CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : LCL755-1 : 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 : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  5 04:44:56 PM UTC 2026

% Result   : Unsatisfiable 1.45s 2.67s
% Output   : CNFRefutation 1.50s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_756)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_conjecture_2,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

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_Suc__mult__less__cancel1_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).

cnf(cls_Suc__mult__le__cancel1_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).

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

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

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

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

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

cnf(cls_Suc__mult__le__cancel1_1,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).

cnf(cls_diff__Suc__diff__eq2_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/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_n__less__n__mult__m_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).

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

cnf(cls_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_one__le__mult__iff_0,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).

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

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

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

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

cnf(cls_Suc__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__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__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_Suc__times__mod__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).

cnf(cls_lift__lift_0,axiom,
    ( c_Lambda_Olift(c_Lambda_Olift(X1,X2),c_Suc(X3)) = c_Lambda_Olift(c_Lambda_Olift(X1,X3),X2)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_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_min__Suc__Suc_0,axiom,
    c_Orderings_Oord__class_Omin(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X1,X2,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).

cnf(cls_max__Suc__Suc_0,axiom,
    c_Orderings_Oord__class_Omax(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X1,X2,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).

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

cnf(cls_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__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__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__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__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_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_mult__eq__1__iff_2,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).

cnf(cls_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_mult__Suc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).

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

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

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

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

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

cnf(cls_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__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__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_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__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__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_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_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_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_mult__eq__1__iff_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).

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

cnf(cls_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_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_mod__1_0,axiom,
    c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).

cnf(cls_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_nat__less__add__iff1_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_min__max_Odistrib__inf__le_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),c_Orderings_Oord__class_Omin(X2,X4,X1),X1),c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).

cnf(cls_min__max_Odistrib__sup__le_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),c_Orderings_Oord__class_Omax(X2,X4,X1),X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_mod__diff__cong_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X4,X1),X3,X1)
    | ~ class_Divides_Oring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
    | c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).

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

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

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

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

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

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

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

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

cnf(cls_mult__mono_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_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_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_sum__squares__gt__zero__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

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

cnf(cls_sum__squares__ge__zero_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).

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

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

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

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

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

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

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

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

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

cnf(cls_mult__le__cancel__left__pos_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

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

cnf(cls_mult__le__cancel__left__neg_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).

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

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

cnf(cls_nat__mult__le__cancel1_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_0) ).

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

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

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

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

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

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

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

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

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

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

cnf(cls_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_zmod__simps_I4_J_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_natgb_Oadd__mul__solve_1,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_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__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_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_natgb_Oadd__scale__eq__noteq_0,axiom,
    ( X3 = X4
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).

cnf(cls_le__diff__conv2_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/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_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_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_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_mult__less__cancel1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).

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

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

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

cnf(cls_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_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_mult__strict__left__mono__comm_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_subst__Abs_0,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_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__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_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__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__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_sum__squares__eq__zero__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

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

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

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

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

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

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

cnf(cls_min__diff__distrib__left_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).

cnf(cls_max__diff__distrib__left_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).

cnf(cls_min__add__distrib__left_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).

cnf(cls_max__add__distrib__left_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).

cnf(cls_min__max_Oinf__sup__distrib2_0,axiom,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X4,X1),c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).

cnf(cls_min__max_Osup__inf__distrib2_0,axiom,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X4,X1),c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).

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

cnf(cls_min__max_Oinf__sup__distrib1_0,axiom,
    ( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),c_Orderings_Oord__class_Omin(X2,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).

cnf(cls_min__max_Osup__inf__distrib1_0,axiom,
    ( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),c_Orderings_Oord__class_Omax(X2,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).

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

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

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

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

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

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

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

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

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

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_mult__le__mono_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X4,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono_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_zero__less__mult__pos2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

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

cnf(cls_min__diff_0,axiom,
    c_Orderings_Oord__class_Omin(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(c_Orderings_Oord__class_Omin(X1,X3,tc_nat),X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff_0) ).

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

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

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

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

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

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

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

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_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_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_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_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_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_mult__le__0__iff_1,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).

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

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

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

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

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

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

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

cnf(cls_min__less__iff__disj_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X2,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).

cnf(cls_min__le__iff__disj_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X4,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_Orderings_Oord__class_Omin(X4,X2,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).

cnf(cls_less__max__iff__disj_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).

cnf(cls_le__max__iff__disj_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).

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

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

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

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

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

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

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

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

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

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

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__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__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__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_less__1__mult_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

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

cnf(cls_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__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__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_mult__nonneg__nonneg_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

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

cnf(cls_split__mult__pos__le_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_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_mult__neg__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

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

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

cnf(cls_mult__nonpos__nonpos_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_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_le__cube_0,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).

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_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__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_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__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_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_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_mult__le__cancel1_2,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).

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

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

cnf(cls_mult__le__mono1_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono1_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_class__semiring_Osemiring__rules_I2_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

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

cnf(cls_max__less__iff__conj_2,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).

cnf(cls_min__max_Ole__supI_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).

cnf(cls_min__max_Osup__least_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).

cnf(cls_min__max_Ole__sup__iff_2,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).

cnf(cls_min__less__iff__conj_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).

cnf(cls_min__max_Oinf__greatest_0,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).

cnf(cls_min__max_Ole__inf__iff_2,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).

cnf(cls_min__max_Ole__infI_0,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).

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

cnf(cls_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_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__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_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_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_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_class__semiring_Osemiring__rules_I16_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

cnf(cls_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_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

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

cnf(cls_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_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_min__max_Oinf__assoc_0,axiom,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).

cnf(cls_min__max_Osup__assoc_0,axiom,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).

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

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

cnf(cls_class__semiring_Osemiring__rules_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_I19_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

cnf(cls_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_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_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_min__max_Oinf__left__commute_0,axiom,
    ( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X2,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).

cnf(cls_min__max_Osup__left__commute_0,axiom,
    ( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X2,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).

cnf(cls_lem0_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem0_0) ).

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

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_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__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_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_mult__le__cancel1_1,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).

cnf(cls_mult__le__cancel2_1,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).

cnf(cls_max__less__iff__conj_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).

cnf(cls_max__less__iff__conj_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).

cnf(cls_min__max_Ole__supE_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).

cnf(cls_min__max_Ole__sup__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).

cnf(cls_min__max_Ole__supE_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).

cnf(cls_min__max_Ole__sup__iff_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).

cnf(cls_min__less__iff__conj_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).

cnf(cls_min__less__iff__conj_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).

cnf(cls_min__max_Ole__infE_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).

cnf(cls_min__max_Ole__inf__iff_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).

cnf(cls_min__max_Ole__infE_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).

cnf(cls_min__max_Ole__inf__iff_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).

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_nat__mult__assoc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).

cnf(cls_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_nat__0__less__mult__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

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

cnf(cls_subst__App_0,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OApp(X1,X2),X3,X4) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_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__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_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__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_le__mod__geq_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).

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

cnf(cls_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_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_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_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_lift_Osimps_I3_J_0,axiom,
    c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X2) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).

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

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_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_subst__gt_0,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).

cnf(cls_subst__Var_0,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_0) ).

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

cnf(cls_min__less__iff__disj_1,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).

cnf(cls_min__max_Oless__infI1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).

cnf(cls_min__less__iff__disj_2,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).

cnf(cls_min__max_Oless__infI2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).

cnf(cls_min__max_Ole__infI1_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).

cnf(cls_min__le__iff__disj_1,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).

cnf(cls_min__max_Ole__infI2_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).

cnf(cls_min__le__iff__disj_2,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).

cnf(cls_less__max__iff__disj_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).

cnf(cls_min__max_Oless__supI1_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).

cnf(cls_less__max__iff__disj_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).

cnf(cls_min__max_Oless__supI2_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).

cnf(cls_min__max_Ole__supI1_0,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).

cnf(cls_le__max__iff__disj_1,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).

cnf(cls_min__max_Ole__supI2_0,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).

cnf(cls_le__max__iff__disj_2,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).

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

cnf(cls_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_class__semiring_Osemiring__rules_I4_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

cnf(cls_not__add__less1_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    file('/export/starexec/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_mod__less__divisor_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).

cnf(cls_mod__le__divisor_0,axiom,
    ( c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_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_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_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_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_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_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_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_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_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_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__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_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__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_mod__mod__trivial_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).

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

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

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

cnf(cls_min__max_Oinf__left__idem_0,axiom,
    ( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X2,X3,X1),X1) = c_Orderings_Oord__class_Omin(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).

cnf(cls_min__max_Osup__left__idem_0,axiom,
    ( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1) = c_Orderings_Oord__class_Omax(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).

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

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_nat__minus__add__max_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = c_Orderings_Oord__class_Omax(X1,X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__minus__add__max_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_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_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_lift_Osimps_I1_J_1,axiom,
    ( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).

cnf(cls_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_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__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_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_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_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_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_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_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__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_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_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_zero__le__square_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

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

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

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

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

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

cnf(cls_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_min__max_Oinf__sup__absorb_0,axiom,
    ( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).

cnf(cls_min__max_Osup__inf__absorb_0,axiom,
    ( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X2,X3,X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).

cnf(cls_min__max_Oinf__le1_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).

cnf(cls_min__max_Oinf__le2_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).

cnf(cls_le__maxI1_0,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).

cnf(cls_le__maxI2_0,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X2,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_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_beta_0,axiom,
    c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X1),X2),c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

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

cnf(cls_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_mod__less__eq__dividend_0,axiom,
    c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).

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

cnf(cls_le__square_0,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_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__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__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_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__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__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__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_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_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_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_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_min__max_Ole__iff__inf_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | c_Orderings_Oord__class_Omin(X2,X3,X1) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).

cnf(cls_min__max_Ole__iff__sup_1,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | c_Orderings_Oord__class_Omax(X2,X3,X1) != X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).

cnf(cls_min__max_Ole__iff__inf_0,axiom,
    ( c_Orderings_Oord__class_Omin(X2,X3,X1) = X2
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).

cnf(cls_min__max_Oinf__absorb2_0,axiom,
    ( c_Orderings_Oord__class_Omin(X2,X3,X1) = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).

cnf(cls_min__max_Osup__absorb1_0,axiom,
    ( c_Orderings_Oord__class_Omax(X2,X3,X1) = X2
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).

cnf(cls_min__max_Ole__iff__sup_0,axiom,
    ( c_Orderings_Oord__class_Omax(X2,X3,X1) = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).

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

cnf(cls_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_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_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_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_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_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_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_mod__if_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).

cnf(cls_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_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_subst__Var_2,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
    | X1 = X3
    | c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

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

cnf(cls_linorder__antisym__conv3_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/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__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__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_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__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_class__semiring_Osemiring__rules_I7_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

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

cnf(cls_class__semiring_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_min__max_Oinf__commute_0,axiom,
    ( c_Orderings_Oord__class_Omin(X2,X3,X1) = c_Orderings_Oord__class_Omin(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).

cnf(cls_min__max_Osup__commute_0,axiom,
    ( c_Orderings_Oord__class_Omax(X2,X3,X1) = c_Orderings_Oord__class_Omax(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).

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

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_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_mult__cancel1_1,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).

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

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

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

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

cnf(cls_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_lift_Osimps_I1_J_0,axiom,
    ( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

cnf(cls_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_lift_Osimps_I2_J_0,axiom,
    c_Lambda_Olift(c_Lambda_OdB_OApp(X1,X2),X3) = c_Lambda_OdB_OApp(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

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

cnf(cls_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_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_mult__is__0_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).

cnf(cls_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_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_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_neq0__conv_1,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

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

cnf(cls_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_nat__mult__eq__1__iff_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).

cnf(cls_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_nat__mult__eq__1__iff_1,axiom,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).

cnf(cls_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_nat__1__eq__mult__iff_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).

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

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

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

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

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_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_subst__lift_0,axiom,
    c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).

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

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__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_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_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_mod__0_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_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_mod__by__0_0,axiom,
    ( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).

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

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

cnf(cls_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_mod__self_0,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).

cnf(cls_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_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_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_mult__idem_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X2,X1) = X2
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).

cnf(cls_min__max_Oinf__idem_0,axiom,
    ( c_Orderings_Oord__class_Omin(X2,X2,X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).

cnf(cls_min__max_Osup__idem_0,axiom,
    ( c_Orderings_Oord__class_Omax(X2,X2,X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_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_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_nat__mult__eq__1__iff_2,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).

cnf(cls_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_nat__1__eq__mult__iff_2,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).

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

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

cnf(cls_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_mult__is__0_1,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).

cnf(cls_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_min__0L_0,axiom,
    c_Orderings_Oord__class_Omin(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_min__0L_0) ).

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

cnf(cls_min__0R_0,axiom,
    c_Orderings_Oord__class_Omin(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0R_0) ).

cnf(cls_nat__mult__1_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1_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_max__0L_0,axiom,
    c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0L_0) ).

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

cnf(cls_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_max__0R_0,axiom,
    c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0R_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_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_abs_0,axiom,
    ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_conjecture_0,negated_conjecture,
    c_InductTermi_OIT(v_ra),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

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

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

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

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

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

cnf(clsarity_nat__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_Omult__mono1,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

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

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__Ring__and__Field_Opordered__cancel__semiring,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(i_0_755,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    cls_conjecture_2 ).

cnf(i_0_756,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_757,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
    cls_Suc__mult__less__cancel1_0 ).

cnf(i_0_758,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
    cls_Suc__mult__le__cancel1_0 ).

cnf(i_0_759,axiom,
    ( c_Lambda_Osubst(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,X3),c_Suc(X4)),c_Lambda_Osubst(X5,X2,X4),X3) = c_Lambda_Osubst(c_Lambda_Osubst(X1,X5,X3),X2,X4)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    cls_subst__subst_0 ).

cnf(i_0_760,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
    cls_mod__mult__self4_0 ).

cnf(i_0_761,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    cls_one__less__mult_0 ).

cnf(i_0_762,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    cls_one__le__mult__iff_2 ).

cnf(i_0_763,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    cls_Suc__mult__less__cancel1_1 ).

cnf(i_0_764,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    cls_Suc__mult__le__cancel1_1 ).

cnf(i_0_765,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_766,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_767,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    cls_n__less__n__mult__m_0 ).

cnf(i_0_768,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    cls_n__less__m__mult__n_0 ).

cnf(i_0_769,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_770,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    cls_one__le__mult__iff_0 ).

cnf(i_0_771,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    cls_one__le__mult__iff_1 ).

cnf(i_0_772,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat),
    cls_mod__Suc__eq__Suc__mod_0 ).

cnf(i_0_773,axiom,
    ( X2 = X3
    | c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat) ),
    cls_Suc__mult__cancel1_0 ).

cnf(i_0_774,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat))
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2 ),
    cls_mod__Suc_1 ).

cnf(i_0_775,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_776,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_777,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_778,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_779,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    cls_Suc__times__mod__eq_0 ).

cnf(i_0_780,axiom,
    ( c_Lambda_Olift(c_Lambda_Olift(X1,X2),c_Suc(X3)) = c_Lambda_Olift(c_Lambda_Olift(X1,X3),X2)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    cls_lift__lift_0 ).

cnf(i_0_781,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_782,axiom,
    c_Orderings_Oord__class_Omin(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X1,X2,tc_nat)),
    cls_min__Suc__Suc_0 ).

cnf(i_0_783,axiom,
    c_Orderings_Oord__class_Omax(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X1,X2,tc_nat)),
    cls_max__Suc__Suc_0 ).

cnf(i_0_784,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
    cls_mod__Suc_0 ).

cnf(i_0_785,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_786,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_787,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_788,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_789,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_790,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_791,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_792,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_793,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_mult__eq__1__iff_2 ).

cnf(i_0_794,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_795,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    cls_not__less__eq__eq_1 ).

cnf(i_0_796,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_797,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_798,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_799,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_800,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_801,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_802,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_803,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    cls_mult__Suc_0 ).

cnf(i_0_804,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    cls_mult__Suc__right_0 ).

cnf(i_0_805,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_806,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_807,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_808,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_809,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_810,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_811,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    cls_Suc__leD_0 ).

cnf(i_0_812,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_813,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_814,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_815,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_816,axiom,
    c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
    cls_le__Suc__eq_2 ).

cnf(i_0_817,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_818,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_819,axiom,
    ~ c_lessequals(c_Suc(X1),X1,tc_nat),
    cls_Suc__n__not__le__n_0 ).

cnf(i_0_820,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_821,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_822,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_823,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_824,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_825,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_826,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_827,axiom,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__SucI_0 ).

cnf(i_0_828,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_829,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_830,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_831,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_832,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_mult__eq__1__iff_0 ).

cnf(i_0_833,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_mult__eq__1__iff_1 ).

cnf(i_0_834,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_835,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_836,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_837,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_838,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    cls_not__less__eq__eq_0 ).

cnf(i_0_839,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_840,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_841,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_842,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_843,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_844,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_Suc__inject_0 ).

cnf(i_0_845,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_nat_Oinject_0 ).

cnf(i_0_846,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_847,axiom,
    c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_mod__1_0 ).

cnf(i_0_848,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_849,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_850,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_851,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_lessI_0 ).

cnf(i_0_852,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_less__Suc__eq_2 ).

cnf(i_0_853,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_854,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_nat_Osimps_I3_J_0 ).

cnf(i_0_855,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_Suc__neq__Zero_0 ).

cnf(i_0_856,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_nat_Osimps_I2_J_0 ).

cnf(i_0_857,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_Zero__neq__Suc_0 ).

cnf(i_0_858,axiom,
    c_Suc(X1) != X1,
    cls_Suc__n__not__n_0 ).

cnf(i_0_859,axiom,
    X1 != c_Suc(X1),
    cls_n__not__Suc__n_0 ).

cnf(i_0_860,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_861,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oplus__class_Oplus(v_ja,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_755,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_862,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    cls_nat__less__add__iff1_1,
    [final] ).

cnf(i_0_863,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    cls_nat__le__add__iff1_1,
    [final] ).

cnf(i_0_864,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    cls_nat__less__add__iff2_1,
    [final] ).

cnf(i_0_865,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    cls_nat__le__add__iff2_1,
    [final] ).

cnf(i_0_866,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
    cls_less__add__iff1_1,
    [final] ).

cnf(i_0_867,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
    cls_le__add__iff1_1,
    [final] ).

cnf(i_0_868,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
    cls_less__add__iff2_1,
    [final] ).

cnf(i_0_869,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
    cls_le__add__iff2_1,
    [final] ).

cnf(i_0_870,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_nat__less__add__iff1_0,
    [final] ).

cnf(i_0_871,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_nat__le__add__iff1_0,
    [final] ).

cnf(i_0_872,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_nat__less__add__iff2_0,
    [final] ).

cnf(i_0_873,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_nat__le__add__iff2_0,
    [final] ).

cnf(i_0_874,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
    cls_less__add__iff1_0,
    [final] ).

cnf(i_0_875,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
    cls_le__add__iff1_0,
    [final] ).

cnf(i_0_876,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
    cls_less__add__iff2_0,
    [final] ).

cnf(i_0_877,axiom,
    ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
    cls_le__add__iff2_0,
    [final] ).

cnf(i_0_878,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    cls_nat__diff__add__eq1_0,
    [final] ).

cnf(i_0_879,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    cls_nat__diff__add__eq2_0,
    [final] ).

cnf(i_0_880,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_757,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_881,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_758,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_882,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_nat__eq__add__iff2_1,
    [final] ).

cnf(i_0_883,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_nat__eq__add__iff1_1,
    [final] ).

cnf(i_0_884,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),X1) ),
    cls_sum__squares__gt__zero__iff_0,
    [final] ).

cnf(i_0_885,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X1),X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    cls_eq__add__iff2_1,
    [final] ).

cnf(i_0_886,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    cls_eq__add__iff1_1,
    [final] ).

cnf(i_0_887,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),X4,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X4,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    cls_mod__lemma_0,
    [final] ).

cnf(i_0_888,plain,
    ( c_Lambda_Osubst(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,X3),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Osubst(X5,X2,X4),X3) = c_Lambda_Osubst(c_Lambda_Osubst(X1,X5,X3),X2,X4)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_759,c_0_756]),
    [final] ).

cnf(i_0_889,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_760,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_890,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_sum__squares__le__zero__iff_0,
    [final] ).

cnf(i_0_891,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_sum__squares__le__zero__iff_1,
    [final] ).

cnf(i_0_892,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_not__sum__squares__lt__zero_0,
    [final] ).

cnf(i_0_893,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat) = X5
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    cls_nat__eq__add__iff1_0,
    [final] ).

cnf(i_0_894,axiom,
    ( X3 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,tc_nat),X2,tc_nat),X5,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X4,tc_nat) ),
    cls_nat__eq__add__iff2_0,
    [final] ).

cnf(i_0_895,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),c_Orderings_Oord__class_Omin(X2,X4,X1),X1),c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Odistrib__inf__le_0,
    [final] ).

cnf(i_0_896,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),c_Orderings_Oord__class_Omax(X2,X4,X1),X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Odistrib__sup__le_0,
    [final] ).

cnf(i_0_897,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1) = X6
    | ~ class_Ring__and__Field_Oring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
    cls_eq__add__iff1_0,
    [final] ).

cnf(i_0_898,axiom,
    ( X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1)
    | ~ class_Ring__and__Field_Oring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
    cls_eq__add__iff2_0,
    [final] ).

cnf(i_0_899,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1),X5,X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    cls_combine__common__factor_0,
    [final] ).

cnf(i_0_900,axiom,
    ( X3 = X5
    | X2 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_class__ringb_Onoteq__reduce_0,
    [final] ).

cnf(i_0_901,axiom,
    ( X3 = X5
    | X2 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_class__ringb_Oadd__mul__solve_0,
    [final] ).

cnf(i_0_902,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
    cls_left__add__mult__distrib_0,
    [final] ).

cnf(i_0_903,axiom,
    ( X2 = X4
    | X1 = X3
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    cls_natgb_Oadd__mul__solve_0,
    [final] ).

cnf(i_0_904,axiom,
    ( X2 = X4
    | X1 = X3
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    cls_natgb_Onoteq__reduce_0,
    [final] ).

cnf(i_0_905,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_761,c_0_756]),c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_906,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_762,c_0_756]),c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_907,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_763,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_908,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_764,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_909,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__eq_0,
    [final] ).

cnf(i_0_910,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    cls_mod__diff__eq_0,
    [final] ).

cnf(i_0_911,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__eq_0,
    [final] ).

cnf(i_0_912,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_765,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_913,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_766,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_914,axiom,
    ( c_Lambda_Olift(c_Lambda_Osubst(X1,X2,X3),X4) = c_Lambda_Osubst(c_Lambda_Olift(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X2,X4),X3)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    cls_lift__subst_0,
    [final] ).

cnf(i_0_915,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_sum__squares__le__zero__iff_2,
    [final] ).

cnf(i_0_916,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_767,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_917,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_768,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_918,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
    | c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
    cls_mod__mult__cong_0,
    [final] ).

cnf(i_0_919,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X4,X1),X3,X1)
    | ~ class_Divides_Oring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
    | c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
    cls_mod__diff__cong_0,
    [final] ).

cnf(i_0_920,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X6,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
    | c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
    cls_mod__add__cong_0,
    [final] ).

cnf(i_0_921,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I15_J_0,
    [final] ).

cnf(i_0_922,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I14_J_0,
    [final] ).

cnf(i_0_923,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_769,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_924,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_mult__strict__mono_0,
    [final] ).

cnf(i_0_925,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_mult__strict__mono_H_0,
    [final] ).

cnf(i_0_926,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_mult__le__less__imp__less_0,
    [final] ).

cnf(i_0_927,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_mult__less__le__imp__less_0,
    [final] ).

cnf(i_0_928,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_mult__mono_H_0,
    [final] ).

cnf(i_0_929,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_mult__mono_0,
    [final] ).

cnf(i_0_930,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_931,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_932,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_sum__squares__gt__zero__iff_1,
    [final] ).

cnf(i_0_933,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_sum__squares__gt__zero__iff_2,
    [final] ).

cnf(i_0_934,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_sum__squares__ge__zero_0,
    [final] ).

cnf(i_0_935,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X4,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
    cls_nat__mod__eq__iff_1,
    [final] ).

cnf(i_0_936,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_770,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_937,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_771,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_938,axiom,
    ( c_Lambda_Olift(c_Lambda_Osubst(X1,X2,X3),X4) = c_Lambda_Osubst(c_Lambda_Olift(X1,X4),c_Lambda_Olift(X2,X4),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    cls_lift__subst__lt_0,
    [final] ).

cnf(i_0_939,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    cls_mult__right__less__imp__less_0,
    [final] ).

cnf(i_0_940,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_mult__left__less__imp__less_0,
    [final] ).

cnf(i_0_941,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    cls_mult__less__imp__less__right_0,
    [final] ).

cnf(i_0_942,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_mult__less__imp__less__left_0,
    [final] ).

cnf(i_0_943,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
    cls_mult__less__cancel__left__pos_0,
    [final] ).

cnf(i_0_944,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
    cls_mult__right__le__imp__le_0,
    [final] ).

cnf(i_0_945,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
    cls_mult__left__le__imp__le_0,
    [final] ).

cnf(i_0_946,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
    cls_mult__le__cancel__left__pos_0,
    [final] ).

cnf(i_0_947,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__less__cancel__left__neg_0,
    [final] ).

cnf(i_0_948,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__cancel__left__neg_0,
    [final] ).

cnf(i_0_949,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    cls_nat__mult__less__cancel1_0,
    [final] ).

cnf(i_0_950,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    cls_mult__le__cancel2_0,
    [final] ).

cnf(i_0_951,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    cls_nat__mult__le__cancel1_0,
    [final] ).

cnf(i_0_952,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    cls_mult__le__cancel1_0,
    [final] ).

cnf(i_0_953,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    cls_mult__less__cancel__left__disj_0,
    [final] ).

cnf(i_0_954,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    cls_mult__less__cancel__right__disj_0,
    [final] ).

cnf(i_0_955,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Oadd__mul__solve_1,
    [final] ).

cnf(i_0_956,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Onoteq__reduce_1,
    [final] ).

cnf(i_0_957,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    cls_mult__less__cancel__right__disj_1,
    [final] ).

cnf(i_0_958,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    cls_mult__less__cancel__left__disj_1,
    [final] ).

cnf(i_0_959,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    cls_mult__less__cancel__left__disj_2,
    [final] ).

cnf(i_0_960,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    cls_mult__less__cancel__right__disj_2,
    [final] ).

cnf(i_0_961,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I13_J_0,
    [final] ).

cnf(i_0_962,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_963,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_zmod__simps_I4_J_0,
    [final] ).

cnf(i_0_964,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X3,X1),X4,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_zmod__simps_I1_J_0,
    [final] ).

cnf(i_0_965,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_zmod__simps_I2_J_0,
    [final] ).

cnf(i_0_966,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__left__eq_0,
    [final] ).

cnf(i_0_967,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    cls_mod__diff__left__eq_0,
    [final] ).

cnf(i_0_968,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__left__eq_0,
    [final] ).

cnf(i_0_969,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__right__eq_0,
    [final] ).

cnf(i_0_970,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    cls_mod__diff__right__eq_0,
    [final] ).

cnf(i_0_971,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__right__eq_0,
    [final] ).

cnf(i_0_972,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    cls_mult__less__cancel__right__disj_3,
    [final] ).

cnf(i_0_973,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    cls_mult__less__cancel__left__disj_3,
    [final] ).

cnf(i_0_974,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_772,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_975,axiom,
    ( X4 = X5
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X5,X1),X1) ),
    cls_class__ringb_Oadd__scale__eq__noteq_0,
    [final] ).

cnf(i_0_976,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    cls_natgb_Onoteq__reduce_1,
    [final] ).

cnf(i_0_977,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    cls_natgb_Oadd__mul__solve_1,
    [final] ).

cnf(i_0_978,plain,
    ( X2 = X3
    | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) != c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_773,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_979,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_980,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_981,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_982,axiom,
    ( X3 = X4
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) ),
    cls_natgb_Oadd__scale__eq__noteq_0,
    [final] ).

cnf(i_0_983,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_984,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_985,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_986,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_987,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_988,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_989,plain,
    ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_774,c_0_756]),c_0_756]),c_0_756]),
    [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),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_775,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_991,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_776,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_992,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_777,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_993,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_994,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    cls_mult__less__cancel1_0,
    [final] ).

cnf(i_0_995,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
    cls_mult__less__cancel2_0,
    [final] ).

cnf(i_0_996,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_778,c_0_756]),
    [final] ).

cnf(i_0_997,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    cls_mult__less__cancel2_1,
    [final] ).

cnf(i_0_998,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    cls_mult__less__cancel1_1,
    [final] ).

cnf(i_0_999,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_1000,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_1001,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[i_0_779,c_0_756]),
    [final] ).

cnf(i_0_1002,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_mult__strict__left__mono__comm_0,
    [final] ).

cnf(i_0_1003,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_mult__strict__left__mono_0,
    [final] ).

cnf(i_0_1004,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__less__cancel__left__disj_4,
    [final] ).

cnf(i_0_1005,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__less__cancel__left__pos_1,
    [final] ).

cnf(i_0_1006,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_mult__strict__right__mono_0,
    [final] ).

cnf(i_0_1007,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_mult__less__cancel__right__disj_4,
    [final] ).

cnf(i_0_1008,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Omult__mono1(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_mult__mono1_0,
    [final] ).

cnf(i_0_1009,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Omult__mono(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_mult__left__mono_0,
    [final] ).

cnf(i_0_1010,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__le__cancel__left__pos_1,
    [final] ).

cnf(i_0_1011,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Omult__mono(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_mult__right__mono_0,
    [final] ).

cnf(i_0_1012,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__less__cancel__left__disj_5,
    [final] ).

cnf(i_0_1013,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    cls_mult__strict__left__mono__neg_0,
    [final] ).

cnf(i_0_1014,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__less__cancel__left__neg_1,
    [final] ).

cnf(i_0_1015,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__less__cancel__right__disj_5,
    [final] ).

cnf(i_0_1016,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X1) ),
    cls_mult__strict__right__mono__neg_0,
    [final] ).

cnf(i_0_1017,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__cancel__left__neg_1,
    [final] ).

cnf(i_0_1018,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X4,X3,X1) ),
    cls_mult__left__mono__neg_0,
    [final] ).

cnf(i_0_1019,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X4,X2,X1) ),
    cls_mult__right__mono__neg_0,
    [final] ).

cnf(i_0_1020,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__right__le__one__le_0,
    [final] ).

cnf(i_0_1021,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_mult__left__le__one__le_0,
    [final] ).

cnf(i_0_1022,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    cls_subst__Abs_0,
    [final] ).

cnf(i_0_1023,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_1024,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_1025,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_1026,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_1027,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_1028,plain,
    ( c_Lambda_Olift(c_Lambda_Olift(X1,X2),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_Olift(X1,X3),X2)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[i_0_780,c_0_756]),
    [final] ).

cnf(i_0_1029,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_sum__squares__eq__zero__iff_0,
    [final] ).

cnf(i_0_1030,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_sum__squares__eq__zero__iff_1,
    [final] ).

cnf(i_0_1031,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__mult2_0,
    [final] ).

cnf(i_0_1032,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I1_J_0,
    [final] ).

cnf(i_0_1033,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__mult1_0,
    [final] ).

cnf(i_0_1034,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    cls_comm__semiring__class_Odistrib_0,
    [final] ).

cnf(i_0_1035,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I8_J_0,
    [final] ).

cnf(i_0_1036,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    cls_min__diff__distrib__left_0,
    [final] ).

cnf(i_0_1037,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    cls_max__diff__distrib__left_0,
    [final] ).

cnf(i_0_1038,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    cls_min__add__distrib__left_0,
    [final] ).

cnf(i_0_1039,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    cls_max__add__distrib__left_0,
    [final] ).

cnf(i_0_1040,axiom,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X4,X1),c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Oinf__sup__distrib2_0,
    [final] ).

cnf(i_0_1041,axiom,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X4,X1),c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Osup__inf__distrib2_0,
    [final] ).

cnf(i_0_1042,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__d_0,
    [final] ).

cnf(i_0_1043,axiom,
    ( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X3,X1),c_Orderings_Oord__class_Omin(X2,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Oinf__sup__distrib1_0,
    [final] ).

cnf(i_0_1044,axiom,
    ( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X3,X1),c_Orderings_Oord__class_Omax(X2,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Osup__inf__distrib1_0,
    [final] ).

cnf(i_0_1045,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__self2_0,
    [final] ).

cnf(i_0_1046,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__self1_0,
    [final] ).

cnf(i_0_1047,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_781,c_0_756]),
    [final] ).

cnf(i_0_1048,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__mult__less__cancel1_1,
    [final] ).

cnf(i_0_1049,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    cls_mult__less__mono2_0,
    [final] ).

cnf(i_0_1050,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_mult__less__cancel1_2,
    [final] ).

cnf(i_0_1051,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_mult__less__mono1_0,
    [final] ).

cnf(i_0_1052,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_mult__less__cancel2_2,
    [final] ).

cnf(i_0_1053,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__mult__le__cancel1_1,
    [final] ).

cnf(i_0_1054,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_mult__eq__if_1,
    [final] ).

cnf(i_0_1055,plain,
    c_Orderings_Oord__class_Omin(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_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_782,c_0_756]),c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1056,plain,
    c_Orderings_Oord__class_Omax(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_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_783,c_0_756]),c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1057,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_1058,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_1059,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_1060,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X4,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_mult__le__mono_0,
    [final] ).

cnf(i_0_1061,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_1062,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    cls_zero__less__mult__pos2_0,
    [final] ).

cnf(i_0_1063,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
    cls_zero__less__mult__pos_0,
    [final] ).

cnf(i_0_1064,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X2 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_784,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1065,axiom,
    c_Orderings_Oord__class_Omin(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(c_Orderings_Oord__class_Omin(X1,X3,tc_nat),X2,tc_nat),
    cls_min__diff_0,
    [final] ).

cnf(i_0_1066,axiom,
    c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    cls_mod__mult__distrib_0,
    [final] ).

cnf(i_0_1067,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    cls_diff__mult__distrib_0,
    [final] ).

cnf(i_0_1068,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    cls_add__mult__distrib_0,
    [final] ).

cnf(i_0_1069,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    cls_mod__mult__distrib2_0,
    [final] ).

cnf(i_0_1070,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    cls_diff__mult__distrib2_0,
    [final] ).

cnf(i_0_1071,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    cls_add__mult__distrib2_0,
    [final] ).

cnf(i_0_1072,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
    cls_mod__mult__self3_0,
    [final] ).

cnf(i_0_1073,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_785,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1074,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_1075,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_1076,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_1077,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_1078,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_1079,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_1080,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_1081,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_1082,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_1083,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_1084,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_1085,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__0__iff_1,
    [final] ).

cnf(i_0_1086,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__0__iff_0,
    [final] ).

cnf(i_0_1087,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__0__iff_3,
    [final] ).

cnf(i_0_1088,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    cls_zero__le__mult__iff_0,
    [final] ).

cnf(i_0_1089,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
    cls_zero__le__mult__iff_3,
    [final] ).

cnf(i_0_1090,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    cls_zero__le__mult__iff_2,
    [final] ).

cnf(i_0_1091,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
    cls_zero__le__mult__iff_1,
    [final] ).

cnf(i_0_1092,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__0__iff_2,
    [final] ).

cnf(i_0_1093,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X2,X1),X3,X1) ),
    cls_min__less__iff__disj_0,
    [final] ).

cnf(i_0_1094,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X4,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_Orderings_Oord__class_Omin(X4,X2,X1),X3,X1) ),
    cls_min__le__iff__disj_0,
    [final] ).

cnf(i_0_1095,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
    cls_less__max__iff__disj_0,
    [final] ).

cnf(i_0_1096,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X2,X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,c_Orderings_Oord__class_Omax(X4,X3,X1),X1) ),
    cls_le__max__iff__disj_0,
    [final] ).

cnf(i_0_1097,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_786,c_0_756]),
    [final] ).

cnf(i_0_1098,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_787,c_0_756]),
    [final] ).

cnf(i_0_1099,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_788,c_0_756]),
    [final] ).

cnf(i_0_1100,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_789,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1101,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__neg__pos_0,
    [final] ).

cnf(i_0_1102,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_mult__pos__neg2_0,
    [final] ).

cnf(i_0_1103,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__pos__neg_0,
    [final] ).

cnf(i_0_1104,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_mult__nonneg__nonpos2_0,
    [final] ).

cnf(i_0_1105,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__nonpos__nonneg_0,
    [final] ).

cnf(i_0_1106,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_split__mult__neg__le_1,
    [final] ).

cnf(i_0_1107,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__nonneg__nonpos_0,
    [final] ).

cnf(i_0_1108,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_split__mult__neg__le_0,
    [final] ).

cnf(i_0_1109,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__le__0__iff_5,
    [final] ).

cnf(i_0_1110,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__le__0__iff_4,
    [final] ).

cnf(i_0_1111,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_1112,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_1113,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_1114,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_1115,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    cls_less__1__mult_0,
    [final] ).

cnf(i_0_1116,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__pos__pos_0,
    [final] ).

cnf(i_0_1117,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_1118,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_1119,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_1120,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_mult__nonneg__nonneg_0,
    [final] ).

cnf(i_0_1121,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_zero__le__mult__iff_4,
    [final] ).

cnf(i_0_1122,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_split__mult__pos__le_0,
    [final] ).

cnf(i_0_1123,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_1124,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__neg__neg_0,
    [final] ).

cnf(i_0_1125,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_zero__le__mult__iff_5,
    [final] ).

cnf(i_0_1126,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_split__mult__pos__le_1,
    [final] ).

cnf(i_0_1127,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_mult__nonpos__nonpos_0,
    [final] ).

cnf(i_0_1128,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_1129,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
    cls_le__cube_0,
    [final] ).

cnf(i_0_1130,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_1131,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_1132,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_1133,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_1134,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_1135,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_1136,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_1137,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_1138,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_1139,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_1140,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_1141,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_1142,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_790,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1143,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_791,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1144,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_792,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1145,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_1146,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_1147,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_1148,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    cls_mult__le__cancel1_2,
    [final] ).

cnf(i_0_1149,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    cls_mult__le__mono2_0,
    [final] ).

cnf(i_0_1150,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_mult__le__cancel2_2,
    [final] ).

cnf(i_0_1151,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_mult__le__mono1_0,
    [final] ).

cnf(i_0_1152,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_1153,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_1154,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_1155,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_1156,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_793,c_0_756]),c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1157,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_794,c_0_756]),
    [final] ).

cnf(i_0_1158,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I2_J_0,
    [final] ).

cnf(i_0_1159,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I3_J_0,
    [final] ).

cnf(i_0_1160,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_max__less__iff__conj_2,
    [final] ).

cnf(i_0_1161,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_min__max_Ole__supI_0,
    [final] ).

cnf(i_0_1162,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_min__max_Osup__least_0,
    [final] ).

cnf(i_0_1163,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_min__max_Ole__sup__iff_2,
    [final] ).

cnf(i_0_1164,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_min__less__iff__conj_2,
    [final] ).

cnf(i_0_1165,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_min__max_Oinf__greatest_0,
    [final] ).

cnf(i_0_1166,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_min__max_Ole__inf__iff_2,
    [final] ).

cnf(i_0_1167,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_min__max_Ole__infI_0,
    [final] ).

cnf(i_0_1168,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_795,c_0_756]),
    [final] ).

cnf(i_0_1169,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_796,c_0_756]),
    [final] ).

cnf(i_0_1170,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__0__less__mult__iff_2,
    [final] ).

cnf(i_0_1171,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_1172,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_1173,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_1174,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_1175,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_1176,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_1177,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_1178,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_797,c_0_756]),
    [final] ).

cnf(i_0_1179,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I16_J_0,
    [final] ).

cnf(i_0_1180,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_1181,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,
    [final] ).

cnf(i_0_1182,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I17_J_0,
    [final] ).

cnf(i_0_1183,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_1184,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_1185,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_1186,axiom,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Oinf__assoc_0,
    [final] ).

cnf(i_0_1187,axiom,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X2,X3,X1),X4,X1) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Osup__assoc_0,
    [final] ).

cnf(i_0_1188,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__a_0,
    [final] ).

cnf(i_0_1189,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I18_J_0,
    [final] ).

cnf(i_0_1190,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_1191,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_1192,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I19_J_0,
    [final] ).

cnf(i_0_1193,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_1194,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_1195,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_1196,axiom,
    ( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X2,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Oinf__left__commute_0,
    [final] ).

cnf(i_0_1197,axiom,
    ( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X2,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Osup__left__commute_0,
    [final] ).

cnf(i_0_1198,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    cls_lem0_0,
    [final] ).

cnf(i_0_1199,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_sum__squares__eq__zero__iff_2,
    [final] ).

cnf(i_0_1200,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_1201,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_1202,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_798,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1203,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_799,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1204,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_800,c_0_756]),
    [final] ).

cnf(i_0_1205,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_801,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1206,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_802,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1207,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_1208,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_1209,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_1210,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_1211,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_803,c_0_756]),
    [final] ).

cnf(i_0_1212,plain,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_804,c_0_756]),
    [final] ).

cnf(i_0_1213,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_mult__le__cancel1_1,
    [final] ).

cnf(i_0_1214,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_mult__le__cancel2_1,
    [final] ).

cnf(i_0_1215,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
    cls_max__less__iff__conj_0,
    [final] ).

cnf(i_0_1216,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
    cls_max__less__iff__conj_1,
    [final] ).

cnf(i_0_1217,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
    cls_min__max_Ole__supE_0,
    [final] ).

cnf(i_0_1218,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X2,X4,X1),X3,X1) ),
    cls_min__max_Ole__sup__iff_0,
    [final] ).

cnf(i_0_1219,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
    cls_min__max_Ole__supE_1,
    [final] ).

cnf(i_0_1220,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
    cls_min__max_Ole__sup__iff_1,
    [final] ).

cnf(i_0_1221,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
    cls_min__less__iff__conj_0,
    [final] ).

cnf(i_0_1222,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
    cls_min__less__iff__conj_1,
    [final] ).

cnf(i_0_1223,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
    cls_min__max_Ole__infE_0,
    [final] ).

cnf(i_0_1224,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X3,X4,X1),X1) ),
    cls_min__max_Ole__inf__iff_0,
    [final] ).

cnf(i_0_1225,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
    cls_min__max_Ole__infE_1,
    [final] ).

cnf(i_0_1226,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X4,X3,X1),X1) ),
    cls_min__max_Ole__inf__iff_1,
    [final] ).

cnf(i_0_1227,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_1228,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_1229,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_1230,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    cls_nat__mult__assoc_0,
    [final] ).

cnf(i_0_1231,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_1232,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_1233,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_1234,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_805,c_0_756]),
    [final] ).

cnf(i_0_1235,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_806,c_0_756]),
    [final] ).

cnf(i_0_1236,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_807,c_0_756]),
    [final] ).

cnf(i_0_1237,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_808,c_0_756]),
    [final] ).

cnf(i_0_1238,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_809,c_0_756]),
    [final] ).

cnf(i_0_1239,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_810,c_0_756]),
    [final] ).

cnf(i_0_1240,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_811,c_0_756]),
    [final] ).

cnf(i_0_1241,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_812,c_0_756]),
    [final] ).

cnf(i_0_1242,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    cls_nat__0__less__mult__iff_0,
    [final] ).

cnf(i_0_1243,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    cls_nat__0__less__mult__iff_1,
    [final] ).

cnf(i_0_1244,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OApp(X1,X2),X3,X4) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4)),
    cls_subst__App_0,
    [final] ).

cnf(i_0_1245,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_1246,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_813,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1247,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_1248,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_1249,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_1250,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_1251,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_814,c_0_756]),c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1252,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_815,c_0_756]),c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1253,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_1254,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_1255,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_le__mod__geq_0,
    [final] ).

cnf(i_0_1256,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_816,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1257,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_not__square__less__zero_0,
    [final] ).

cnf(i_0_1258,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_1259,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_1260,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_1261,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_1262,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_1263,axiom,
    c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X2) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    cls_lift_Osimps_I3_J_0,
    [final] ).

cnf(i_0_1264,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_817,c_0_756]),
    [final] ).

cnf(i_0_1265,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_818,c_0_756]),
    [final] ).

cnf(i_0_1266,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_mod__if_1,
    [final] ).

cnf(i_0_1267,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_1268,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_1269,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    cls_subst__gt_0,
    [final] ).

cnf(i_0_1270,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    cls_subst__Var_0,
    [final] ).

cnf(i_0_1271,axiom,
    ( X2 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_nat__mult__eq__cancel1_0,
    [final] ).

cnf(i_0_1272,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_819,c_0_756]),
    [final] ).

cnf(i_0_1273,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_820,c_0_756]),
    [final] ).

cnf(i_0_1274,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_821,c_0_756]),
    [final] ).

cnf(i_0_1275,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_min__less__iff__disj_1,
    [final] ).

cnf(i_0_1276,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_min__max_Oless__infI1_0,
    [final] ).

cnf(i_0_1277,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_min__less__iff__disj_2,
    [final] ).

cnf(i_0_1278,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_min__max_Oless__infI2_0,
    [final] ).

cnf(i_0_1279,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_min__max_Ole__infI1_0,
    [final] ).

cnf(i_0_1280,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_min__le__iff__disj_1,
    [final] ).

cnf(i_0_1281,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_min__max_Ole__infI2_0,
    [final] ).

cnf(i_0_1282,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X4,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_min__le__iff__disj_2,
    [final] ).

cnf(i_0_1283,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_less__max__iff__disj_1,
    [final] ).

cnf(i_0_1284,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_min__max_Oless__supI1_0,
    [final] ).

cnf(i_0_1285,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_less__max__iff__disj_2,
    [final] ).

cnf(i_0_1286,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_min__max_Oless__supI2_0,
    [final] ).

cnf(i_0_1287,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_min__max_Ole__supI1_0,
    [final] ).

cnf(i_0_1288,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__max__iff__disj_1,
    [final] ).

cnf(i_0_1289,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_min__max_Ole__supI2_0,
    [final] ).

cnf(i_0_1290,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X4,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_le__max__iff__disj_2,
    [final] ).

cnf(i_0_1291,axiom,
    ( c_Lambda_Obeta(c_Lambda_Osubst(X1,X2,X3),c_Lambda_Osubst(X4,X2,X3))
    | ~ c_Lambda_Obeta(X1,X4) ),
    cls_subst__preserves__beta_0,
    [final] ).

cnf(i_0_1292,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_1293,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_1294,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I4_J_0,
    [final] ).

cnf(i_0_1295,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_822,c_0_756]),
    [final] ).

cnf(i_0_1296,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_823,c_0_756]),
    [final] ).

cnf(i_0_1297,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_824,c_0_756]),
    [final] ).

cnf(i_0_1298,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_825,c_0_756]),
    [final] ).

cnf(i_0_1299,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_826,c_0_756]),
    [final] ).

cnf(i_0_1300,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_827,c_0_756]),
    [final] ).

cnf(i_0_1301,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_1302,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_1303,axiom,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_mod__less__divisor_0,
    [final] ).

cnf(i_0_1304,axiom,
    ( c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_mod__le__divisor_0,
    [final] ).

cnf(i_0_1305,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_1306,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_1307,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_1308,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_1309,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_1310,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_1311,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_1312,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_1313,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_1314,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_1315,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_1316,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_1317,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_1318,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_1319,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_828,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1320,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_829,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1321,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_830,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1322,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_831,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1323,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_832,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1324,plain,
    ( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_833,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1325,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_1326,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_1327,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_1328,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_1329,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_1330,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_1331,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_1332,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_1333,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_834,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1334,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_835,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1335,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_836,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1336,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_837,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1337,axiom,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mod__trivial_0,
    [final] ).

cnf(i_0_1338,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__self1_0,
    [final] ).

cnf(i_0_1339,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__self2_0,
    [final] ).

cnf(i_0_1340,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
    cls_mult__left__idem_0,
    [final] ).

cnf(i_0_1341,axiom,
    ( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X2,X3,X1),X1) = c_Orderings_Oord__class_Omin(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Oinf__left__idem_0,
    [final] ).

cnf(i_0_1342,axiom,
    ( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1) = c_Orderings_Oord__class_Omax(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Osup__left__idem_0,
    [final] ).

cnf(i_0_1343,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_1344,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_838,c_0_756]),
    [final] ).

cnf(i_0_1345,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_839,c_0_756]),
    [final] ).

cnf(i_0_1346,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_840,c_0_756]),
    [final] ).

cnf(i_0_1347,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_1348,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = c_Orderings_Oord__class_Omax(X1,X2,tc_nat),
    cls_nat__minus__add__max_0,
    [final] ).

cnf(i_0_1349,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_1350,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_1351,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_1352,axiom,
    ( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_lift_Osimps_I1_J_1,
    [final] ).

cnf(i_0_1353,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_841,c_0_756]),
    [final] ).

cnf(i_0_1354,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_842,c_0_756]),
    [final] ).

cnf(i_0_1355,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_843]),
    [final] ).

cnf(i_0_1356,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_1357,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_1358,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_1359,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_1360,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_1361,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_1362,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_1363,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_1364,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_1365,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_1366,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_1367,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_1368,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_1369,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_1370,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_1371,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_1372,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_1373,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_844,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1374,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_845,c_0_756]),c_0_756]),
    [final] ).

cnf(i_0_1375,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_1376,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    cls_zero__le__square_0,
    [final] ).

cnf(i_0_1377,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    cls_mult__cancel2_0,
    [final] ).

cnf(i_0_1378,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
    cls_mult__cancel1_0,
    [final] ).

cnf(i_0_1379,axiom,
    ( X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
    cls_nat__mult__eq__cancel__disj_0,
    [final] ).

cnf(i_0_1380,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__self1__is__0_0,
    [final] ).

cnf(i_0_1381,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mult__self2__is__0_0,
    [final] ).

cnf(i_0_1382,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_846,c_0_756]),
    [final] ).

cnf(i_0_1383,plain,
    c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rw,[status(thm)],[i_0_847,c_0_756]),
    [final] ).

cnf(i_0_1384,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__antisym_0,
    [final] ).

cnf(i_0_1385,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_1386,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_1387,axiom,
    ( c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Oinf__sup__absorb_0,
    [final] ).

cnf(i_0_1388,axiom,
    ( c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X2,X3,X1),X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Osup__inf__absorb_0,
    [final] ).

cnf(i_0_1389,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Oinf__le1_0,
    [final] ).

cnf(i_0_1390,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Oinf__le2_0,
    [final] ).

cnf(i_0_1391,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X2,X3,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_le__maxI1_0,
    [final] ).

cnf(i_0_1392,axiom,
    ( c_lessequals(X2,c_Orderings_Oord__class_Omax(X3,X2,X1),X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_le__maxI2_0,
    [final] ).

cnf(i_0_1393,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_1394,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_1395,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_1396,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_848,c_0_756]),
    [final] ).

cnf(i_0_1397,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_849,c_0_756]),
    [final] ).

cnf(i_0_1398,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_850,c_0_756]),
    [final] ).

cnf(i_0_1399,axiom,
    c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X1),X2),c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_beta_0,
    [final] ).

cnf(i_0_1400,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_851,c_0_756]),
    [final] ).

cnf(i_0_1401,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_852,c_0_756]),
    [final] ).

cnf(i_0_1402,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_mod__eq__0__iff_1,
    [final] ).

cnf(i_0_1403,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_1404,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_1405,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_1406,axiom,
    c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
    cls_mod__less__eq__dividend_0,
    [final] ).

cnf(i_0_1407,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
    cls_diff__le__self_0,
    [final] ).

cnf(i_0_1408,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
    cls_le__square_0,
    [final] ).

cnf(i_0_1409,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    cls_le__iff__add_1,
    [final] ).

cnf(i_0_1410,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    cls_le__add1_0,
    [final] ).

cnf(i_0_1411,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    cls_le__add2_0,
    [final] ).

cnf(i_0_1412,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_1413,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_1414,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_1415,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_1416,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_1417,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_1418,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_1419,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_1420,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | c_Orderings_Oord__class_Omin(X2,X3,X1) != X2 ),
    cls_min__max_Ole__iff__inf_1,
    [final] ).

cnf(i_0_1421,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | c_Orderings_Oord__class_Omax(X2,X3,X1) != X3 ),
    cls_min__max_Ole__iff__sup_1,
    [final] ).

cnf(i_0_1422,axiom,
    ( c_Orderings_Oord__class_Omin(X2,X3,X1) = X2
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_min__max_Ole__iff__inf_0,
    [final] ).

cnf(i_0_1423,axiom,
    ( c_Orderings_Oord__class_Omin(X2,X3,X1) = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_min__max_Oinf__absorb2_0,
    [final] ).

cnf(i_0_1424,axiom,
    ( c_Orderings_Oord__class_Omax(X2,X3,X1) = X2
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_min__max_Osup__absorb1_0,
    [final] ).

cnf(i_0_1425,axiom,
    ( c_Orderings_Oord__class_Omax(X2,X3,X1) = X3
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_min__max_Ole__iff__sup_0,
    [final] ).

cnf(i_0_1426,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_subst__lt_0,
    [final] ).

cnf(i_0_1427,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_1428,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_1429,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_1430,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_1431,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_1432,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_1433,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_1434,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_mod__if_0,
    [final] ).

cnf(i_0_1435,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_1436,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_1437,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
    | X1 = X3
    | c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    cls_subst__Var_2,
    [final] ).

cnf(i_0_1438,negated_conjecture,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X1),X2)),
    cls_conjecture_1,
    [final] ).

cnf(i_0_1439,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_1440,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_1441,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_1442,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_1443,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_1444,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_1445,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_1446,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_1447,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_1448,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__linear_0,
    [final] ).

cnf(i_0_1449,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I7_J_0,
    [final] ).

cnf(i_0_1450,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__c_0,
    [final] ).

cnf(i_0_1451,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_1452,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_1453,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_1454,axiom,
    ( c_Orderings_Oord__class_Omin(X2,X3,X1) = c_Orderings_Oord__class_Omin(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Oinf__commute_0,
    [final] ).

cnf(i_0_1455,axiom,
    ( c_Orderings_Oord__class_Omax(X2,X3,X1) = c_Orderings_Oord__class_Omax(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Osup__commute_0,
    [final] ).

cnf(i_0_1456,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2 ),
    cls_subst__Var_1,
    [final] ).

cnf(i_0_1457,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_1458,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_1459,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
    cls_mult__cancel1_1,
    [final] ).

cnf(i_0_1460,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_853,c_0_756]),
    [final] ).

cnf(i_0_1461,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_mult__cancel2_1,
    [final] ).

cnf(i_0_1462,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_no__zero__divirors__neq0_0,
    [final] ).

cnf(i_0_1463,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_no__zero__divisors_0,
    [final] ).

cnf(i_0_1464,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
    | c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_mult__eq__0__iff_0,
    [final] ).

cnf(i_0_1465,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_1466,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_1467,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_1468,axiom,
    ( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_lift_Osimps_I1_J_0,
    [final] ).

cnf(i_0_1469,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_1470,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    cls_nat__le__linear_0,
    [final] ).

cnf(i_0_1471,axiom,
    c_Lambda_Olift(c_Lambda_OdB_OApp(X1,X2),X3) = c_Lambda_OdB_OApp(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3)),
    cls_lift_Osimps_I2_J_0,
    [final] ).

cnf(i_0_1472,axiom,
    c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
    cls_nat__mult__commute_0,
    [final] ).

cnf(i_0_1473,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_1474,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_1475,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_1476,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_1477,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_mult__is__0_0,
    [final] ).

cnf(i_0_1478,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__le_1,
    [final] ).

cnf(i_0_1479,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__irrefl_0,
    [final] ).

cnf(i_0_1480,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__neq__iff_1,
    [final] ).

cnf(i_0_1481,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_1482,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Oone__class_Oone(tc_nat)
    | X1 != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    cls_mult__eq__self__implies__10_0,
    [final] ).

cnf(i_0_1483,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_1484,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_854,c_0_756]),
    [final] ).

cnf(i_0_1485,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_855,c_0_756]),
    [final] ).

cnf(i_0_1486,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_856,c_0_756]),
    [final] ).

cnf(i_0_1487,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_857,c_0_756]),
    [final] ).

cnf(i_0_1488,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    cls_nat__mult__eq__1__iff_0,
    [final] ).

cnf(i_0_1489,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_1490,axiom,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    cls_nat__mult__eq__1__iff_1,
    [final] ).

cnf(i_0_1491,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_1492,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    cls_nat__1__eq__mult__iff_0,
    [final] ).

cnf(i_0_1493,axiom,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    cls_nat__1__eq__mult__iff_1,
    [final] ).

cnf(i_0_1494,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X1,
    inference(rw,[status(thm)],[i_0_858,c_0_756]),
    [final] ).

cnf(i_0_1495,plain,
    X1 != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(rw,[status(thm)],[i_0_859,c_0_756]),
    [final] ).

cnf(i_0_1496,axiom,
    ( c_Lambda_Obeta(c_Lambda_Olift(X1,X2),c_Lambda_Olift(X3,X2))
    | ~ c_Lambda_Obeta(X1,X3) ),
    cls_lift__preserves__beta_0,
    [final] ).

cnf(i_0_1497,axiom,
    ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X2),c_Lambda_OdB_OApp(X1,X3))
    | ~ c_Lambda_Obeta(X2,X3) ),
    cls_appR_0,
    [final] ).

cnf(i_0_1498,axiom,
    ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X2),c_Lambda_OdB_OApp(X3,X2))
    | ~ c_Lambda_Obeta(X1,X3) ),
    cls_appL_0,
    [final] ).

cnf(i_0_1499,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_1500,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_1501,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_not__less0_0,
    [final] ).

cnf(i_0_1502,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_1503,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_less__not__refl_0,
    [final] ).

cnf(i_0_1504,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_nat__less__le_1,
    [final] ).

cnf(i_0_1505,axiom,
    c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
    cls_subst__lift_0,
    [final] ).

cnf(i_0_1506,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_1507,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_1508,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_1509,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_1510,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_1511,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__0_0,
    [final] ).

cnf(i_0_1512,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    cls_mult__zero__left_0,
    [final] ).

cnf(i_0_1513,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
    cls_mult__eq__0__iff_1,
    [final] ).

cnf(i_0_1514,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__0_0,
    [final] ).

cnf(i_0_1515,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I9_J_0,
    [final] ).

cnf(i_0_1516,axiom,
    ( c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__by__1_0,
    [final] ).

cnf(i_0_1517,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    cls_mult__zero__right_0,
    [final] ).

cnf(i_0_1518,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
    cls_mult__eq__0__iff_2,
    [final] ).

cnf(i_0_1519,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I10_J_0,
    [final] ).

cnf(i_0_1520,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    cls_mult__1__left_0,
    [final] ).

cnf(i_0_1521,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    cls_mult__1_0,
    [final] ).

cnf(i_0_1522,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I11_J_0,
    [final] ).

cnf(i_0_1523,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Omul__1_0,
    [final] ).

cnf(i_0_1524,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_1525,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_1526,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_1527,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_1528,axiom,
    ( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__by__0_0,
    [final] ).

cnf(i_0_1529,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    cls_mult__1__right_0,
    [final] ).

cnf(i_0_1530,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I12_J_0,
    [final] ).

cnf(i_0_1531,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_1532,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_1533,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_1534,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_1535,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__self_0,
    [final] ).

cnf(i_0_1536,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_1537,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_1538,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_1539,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X2,X1) = X2
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
    cls_mult__idem_0,
    [final] ).

cnf(i_0_1540,axiom,
    ( c_Orderings_Oord__class_Omin(X2,X2,X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Oinf__idem_0,
    [final] ).

cnf(i_0_1541,axiom,
    ( c_Orderings_Oord__class_Omax(X2,X2,X1) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    cls_min__max_Osup__idem_0,
    [final] ).

cnf(i_0_1542,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_order__eq__iff_0,
    [final] ).

cnf(i_0_1543,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    cls_order__eq__refl_0,
    [final] ).

cnf(i_0_1544,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    cls_nat__mult__eq__1__iff_2,
    [final] ).

cnf(i_0_1545,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_1546,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    cls_nat__1__eq__mult__iff_2,
    [final] ).

cnf(i_0_1547,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_860,c_0_756]),
    [final] ).

cnf(i_0_1548,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
    cls_subst__eq_0,
    [final] ).

cnf(i_0_1549,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_1550,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_1551,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_mult__is__0_1,
    [final] ).

cnf(i_0_1552,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_1553,axiom,
    c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_min__0L_0,
    [final] ).

cnf(i_0_1554,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_mult__is__0_2,
    [final] ).

cnf(i_0_1555,axiom,
    c_Orderings_Oord__class_Omin(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_min__0R_0,
    [final] ).

cnf(i_0_1556,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
    cls_nat__mult__1_0,
    [final] ).

cnf(i_0_1557,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_1558,axiom,
    c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    cls_max__0L_0,
    [final] ).

cnf(i_0_1559,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    cls_nat__mult__1__right_0,
    [final] ).

cnf(i_0_1560,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_1561,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_1562,axiom,
    c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    cls_max__0R_0,
    [final] ).

cnf(i_0_1563,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_1564,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    cls_le0_0,
    [final] ).

cnf(i_0_1565,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_1566,axiom,
    c_lessequals(X1,X1,tc_nat),
    cls_eq__imp__le_0,
    [final] ).

cnf(i_0_1567,axiom,
    c_lessequals(X1,X1,tc_nat),
    cls_le__refl_0,
    [final] ).

cnf(i_0_1568,axiom,
    ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    cls_abs_0,
    [final] ).

cnf(i_0_1569,axiom,
    ( X1 = X3
    | c_Lambda_OdB_OApp(X1,X2) != c_Lambda_OdB_OApp(X3,X4) ),
    cls_dB_Osimps_I2_J_0,
    [final] ).

cnf(i_0_1570,axiom,
    ( X2 = X4
    | c_Lambda_OdB_OApp(X1,X2) != c_Lambda_OdB_OApp(X3,X4) ),
    cls_dB_Osimps_I2_J_1,
    [final] ).

cnf(i_0_1571,axiom,
    ( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
    | ~ c_InductTermi_OIT(X1) ),
    cls_lift__IT_0,
    [final] ).

cnf(i_0_1572,axiom,
    ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X1),X2),
    cls_beta__cases_I1_J_0,
    [final] ).

cnf(i_0_1573,axiom,
    c_Lambda_OdB_OApp(X1,X2) != c_Lambda_OdB_OAbs(X3),
    cls_dB_Osimps_I8_J_0,
    [final] ).

cnf(i_0_1574,axiom,
    c_Lambda_OdB_OApp(X1,X2) != c_Lambda_OdB_OVar(X3),
    cls_dB_Osimps_I5_J_0,
    [final] ).

cnf(i_0_1575,axiom,
    c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OApp(X2,X3),
    cls_dB_Osimps_I9_J_0,
    [final] ).

cnf(i_0_1576,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OApp(X2,X3),
    cls_dB_Osimps_I4_J_0,
    [final] ).

cnf(i_0_1577,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_1578,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_1579,axiom,
    ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
    | ~ c_InductTermi_OIT(X1) ),
    cls_Lambda_0,
    [final] ).

cnf(i_0_1580,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    cls_dB_Osimps_I3_J_0,
    [final] ).

cnf(i_0_1581,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    cls_dB_Osimps_I1_J_0,
    [final] ).

cnf(i_0_1582,axiom,
    c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
    cls_dB_Osimps_I7_J_0,
    [final] ).

cnf(i_0_1583,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    cls_dB_Osimps_I6_J_0,
    [final] ).

cnf(i_0_1584,negated_conjecture,
    c_InductTermi_OIT(v_ra),
    cls_conjecture_0,
    [final] ).

cnf(i_0_1585,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring,
    [final] ).

cnf(i_0_1586,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__mult,
    [final] ).

cnf(i_0_1587,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__add,
    [final] ).

cnf(i_0_1588,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    clsarity_nat__Ring__and__Field_Opordered__semiring,
    [final] ).

cnf(i_0_1589,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,
    [final] ).

cnf(i_0_1590,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
    [final] ).

cnf(i_0_1591,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1592,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    clsarity_nat__Ring__and__Field_Omult__mono1,
    [final] ).

cnf(i_0_1593,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    clsarity_nat__Ring__and__Field_Omult__mono,
    [final] ).

cnf(i_0_1594,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1595,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,
    [final] ).

cnf(i_0_1596,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    clsarity_nat__Ring__and__Field_Osemiring,
    [final] ).

cnf(i_0_1597,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    clsarity_nat__Ring__and__Field_Omult__zero,
    [final] ).

cnf(i_0_1598,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    clsarity_nat__Ring__and__Field_Ozero__neq__one,
    [final] ).

cnf(i_0_1599,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semidom,
    [final] ).

cnf(i_0_1600,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    clsarity_nat__Ring__and__Field_Ono__zero__divisors,
    [final] ).

cnf(i_0_1601,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__add,
    [final] ).

cnf(i_0_1602,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_1603,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_1604,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
    [final] ).

cnf(i_0_1605,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,
    [final] ).

cnf(i_0_1606,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__mult,
    [final] ).

cnf(i_0_1607,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__mult,
    [final] ).

cnf(i_0_1608,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semiring,
    [final] ).

cnf(i_0_1609,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semiring__strict,
    [final] ).

cnf(i_0_1610,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
    [final] ).

cnf(i_0_1611,axiom,
    class_Divides_Osemiring__div(tc_nat),
    clsarity_nat__Divides_Osemiring__div,
    [final] ).

cnf(i_0_1612,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__add,
    [final] ).

cnf(i_0_1613,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    [final] ).

cnf(i_0_1614,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_1615,axiom,
    X1 = X1 ).

cnf(i_0_1616,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1617,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1618,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_1619,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X1,X3) = c_Lambda_Olift(X2,X3) ) ).

cnf(i_0_1620,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X3,X1) = c_Lambda_Olift(X3,X2) ) ).

cnf(i_0_1621,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X1,X3,X4) = c_Orderings_Oord__class_Omax(X2,X3,X4) ) ).

cnf(i_0_1622,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X3,X1,X4) = c_Orderings_Oord__class_Omax(X3,X2,X4) ) ).

cnf(i_0_1623,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X3,X4,X1) = c_Orderings_Oord__class_Omax(X3,X4,X2) ) ).

cnf(i_0_1624,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X1,X3,X4) = c_Orderings_Oord__class_Omin(X2,X3,X4) ) ).

cnf(i_0_1625,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X3,X1,X4) = c_Orderings_Oord__class_Omin(X3,X2,X4) ) ).

cnf(i_0_1626,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X3,X4,X1) = c_Orderings_Oord__class_Omin(X3,X4,X2) ) ).

cnf(i_0_1627,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OApp(X1,X3) = c_Lambda_OdB_OApp(X2,X3) ) ).

cnf(i_0_1628,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OApp(X3,X1) = c_Lambda_OdB_OApp(X3,X2) ) ).

cnf(i_0_1629,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X1,X3,X4) = c_Lambda_Osubst(X2,X3,X4) ) ).

cnf(i_0_1630,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X1,X4) = c_Lambda_Osubst(X3,X2,X4) ) ).

cnf(i_0_1631,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X4,X1) = c_Lambda_Osubst(X3,X4,X2) ) ).

cnf(i_0_1632,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_1633,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_1634,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_1635,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_1636,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_1637,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).

cnf(i_0_1638,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).

cnf(i_0_1639,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).

cnf(i_0_1640,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1641,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1642,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1643,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1644,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_1645,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_1646,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_1647,axiom,
    ( X1 != X2
    | ~ c_InductTermi_OIT(X1)
    | c_InductTermi_OIT(X2) ) ).

cnf(i_0_1648,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_1649,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_1650,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_1651,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1652,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).

cnf(i_0_1653,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Ring__and__Field_Opordered__semiring(X2) ) ).

cnf(i_0_1654,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semiring(X1)
    | class_Ring__and__Field_Oordered__semiring(X2) ) ).

cnf(i_0_1655,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1656,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1657,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).

cnf(i_0_1658,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_1659,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_1660,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_1661,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__mono1(X1)
    | class_Ring__and__Field_Omult__mono1(X2) ) ).

cnf(i_0_1662,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__mono(X1)
    | class_Ring__and__Field_Omult__mono(X2) ) ).

cnf(i_0_1663,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_1664,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1665,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1666,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X2) ) ).

cnf(i_0_1667,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1668,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).

cnf(i_0_1669,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_1670,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_1671,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1672,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1673,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1674,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1675,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1676,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X2) ) ).

cnf(i_0_1677,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_1678,axiom,
    ( X1 != X2
    | ~ c_Lambda_Obeta(X1,X3)
    | c_Lambda_Obeta(X2,X3) ) ).

cnf(i_0_1679,axiom,
    ( X1 != X2
    | ~ c_Lambda_Obeta(X3,X1)
    | c_Lambda_Obeta(X3,X2) ) ).

cnf(i_0_1680,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1681,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1682,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
    | class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_1683,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1684,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1685,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Opordered__ring(X2) ) ).

cnf(i_0_1686,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1687,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | class_Ring__and__Field_Ono__zero__divisors(X2) ) ).

cnf(i_0_1688,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
    | class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_1689,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | class_Ring__and__Field_Omult__zero(X2) ) ).

cnf(i_0_1690,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_OrderedGroup_Omonoid__mult(X2) ) ).

cnf(i_0_1691,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_1692,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_1693,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_1694,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oordered__ring__strict(X2) ) ).

cnf(i_0_1695,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Oring(X2) ) ).

cnf(i_0_1696,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1697,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring(X1)
    | class_Ring__and__Field_Osemiring(X2) ) ).

cnf(i_0_1698,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_1615_001,axiom,
    X1 = X1 ).

cnf(i_0_1616_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1617_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1618_004,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_1619_005,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X1,X3) = c_Lambda_Olift(X2,X3) ) ).

cnf(i_0_1620_006,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X3,X1) = c_Lambda_Olift(X3,X2) ) ).

cnf(i_0_1621_007,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X1,X3,X4) = c_Orderings_Oord__class_Omax(X2,X3,X4) ) ).

cnf(i_0_1622_008,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X3,X1,X4) = c_Orderings_Oord__class_Omax(X3,X2,X4) ) ).

cnf(i_0_1623_009,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X3,X4,X1) = c_Orderings_Oord__class_Omax(X3,X4,X2) ) ).

cnf(i_0_1624_010,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X1,X3,X4) = c_Orderings_Oord__class_Omin(X2,X3,X4) ) ).

cnf(i_0_1625_011,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X3,X1,X4) = c_Orderings_Oord__class_Omin(X3,X2,X4) ) ).

cnf(i_0_1626_012,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X3,X4,X1) = c_Orderings_Oord__class_Omin(X3,X4,X2) ) ).

cnf(i_0_1627_013,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OApp(X1,X3) = c_Lambda_OdB_OApp(X2,X3) ) ).

cnf(i_0_1628_014,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OApp(X3,X1) = c_Lambda_OdB_OApp(X3,X2) ) ).

cnf(i_0_1629_015,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X1,X3,X4) = c_Lambda_Osubst(X2,X3,X4) ) ).

cnf(i_0_1630_016,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X1,X4) = c_Lambda_Osubst(X3,X2,X4) ) ).

cnf(i_0_1631_017,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X4,X1) = c_Lambda_Osubst(X3,X4,X2) ) ).

cnf(i_0_1632_018,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_1633_019,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).

cnf(i_0_1634_020,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).

cnf(i_0_1635_021,axiom,
    ( X1 != X2
    | c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).

cnf(i_0_1636_022,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_1637_023,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).

cnf(i_0_1638_024,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).

cnf(i_0_1639_025,axiom,
    ( X1 != X2
    | c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).

cnf(i_0_1640_026,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1641_027,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1642_028,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1643_029,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1644_030,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_1645_031,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_1646_032,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_1647_033,axiom,
    ( X1 != X2
    | ~ c_InductTermi_OIT(X1)
    | c_InductTermi_OIT(X2) ) ).

cnf(i_0_1648_034,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_1649_035,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_1650_036,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_1651_037,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1652_038,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).

cnf(i_0_1653_039,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Ring__and__Field_Opordered__semiring(X2) ) ).

cnf(i_0_1654_040,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semiring(X1)
    | class_Ring__and__Field_Oordered__semiring(X2) ) ).

cnf(i_0_1655_041,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1656_042,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1657_043,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).

cnf(i_0_1658_044,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_1659_045,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_1660_046,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_1661_047,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__mono1(X1)
    | class_Ring__and__Field_Omult__mono1(X2) ) ).

cnf(i_0_1662_048,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__mono(X1)
    | class_Ring__and__Field_Omult__mono(X2) ) ).

cnf(i_0_1663_049,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_1664_050,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1665_051,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1666_052,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X2) ) ).

cnf(i_0_1667_053,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1668_054,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).

cnf(i_0_1669_055,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_1670_056,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_1671_057,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1672_058,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1673_059,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1674_060,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1675_061,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1676_062,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X2) ) ).

cnf(i_0_1677_063,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_1678_064,axiom,
    ( X1 != X2
    | ~ c_Lambda_Obeta(X1,X3)
    | c_Lambda_Obeta(X2,X3) ) ).

cnf(i_0_1679_065,axiom,
    ( X1 != X2
    | ~ c_Lambda_Obeta(X3,X1)
    | c_Lambda_Obeta(X3,X2) ) ).

cnf(i_0_1680_066,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1681_067,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1682_068,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
    | class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_1683_069,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1684_070,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1685_071,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Opordered__ring(X2) ) ).

cnf(i_0_1686_072,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1687_073,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ono__zero__divisors(X1)
    | class_Ring__and__Field_Ono__zero__divisors(X2) ) ).

cnf(i_0_1688_074,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
    | class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_1689_075,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Omult__zero(X1)
    | class_Ring__and__Field_Omult__zero(X2) ) ).

cnf(i_0_1690_076,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_OrderedGroup_Omonoid__mult(X2) ) ).

cnf(i_0_1691_077,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_1692_078,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_1693_079,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_1694_080,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oordered__ring__strict(X2) ) ).

cnf(i_0_1695_081,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Oring(X2) ) ).

cnf(i_0_1696_082,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1697_083,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring(X1)
    | class_Ring__and__Field_Osemiring(X2) ) ).

cnf(i_0_1698_084,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_1699,plain,
    ( ~ c_lessequals(X1,X1,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),X2,tc_nat),X3,tc_nat) = X3 ),
    inference(equality_inference,[],[893]) ).

cnf(i_0_1700,plain,
    ( ~ c_lessequals(X1,X1,tc_nat)
    | X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),X3,tc_nat),X2,tc_nat) ),
    inference(equality_inference,[],[894]) ).

cnf(i_0_1701,plain,
    ( ~ class_Ring__and__Field_Oring(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X2,X1),X3,X1),X4,X1) = X4 ),
    inference(equality_inference,[],[897]) ).

cnf(i_0_1702,plain,
    ( ~ class_Ring__and__Field_Oring(X1)
    | X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X3,X1),X4,X1),X2,X1) ),
    inference(equality_inference,[],[898]) ).

cnf(i_0_1703,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[901]) ).

cnf(i_0_1704,plain,
    ( X1 = X1
    | X2 = X3 ),
    inference(equality_inference,[],[904]) ).

cnf(i_0_1705,plain,
    c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat),
    inference(equality_inference,[],[935]) ).

cnf(i_0_1706,plain,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | X3 = c_HOL_Ozero__class_Ozero(X1) ),
    inference(equality_inference,[],[975]) ).

cnf(i_0_1707,plain,
    X1 = X1,
    inference(equality_inference,[],[978]) ).

cnf(i_0_1708,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[982]) ).

cnf(i_0_1709,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,[],[1079]) ).

cnf(i_0_1710,plain,
    ( X1 = X1
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(equality_inference,[],[1171]) ).

cnf(i_0_1711,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(equality_inference,[],[1251]) ).

cnf(i_0_1712,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(equality_inference,[],[1252]) ).

cnf(i_0_1713,plain,
    ( X1 = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(equality_inference,[],[1271]) ).

cnf(i_0_1714,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,[],[1319]) ).

cnf(i_0_1715,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,[],[1320]) ).

cnf(i_0_1716,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,[],[1321]) ).

cnf(i_0_1717,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,[],[1322]) ).

cnf(i_0_1718,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[1351]) ).

cnf(i_0_1719,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,[],[1353]) ).

cnf(i_0_1720,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,[],[1354]) ).

cnf(i_0_1721,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1360]) ).

cnf(i_0_1722,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1361]) ).

cnf(i_0_1723,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1362]) ).

cnf(i_0_1724,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1363]) ).

cnf(i_0_1725,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[1364]) ).

cnf(i_0_1726,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[1377]) ).

cnf(i_0_1727,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[1379]) ).

cnf(i_0_1728,plain,
    X1 = X1,
    inference(equality_inference,[],[1393]) ).

cnf(i_0_1729,plain,
    X1 = X1,
    inference(equality_inference,[],[1395]) ).

cnf(i_0_1730,plain,
    X1 = X1,
    inference(equality_inference,[],[1569]) ).

cnf(i_0_1731,plain,
    X1 = X1,
    inference(equality_inference,[],[1570]) ).

cnf(i_0_1732,plain,
    X1 = X1,
    inference(equality_inference,[],[1580]) ).

cnf(i_0_1733,plain,
    X1 = X1,
    inference(equality_inference,[],[1581]) ).

cnf(i_0_1734,plain,
    $false,
    inference(scs_inference,[],[i_0_861,i_0_1438,i_0_1579]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LCL755-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33  % Computer : n010.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Mon May  4 23:04:36 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 1.45/2.67  % Version  : CSE_E---1.7
% 1.45/2.67  % Problem  : theBenchmark.p
% 1.45/2.67  % SZS status Unsatisfiable for theBenchmark.p
% 1.45/2.67  % SZS output start CNFRefutation
% See solution above
% 1.50/2.74  % Total time : 2.327s
%------------------------------------------------------------------------------