final] ).

cnf(i_0_1265,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_1266,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_1267,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_1268,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_1269,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_1270,negated_conjecture,
    c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
    cls_conjecture_5,
    [final] ).

cnf(i_0_1271,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_1272,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_1273,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_1274,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_1275,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_1276,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_1277,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_1278,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_1279,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_1280,axiom,
    ( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
    | ~ class_Orderings_Obot(X1) ),
    cls_bot__least_0,
    [final] ).

cnf(i_0_1281,axiom,
    c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
    cls_finite_OemptyI_0,
    [final] ).

cnf(i_0_1282,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_1283,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_1284,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_1285,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    cls_order__eq__refl_0,
    [final] ).

cnf(i_0_1286,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_order__eq__iff_0,
    [final] ).

cnf(i_0_1287,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_1288,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_714,c_0_628]),
    [final] ).

cnf(i_0_1289,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_1290,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_1291,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_1292,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_1293,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_1294,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_1295,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_1296,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    cls_le0_0,
    [final] ).

cnf(i_0_1297,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_1298,axiom,
    c_fequal(X1,X1,X2),
    cls_ATP__Linkup_Oequal__imp__fequal_0,
    [final] ).

cnf(i_0_1299,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_1300,axiom,
    c_lessequals(X1,X1,tc_nat),
    cls_eq__imp__le_0,
    [final] ).

cnf(i_0_1301,axiom,
    c_lessequals(X1,X1,tc_nat),
    cls_le__refl_0,
    [final] ).

cnf(i_0_1302,negated_conjecture,
    c_in(v_pn,v_U,tc_Com_Opname),
    cls_conjecture_4,
    [final] ).

cnf(i_0_1303,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_1304,axiom,
    ( class_Orderings_Obot(tc_fun(X1,X2))
    | ~ class_Orderings_Obot(X2) ),
    clsarity_fun__Orderings_Obot,
    [final] ).

cnf(i_0_1305,axiom,
    ( class_HOL_Oord(tc_fun(X1,X2))
    | ~ class_HOL_Oord(X2) ),
    clsarity_fun__HOL_Oord,
    [final] ).

cnf(i_0_1306,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_1307,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_1308,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_1309,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_1310,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_1311,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_1312,axiom,
    ( c_Finite__Set_Ofinite(X2,X1)
    | ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
    cls_finite_0,
    [final] ).

cnf(i_0_1313,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_1314,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_1315,negated_conjecture,
    c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
    cls_conjecture_0,
    [final] ).

cnf(i_0_1316,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    clsarity_bool__Finite__Set_Ofinite_Ofinite,
    [final] ).

cnf(i_0_1317,axiom,
    class_Orderings_Obot(tc_bool),
    clsarity_bool__Orderings_Obot,
    [final] ).

cnf(i_0_1318,axiom,
    class_Orderings_Obot(tc_nat),
    clsarity_nat__Orderings_Obot,
    [final] ).

cnf(i_0_1319,axiom,
    class_HOL_Oord(tc_bool),
    clsarity_bool__HOL_Oord,
    [final] ).

cnf(i_0_1320,axiom,
    class_HOL_Oord(tc_nat),
    clsarity_nat__HOL_Oord,
    [final] ).

cnf(i_0_1321,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,
    [final] ).

cnf(i_0_1322,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    clsarity_bool__Complete__Lattice_Ocomplete__lattice,
    [final] ).

cnf(i_0_1323,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1324,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__add,
    [final] ).

cnf(i_0_1325,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
    [final] ).

cnf(i_0_1326,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1327,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Osemiring__1,
    [final] ).

cnf(i_0_1328,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_1329,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    clsarity_nat__Ring__and__Field_Ozero__neq__one,
    [final] ).

cnf(i_0_1330,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semidom,
    [final] ).

cnf(i_0_1331,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    clsarity_nat__Nat_Osemiring__char__0,
    [final] ).

cnf(i_0_1332,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    [final] ).

cnf(i_0_1333,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
    [final] ).

cnf(i_0_1334,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_1335,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_1336,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_1337,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_1338,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
    [final] ).

cnf(i_0_1339,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__add,
    [final] ).

cnf(i_0_1340,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__add,
    [final] ).

cnf(i_0_1341,axiom,
    X1 = X1 ).

cnf(i_0_1342,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1343,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1344,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_1345,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_1346,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_1347,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_1348,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).

cnf(i_0_1349,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).

cnf(i_0_1350,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1351,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1352,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1353,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X1,X3,X4,X5) = c_Finite__Set_Osetsum(X2,X3,X4,X5) ) ).

cnf(i_0_1354,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X1,X4,X5) = c_Finite__Set_Osetsum(X3,X2,X4,X5) ) ).

cnf(i_0_1355,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X4,X1,X5) = c_Finite__Set_Osetsum(X3,X4,X2,X5) ) ).

cnf(i_0_1356,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X4,X5,X1) = c_Finite__Set_Osetsum(X3,X4,X5,X2) ) ).

cnf(i_0_1357,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_1358,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_1359,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_1360,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_1361,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_1362,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_1363,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_1364,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_1365,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1366,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_1367,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_1368,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_1369,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_1370,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_1371,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_1372,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1373,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1374,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1375,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1376,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1377,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1378,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1379,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1380,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1381,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Oring(X2) ) ).

cnf(i_0_1382,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1383,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1384,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1385,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1386,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1387,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1388,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_1389,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_1390,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3)
    | c_OrderedGroup_Oab__semigroup__mult(X2,X3) ) ).

cnf(i_0_1391,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X3,X1)
    | c_OrderedGroup_Oab__semigroup__mult(X3,X2) ) ).

cnf(i_0_1392,axiom,
    ( X1 != X2
    | ~ c_in(X1,X3,X4)
    | c_in(X2,X3,X4) ) ).

cnf(i_0_1393,axiom,
    ( X1 != X2
    | ~ c_in(X3,X1,X4)
    | c_in(X3,X2,X4) ) ).

cnf(i_0_1394,axiom,
    ( X1 != X2
    | ~ c_in(X3,X4,X1)
    | c_in(X3,X4,X2) ) ).

cnf(i_0_1395,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1396,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_1397,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_1398,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Oring__1(X2) ) ).

cnf(i_0_1399,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1400,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1401,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1402,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_1403,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1404,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_1405,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1406,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_1407,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1408,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1409,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1410,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_1411,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_1412,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_1413,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_1414,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1415,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_1416,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_1417,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_1418,axiom,
    ( X1 != X2
    | ~ v_wt(X1)
    | v_wt(X2) ) ).

cnf(i_0_1419,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_1420,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_1421,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_1422,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1423,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1424,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_1425,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_1426,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_1427,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_1428,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1429,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1341_001,axiom,
    X1 = X1 ).

cnf(i_0_1342_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1343_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1344_004,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_1345_005,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_1346_006,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_1347_007,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_1348_008,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).

cnf(i_0_1349_009,axiom,
    ( X1 != X2
    | c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).

cnf(i_0_1350_010,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1351_011,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1352_012,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1353_013,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X1,X3,X4,X5) = c_Finite__Set_Osetsum(X2,X3,X4,X5) ) ).

cnf(i_0_1354_014,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X1,X4,X5) = c_Finite__Set_Osetsum(X3,X2,X4,X5) ) ).

cnf(i_0_1355_015,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X4,X1,X5) = c_Finite__Set_Osetsum(X3,X4,X2,X5) ) ).

cnf(i_0_1356_016,axiom,
    ( X1 != X2
    | c_Finite__Set_Osetsum(X3,X4,X5,X1) = c_Finite__Set_Osetsum(X3,X4,X5,X2) ) ).

cnf(i_0_1357_017,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_1358_018,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_1359_019,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_1360_020,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).

cnf(i_0_1361_021,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).

cnf(i_0_1362_022,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).

cnf(i_0_1363_023,axiom,
    ( X1 != X2
    | c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).

cnf(i_0_1364_024,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_1365_025,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1366_026,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_1367_027,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_1368_028,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X1,X3) = c_Finite__Set_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_1369_029,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMax(X3,X1) = c_Finite__Set_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_1370_030,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X1,X3) = c_Finite__Set_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_1371_031,axiom,
    ( X1 != X2
    | c_Finite__Set_Olinorder__class_OMin(X3,X1) = c_Finite__Set_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_1372_032,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1373_033,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1374_034,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).

cnf(i_0_1375_035,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).

cnf(i_0_1376_036,axiom,
    ( X1 != X2
    | c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).

cnf(i_0_1377_037,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_1378_038,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1379_039,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1380_040,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1381_041,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Oring(X2) ) ).

cnf(i_0_1382_042,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1383_043,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1384_044,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1385_045,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1386_046,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1387_047,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1388_048,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_1389_049,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_1390_050,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3)
    | c_OrderedGroup_Oab__semigroup__mult(X2,X3) ) ).

cnf(i_0_1391_051,axiom,
    ( X1 != X2
    | ~ c_OrderedGroup_Oab__semigroup__mult(X3,X1)
    | c_OrderedGroup_Oab__semigroup__mult(X3,X2) ) ).

cnf(i_0_1392_052,axiom,
    ( X1 != X2
    | ~ c_in(X1,X3,X4)
    | c_in(X2,X3,X4) ) ).

cnf(i_0_1393_053,axiom,
    ( X1 != X2
    | ~ c_in(X3,X1,X4)
    | c_in(X3,X2,X4) ) ).

cnf(i_0_1394_054,axiom,
    ( X1 != X2
    | ~ c_in(X3,X4,X1)
    | c_in(X3,X4,X2) ) ).

cnf(i_0_1395_055,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1396_056,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_1397_057,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_1398_058,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Oring__1(X2) ) ).

cnf(i_0_1399_059,axiom,
    ( X1 != X2
    | ~ class_HOL_Oord(X1)
    | class_HOL_Oord(X2) ) ).

cnf(i_0_1400_060,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1401_061,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1402_062,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_1403_063,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_1404_064,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_1405_065,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1406_066,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_1407_067,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1408_068,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1409_069,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1410_070,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_1411_071,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_1412_072,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_1413_073,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_1414_074,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_1415_075,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_1416_076,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | class_Finite__Set_Ofinite_Ofinite(X2) ) ).

cnf(i_0_1417_077,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_1418_078,axiom,
    ( X1 != X2
    | ~ v_wt(X1)
    | v_wt(X2) ) ).

cnf(i_0_1419_079,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_1420_080,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_1421_081,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_1422_082,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X1,X3)
    | c_Finite__Set_Ofinite(X2,X3) ) ).

cnf(i_0_1423_083,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofinite(X3,X1)
    | c_Finite__Set_Ofinite(X3,X2) ) ).

cnf(i_0_1424_084,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_1425_085,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_1426_086,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_1427_087,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_1428_088,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1429_089,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1430,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[783]) ).

cnf(i_0_1431,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[784]) ).

cnf(i_0_1432,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[785]) ).

cnf(i_0_1433,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[786]) ).

cnf(i_0_1434,plain,
    ( ~ c_in(X1,X2,X3)
    | X1 = X1
    | ~ c_Fun_Oinj__on(X4,X2,X3,X5)
    | ~ c_in(X1,X2,X3) ),
    inference(equality_inference,[],[816]) ).

cnf(i_0_1435,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,[],[878]) ).

cnf(i_0_1436,plain,
    ( X1 = X1
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(equality_inference,[],[936]) ).

cnf(i_0_1437,plain,
    X1 = X1,
    inference(equality_inference,[],[937]) ).

cnf(i_0_1438,plain,
    ( 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_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,[],[1002]) ).

cnf(i_0_1439,plain,
    ( 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_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,[],[1003]) ).

cnf(i_0_1440,plain,
    ( X1 = X1
    | c_in(X2,X1,X3)
    | c_in(X2,X1,X3) ),
    inference(equality_inference,[],[1011]) ).

cnf(i_0_1441,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,[],[1070]) ).

cnf(i_0_1442,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,[],[1071]) ).

cnf(i_0_1443,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,[],[1072]) ).

cnf(i_0_1444,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,[],[1073]) ).

cnf(i_0_1445,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[1124]) ).

cnf(i_0_1446,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,[],[1126]) ).

cnf(i_0_1447,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,[],[1127]) ).

cnf(i_0_1448,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1136]) ).

cnf(i_0_1449,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1137]) ).

cnf(i_0_1450,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1138]) ).

cnf(i_0_1451,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1139]) ).

cnf(i_0_1452,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[1140]) ).

cnf(i_0_1453,plain,
    X1 = X1,
    inference(equality_inference,[],[1156]) ).

cnf(i_0_1454,plain,
    X1 = X1,
    inference(equality_inference,[],[1158]) ).

cnf(i_0_1455,plain,
    ( X1 = X1
    | ~ class_Nat_Osemiring__char__0(X2) ),
    inference(equality_inference,[],[1299]) ).

cnf(i_0_1456,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_818,i_0_756]) ).

cnf(i_0_1457,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_756]) ).

cnf(i_0_1458,plain,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X4),
    inference(scs_inference,[],[i_0_818,i_0_1055,i_0_756,i_0_1237]) ).

cnf(i_0_1459,plain,
    ( ~ hBOOL(hAPP(X1,X2))
    | c_in(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_1237]) ).

cnf(i_0_1460,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_818,i_0_1206,i_0_1055,i_0_756,i_0_1237,i_0_1259]) ).

cnf(i_0_1461,plain,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    inference(rename_variables,[],[i_0_1259]) ).

cnf(i_0_1462,plain,
    c_lessequals(X1,X1,tc_bool),
    inference(scs_inference,[],[i_0_818,i_0_1334,i_0_1206,i_0_1055,i_0_756,i_0_1237,i_0_1259,i_0_1285]) ).

cnf(i_0_1463,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | c_lessequals(X2,X2,X1) ),
    inference(rename_variables,[],[i_0_1285]) ).

cnf(i_0_1464,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_759,i_0_818,i_0_1334,i_0_1206,i_0_1055,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342]) ).

cnf(i_0_1465,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_759,i_0_818,i_0_1334,i_0_1206,i_0_1055,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734]) ).

cnf(i_0_1466,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
    inference(rename_variables,[],[i_0_1104]) ).

cnf(i_0_1467,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    inference(rename_variables,[],[i_0_734]) ).

cnf(i_0_1468,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_759,i_0_818,i_0_1334,i_0_1206,i_0_1055,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757]) ).

cnf(i_0_1469,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_757]) ).

cnf(i_0_1470,plain,
    hBOOL(hAPP(c_Set_Ovimage(X1,c_Set_Oinsert(hAPP(X1,X2),X3,X4),X5,X6),X2)),
    inference(scs_inference,[],[i_0_759,i_0_818,i_0_1334,i_0_1206,i_0_1055,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761]) ).

cnf(i_0_1471,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    inference(rename_variables,[],[i_0_1055]) ).

cnf(i_0_1472,plain,
    ( ~ hBOOL(hAPP(X1,hAPP(X2,X3)))
    | hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
    inference(rename_variables,[],[i_0_761]) ).

cnf(i_0_1473,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_759,i_0_818,i_0_1334,i_0_1206,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769]) ).

cnf(i_0_1474,plain,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    inference(rename_variables,[],[i_0_1055]) ).

cnf(i_0_1475,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_769]) ).

cnf(i_0_1476,plain,
    c_in(v_pn,c_Set_Ovimage(v_mgt__call,v_G,X1,t_a),X1),
    inference(scs_inference,[],[i_0_759,i_0_818,i_0_1270,i_0_1334,i_0_1206,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801]) ).

cnf(i_0_1477,plain,
    ( ~ c_in(hAPP(X1,X2),X3,X4)
    | c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5) ),
    inference(rename_variables,[],[i_0_801]) ).

cnf(i_0_1478,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_759,i_0_818,i_0_1270,i_0_1334,i_0_1206,i_0_891,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839]) ).

cnf(i_0_1479,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_891]) ).

cnf(i_0_1480,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_839]) ).

cnf(i_0_1481,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_759,i_0_818,i_0_1270,i_0_1301,i_0_1334,i_0_1206,i_0_891,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874]) ).

cnf(i_0_1482,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_1301]) ).

cnf(i_0_1483,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_874]) ).

cnf(i_0_1484,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_759,i_0_818,i_0_1270,i_0_1301,i_0_1482,i_0_1334,i_0_1206,i_0_891,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876]) ).

cnf(i_0_1485,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_1301]) ).

cnf(i_0_1486,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_876]) ).

cnf(i_0_1487,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_759,i_0_818,i_0_1270,i_0_1301,i_0_1482,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877]) ).

cnf(i_0_1488,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_1166]) ).

cnf(i_0_1489,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_877]) ).

cnf(i_0_1490,plain,
    c_in(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),X4),
    inference(scs_inference,[],[i_0_759,i_0_818,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925]) ).

cnf(i_0_1491,plain,
    c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
    inference(rename_variables,[],[i_0_1125]) ).

cnf(i_0_1492,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_925]) ).

cnf(i_0_1493,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934]) ).

cnf(i_0_1494,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_934]) ).

cnf(i_0_1495,plain,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1023,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935]) ).

cnf(i_0_1496,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_935]) ).

cnf(i_0_1497,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1023,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989]) ).

cnf(i_0_1498,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_989]) ).

cnf(i_0_1499,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1023,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997]) ).

cnf(i_0_1500,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_997]) ).

cnf(i_0_1501,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1023,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998]) ).

cnf(i_0_1502,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_998]) ).

cnf(i_0_1503,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999]) ).

cnf(i_0_1504,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_891]) ).

cnf(i_0_1505,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_999]) ).

cnf(i_0_1506,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047]) ).

cnf(i_0_1507,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    inference(rename_variables,[],[i_0_1049]) ).

cnf(i_0_1508,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_1047]) ).

cnf(i_0_1509,plain,
    ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1248,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056]) ).

cnf(i_0_1510,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_1248]) ).

cnf(i_0_1511,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_1056]) ).

cnf(i_0_1512,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1334,i_0_1206,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1248,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061]) ).

cnf(i_0_1513,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_1061]) ).

cnf(i_0_1514,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1334,i_0_1206,i_0_1034,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1248,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063]) ).

cnf(i_0_1515,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_1034]) ).

cnf(i_0_1516,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_1063]) ).

cnf(i_0_1517,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1334,i_0_1206,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1248,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065]) ).

cnf(i_0_1518,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_1034]) ).

cnf(i_0_1519,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_1065]) ).

cnf(i_0_1520,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1334,i_0_1206,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1248,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067]) ).

cnf(i_0_1521,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    inference(rename_variables,[],[i_0_1049]) ).

cnf(i_0_1522,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_1067]) ).

cnf(i_0_1523,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1334,i_0_1206,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1248,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069]) ).

cnf(i_0_1524,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    inference(rename_variables,[],[i_0_1049]) ).

cnf(i_0_1525,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_1069]) ).

cnf(i_0_1526,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1248,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084]) ).

cnf(i_0_1527,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_1084]) ).

cnf(i_0_1528,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_759,i_0_818,i_0_762,i_0_1270,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1248,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097]) ).

cnf(i_0_1529,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
    inference(rename_variables,[],[i_0_1050]) ).

cnf(i_0_1530,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_1097]) ).

cnf(i_0_1531,plain,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),v_G,tc_fun(t_a,tc_bool)),
    inference(scs_inference,[],[i_0_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1248,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121]) ).

cnf(i_0_1532,plain,
    ( hBOOL(hAPP(hAPP(v_P,X1),X2))
    | ~ c_lessequals(X2,X1,tc_fun(t_a,tc_bool)) ),
    inference(rename_variables,[],[i_0_1121]) ).

cnf(i_0_1533,plain,
    ~ class_OrderedGroup_Ogroup__add(tc_nat),
    inference(scs_inference,[],[i_0_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155]) ).

cnf(i_0_1534,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_1248]) ).

cnf(i_0_1535,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_1155]) ).

cnf(i_0_1536,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_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1173,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194]) ).

cnf(i_0_1537,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
    inference(rename_variables,[],[i_0_1173]) ).

cnf(i_0_1538,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_1194]) ).

cnf(i_0_1539,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_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1504,i_0_1173,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194,i_0_1202]) ).

cnf(i_0_1540,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(rename_variables,[],[i_0_1202]) ).

cnf(i_0_1541,plain,
    ~ c_in(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),hAPP(v_P,v_G),X1),
    inference(scs_inference,[],[i_0_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1504,i_0_1173,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194,i_0_1202,i_0_1221]) ).

cnf(i_0_1542,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_1221]) ).

cnf(i_0_1543,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_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1504,i_0_1173,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194,i_0_1202,i_0_1221,i_0_1232]) ).

cnf(i_0_1544,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1232]) ).

cnf(i_0_1545,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_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1504,i_0_1173,i_0_1253,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194,i_0_1202,i_0_1221,i_0_1232,i_0_1255]) ).

cnf(i_0_1546,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(rename_variables,[],[i_0_1253]) ).

cnf(i_0_1547,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
    inference(rename_variables,[],[i_0_1255]) ).

cnf(i_0_1548,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_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1504,i_0_1173,i_0_1253,i_0_1546,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194,i_0_1202,i_0_1221,i_0_1232,i_0_1255,i_0_1256]) ).

cnf(i_0_1549,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(rename_variables,[],[i_0_1253]) ).

cnf(i_0_1550,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
    inference(rename_variables,[],[i_0_1256]) ).

cnf(i_0_1551,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_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1504,i_0_1173,i_0_1253,i_0_1546,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194,i_0_1202,i_0_1221,i_0_1232,i_0_1255,i_0_1256,i_0_1289]) ).

cnf(i_0_1552,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_1289]) ).

cnf(i_0_1553,plain,
    c_Finite__Set_Ofinite(X1,tc_bool),
    inference(scs_inference,[],[i_0_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1316,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1504,i_0_1173,i_0_1253,i_0_1546,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194,i_0_1202,i_0_1221,i_0_1232,i_0_1255,i_0_1256,i_0_1289,i_0_1312]) ).

cnf(i_0_1554,plain,
    ( ~ class_Finite__Set_Ofinite_Ofinite(X1)
    | c_Finite__Set_Ofinite(X2,X1) ),
    inference(rename_variables,[],[i_0_1312]) ).

cnf(i_0_1555,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_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1264,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1316,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1504,i_0_1173,i_0_1253,i_0_1546,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194,i_0_1202,i_0_1221,i_0_1232,i_0_1255,i_0_1256,i_0_1289,i_0_1312,i_0_720]) ).

cnf(i_0_1556,plain,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    inference(rename_variables,[],[i_0_1264]) ).

cnf(i_0_1557,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_720]) ).

cnf(i_0_1558,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_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1264,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1316,i_0_1332,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1504,i_0_1173,i_0_1253,i_0_1546,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194,i_0_1202,i_0_1221,i_0_1232,i_0_1255,i_0_1256,i_0_1289,i_0_1312,i_0_720,i_0_834]) ).

cnf(i_0_1559,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_834]) ).

cnf(i_0_1560,plain,
    $false,
    inference(scs_inference,[],[i_0_759,i_0_818,i_0_762,i_0_1270,i_0_782,i_0_1264,i_0_1205,i_0_1301,i_0_1482,i_0_1125,i_0_1049,i_0_1507,i_0_1521,i_0_1050,i_0_1316,i_0_1332,i_0_1334,i_0_1206,i_0_1207,i_0_1034,i_0_1515,i_0_1166,i_0_891,i_0_1479,i_0_1504,i_0_1173,i_0_1253,i_0_1546,i_0_1023,i_0_1248,i_0_1510,i_0_1055,i_0_1471,i_0_1104,i_0_756,i_0_1237,i_0_1259,i_0_1285,i_0_1342,i_0_734,i_0_757,i_0_761,i_0_769,i_0_801,i_0_839,i_0_874,i_0_876,i_0_877,i_0_925,i_0_934,i_0_935,i_0_989,i_0_997,i_0_998,i_0_999,i_0_1047,i_0_1056,i_0_1061,i_0_1063,i_0_1065,i_0_1067,i_0_1069,i_0_1084,i_0_1097,i_0_1121,i_0_1155,i_0_1194,i_0_1202,i_0_1221,i_0_1232,i_0_1255,i_0_1256,i_0_1289,i_0_1312,i_0_720,i_0_834,i_0_884]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV882-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33  % Computer : n015.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Tue May  5 06:06:47 EDT 2026
% 0.14/0.33  % CPUTime    : 
% 0.14/0.34  % start to proof: theBenchmark
% 1.06/1.67  % Version  : CSE_E---1.7
% 1.06/1.67  % Problem  : theBenchmark.p
% 1.06/1.67  % SZS status Unsatisfiable for theBenchmark.p
% 1.06/1.67  % SZS output start CNFRefutation
% See solution above
% 1.61/2.22  % Total time : 1.326s
%------------------------------------------------------------------------------