CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : LCL827-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n011.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 04:45:11 PM UTC 2026

% Result   : Unsatisfiable 0.40s 1.65s
% Output   : CNFRefutation 0.45s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_394)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_subst__subst_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Olift(X2,X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
    | ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__subst_0) ).

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

cnf(cls_shift__commute_0,axiom,
    hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4)),c_HOL_Ozero__class_Ozero(tc_nat)),X5) = hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X5)),c_Suc(X3)),X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__commute_0) ).

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

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

cnf(cls_type_Osize_I4_J_0,axiom,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osize_I4_J_0) ).

cnf(cls_dB_Osize_I5_J_0,axiom,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I5_J_0) ).

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

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

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

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

cnf(cls_type_Osize_I2_J_0,axiom,
    c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osize_I2_J_0) ).

cnf(cls_dB_Osize_I2_J_0,axiom,
    c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I2_J_0) ).

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

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

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

cnf(cls_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,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__lift_0) ).

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

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

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

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

cnf(cls_Suc__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

cnf(cls_less__Suc__eq__0__disj_3,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

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

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

cnf(cls_not__less__eq_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

cnf(cls_less__trans__Suc_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

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

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

cnf(cls_not__less__less__Suc__eq_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

cnf(cls_less__SucE_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).

cnf(cls_less__antisym_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).

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

cnf(cls_Suc__lessI_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | c_Suc(X1) = X2
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

cnf(cls_one__is__add_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).

cnf(cls_add__is__1_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).

cnf(cls_less__Suc0_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

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

cnf(cls_less__SucI_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).

cnf(cls_one__is__add_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).

cnf(cls_one__is__add_3,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).

cnf(cls_add__is__1_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).

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

cnf(cls_dB_Osize_I6_J_0,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).

cnf(cls_add__is__1_5,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).

cnf(cls_one__is__add_5,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).

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

cnf(cls_not__less__less__Suc__eq_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

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

cnf(cls_dB_Osize_I3_J_0,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).

cnf(cls_one__is__add_2,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).

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

cnf(cls_less__Suc0_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).

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

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

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

cnf(cls_zero__less__Suc_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

cnf(cls_gr0__conv__Suc_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

cnf(cls_less__Suc__eq_2,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

cnf(cls_lessI_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).

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

cnf(cls_Suc__neq__Zero_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

cnf(cls_nat_Osimps_I3_J_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

cnf(cls_nat_Osimps_I2_J_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

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

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

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

cnf(cls_One__nat__def_0,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).

cnf(cls_CHAINED_0_01,axiom,
    c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_as____,tc_Lambda_OdB),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

cnf(cls_var__app__types_0,axiom,
    ( X1 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X2,X1,X3,X4),X2,tc_Type_Otype,tc_Type_Otype)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X1))
    | ~ c_Type_Otypings(X3,X6,X7)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_0) ).

cnf(cls_var__app__types_1,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
    | ~ c_Type_Otypings(X1,X6,X7)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_1) ).

cnf(cls_var__app__type__eq_0,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).

cnf(cls_var__app__typesE_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).

cnf(cls_list__app__typeD_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).

cnf(cls_list__app__typeE_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).

cnf(cls_list__app__typeI_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
    | ~ c_Type_Otypings(X1,X3,X5)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).

cnf(cls_head__Var__reduction_1,axiom,
    ( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).

cnf(cls_var__app__typesE_1,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).

cnf(cls_list__app__typeD_1,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).

cnf(cls_list__app__typeE_1,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).

cnf(cls_head__Var__reduction_0,axiom,
    ( c_ListOrder_Ostep1(c_Lambda_Obeta,X1,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X1,X3),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).

cnf(cls_apps__preserves__betas_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X2,X3,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).

cnf(cls_apps__preserves__beta2_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).

cnf(cls_apps__preserves__beta_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).

cnf(cls_Beta_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).

cnf(cls_nT_0,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nT_0) ).

cnf(cls_Var_I2_J_0,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).

cnf(cls_double__induction__lemma_0,axiom,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).

cnf(cls_CHAINED_0,axiom,
    c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

cnf(cls_typing__elims_I2_J_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).

cnf(cls_IT_OVar_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).

cnf(cls_typing__elims_I3_J_1,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X2,X1,X3))),X3),c_Type_Osko__Type__Xtyping__elims__3__2(X2,X1,X3)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X3)),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).

cnf(cls_subst__lemma_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X6))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X3)),X5),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).

cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).

cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).

cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom,
    ( X2 = X4
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).

cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom,
    ( X2 = X4
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).

cnf(cls_foldl__assoc_0,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).

cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).

cnf(cls_apps__eq__tail__conv_0,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).

cnf(cls_foldl__absorb0_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).

cnf(cls_foldl__foldr1__lemma_0,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1))
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).

cnf(cls_MI1_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X5)))
    | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X6),X4),X1))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X6),X5),X1)),X3),X7))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI1_0) ).

cnf(cls_MI2_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X5)))
    | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X6),X4),X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X6),X5),X2)),X3),X7))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI2_0) ).

cnf(cls_CHAINED_0_02,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_a____),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).

cnf(cls_Cons_I1_J_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_a____),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_I1_J_0) ).

cnf(cls_I_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_a____),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_I_0) ).

cnf(cls_Abs_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X3)),X2),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs_0) ).

cnf(cls_abs__typeE_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2))),X2),c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__typeE_0) ).

cnf(cls_CHAINED_1,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_sko__CHAINED__1(v_T____,v_a____,v_e____,v_i____))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).

cnf(cls_Cons_Ohyps_I1_J_1,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_a____,v_e____,v_i____))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_Ohyps_I1_J_1) ).

cnf(cls_Cons_I1_J_1,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_sko__local__XCons__1__1(v_T____,v_a____,v_e____,v_i____))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_I1_J_1) ).

cnf(cls_conjecture_1,negated_conjecture,
    ( v_thesis____
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_that_0,axiom,
    ( v_thesis____
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).

cnf(cls_foldl__foldr1_0,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).

cnf(cls_foldr__conv__foldl_0,axiom,
    ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).

cnf(cls_lift__type_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),X3)),c_Lambda_Olift(X4,X2)),X5))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).

cnf(cls_App__eq__foldl__conv_0,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).

cnf(cls_Abs__App__neq__Var__apps_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).

cnf(cls_Abs__eq__apps__conv_0,axiom,
    ( c_Lambda_OdB_OAbs(X1) = X2
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).

cnf(cls_Var__eq__apps__conv_0,axiom,
    ( c_Lambda_OdB_OVar(X1) = X2
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).

cnf(cls_apps__eq__Abs__conv_0,axiom,
    ( X1 = c_Lambda_OdB_OAbs(X3)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).

cnf(cls_apps__eq__Abs__conv_1,axiom,
    ( X2 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).

cnf(cls_Abs__eq__apps__conv_1,axiom,
    ( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).

cnf(cls_Var__eq__apps__conv_1,axiom,
    ( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).

cnf(cls_typing__elims_I2_J_1,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).

cnf(cls_rtranclp__converseD_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).

cnf(cls_subst__preserves__beta2_H_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).

cnf(cls_subst__preserves__beta_H_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).

cnf(cls_lift__subst_0,axiom,
    ( c_Lambda_Olift(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Olift(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)))),c_Lambda_Olift(X2,X4)),X3)
    | ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__subst_0) ).

cnf(cls_rtranclp__converseI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).

cnf(cls_App__eq__foldl__conv_4,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).

cnf(cls_subst__preserves__beta2_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).

cnf(cls_App_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),X5))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X5),X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_0) ).

cnf(cls_subst__preserves__beta_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

cnf(cls_apps__eq__Abs__conv_2,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).

cnf(cls_Abs__eq__apps__conv_2,axiom,
    c_Lambda_OdB_OAbs(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).

cnf(cls_Var__eq__apps__conv_2,axiom,
    c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).

cnf(cls_foldr_Osimps_I1_J_0,axiom,
    c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).

cnf(cls_foldl__Nil_0,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).

cnf(cls_rtrancl__beta__App_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).

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

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

cnf(cls_subst__App_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).

cnf(cls_conversepD_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversepD_0) ).

cnf(cls_conversep_Ocases_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).

cnf(cls_rtrancl__beta__AppR_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).

cnf(cls_rtrancl__beta__AppL_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).

cnf(cls_beta_0,axiom,
    hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).

cnf(cls_rtranclp__trans_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).

cnf(cls_lift__subst__lt_0,axiom,
    ( c_Lambda_Olift(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Olift(X1,X4)),c_Lambda_Olift(X2,X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).

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

cnf(cls_subject__reduction_H_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X4),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).

cnf(cls_typing__elims_I3_J_0,axiom,
    ( X1 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X1,X2,X3)),c_Type_Osko__Type__Xtyping__elims__3__2(X1,X2,X3))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),c_Lambda_OdB_OAbs(X3)),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).

cnf(cls_conversep__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__iff_1) ).

cnf(cls_conversep_Ointros_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).

cnf(cls_appR_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).

cnf(cls_appL_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).

cnf(cls_converse__rtranclp__into__rtranclp_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X5),X4))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).

cnf(cls_rtranclp_Ortrancl__into__rtrancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).

cnf(cls_subst__Abs_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Abs_0) ).

cnf(cls_lift__preserves__beta_H_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X2)),c_Lambda_Olift(X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).

cnf(cls_subject__reduction_0,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).

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

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

cnf(cls_add__less__cancel__right_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

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

cnf(cls_subst__Var__IT_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).

cnf(cls_rtrancl__beta__Abs_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).

cnf(cls_shift__lt_0,axiom,
    ( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X5) = hAPP(X2,c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X3,X5,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__lt_0) ).

cnf(cls_add__strict__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

cnf(cls_accp__downwards_0,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards_0) ).

cnf(cls_accp__downwards__aux_0,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).

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

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

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

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

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

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

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

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

cnf(cls_not__Nil__step1_0,axiom,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).

cnf(cls_not__step1__Nil_0,axiom,
    ~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).

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

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

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

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

cnf(cls_add__neg__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

cnf(cls_add__pos__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

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

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

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

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

cnf(cls_lift__preserves__beta_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X2)),c_Lambda_Olift(X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

cnf(cls_pos__add__strict_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

cnf(cls_shift__gt_0,axiom,
    ( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X5) = hAPP(X2,X5)
    | ~ c_HOL_Oord__class_Oless(X5,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__gt_0) ).

cnf(cls_diff__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).

cnf(cls_typing__elims_I1_J_0,axiom,
    ( hAPP(X1,X2) = X3
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).

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

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

cnf(cls_even__less__0__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

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

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

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

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

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

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

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

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

cnf(cls_r__into__rtranclp_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).

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

cnf(cls_subst__Var_0,axiom,
    ( hAPP(hAPP(hAPP(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/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_0) ).

cnf(cls_subst__gt_0,axiom,
    ( hAPP(hAPP(hAPP(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/sandbox2/benchmark/theBenchmark.p',cls_subst__gt_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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_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,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

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

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

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

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

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

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

cnf(cls_accp__downward_0,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downward_0) ).

cnf(cls_accp_Ocases_0,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).

cnf(cls_even__less__0__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

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

cnf(cls_termi__implies__IT_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).

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

cnf(cls_typing_OVar_0,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),hAPP(X1,X2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).

cnf(cls_shift__eq_0,axiom,
    hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X3) = X4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).

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

cnf(cls_lift_Osimps_I3_J_0,axiom,
    c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X2) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).

cnf(cls_of__nat__add_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1)),c_Nat_Osemiring__1__class_Oof__nat(X3,X1))
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__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/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

cnf(cls_app__Var__IT_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

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

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

cnf(cls_order__less__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

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

cnf(cls_abs_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).

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

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

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

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

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

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

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

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

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

cnf(cls_lift_Osimps_I2_J_0,axiom,
    c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

cnf(cls_of__nat__0__less__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

cnf(cls_subst__lt_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).

cnf(cls_of__nat__less__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

cnf(cls_IT__implies__termi_0,axiom,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).

cnf(cls_nat__less__cases_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

cnf(cls_subst__lift_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Olift(X1,X2)),X3),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).

cnf(cls_rtranclp_Ortrancl__refl_0,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).

cnf(cls_Nitpick_Ortranclp__def_1,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).

cnf(cls_of__nat__0__less__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

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

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

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

cnf(cls_not__less__iff__gr__or__eq_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

cnf(cls_order__less__asym_H_0,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

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

cnf(cls_xt1_I9_J_0,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

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

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

cnf(cls_lift_Osimps_I1_J_1,axiom,
    ( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).

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

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

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

cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

cnf(cls_subst__Var_2,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
    | X1 = X3
    | c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).

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

cnf(cls_subst__Var_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).

cnf(cls_conversep__conversep_0,axiom,
    c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).

cnf(cls_beta__cases_I1_J_0,axiom,
    ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

cnf(cls_uT_0,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).

cnf(cls_Var_I4_J_0,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).

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

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

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

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

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

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

cnf(cls_of__nat__less__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

cnf(cls_lift__IT_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).

cnf(cls_linorder__antisym__conv3_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

cnf(cls_linorder__less__linear_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

cnf(cls_linorder__neqE_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | X3 = X2
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

cnf(cls_not__less__iff__gr__or__eq_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

cnf(cls_linorder__neqE__ordered__idom_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | X3 = X2
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

cnf(cls_type_Osimps_I2_J_0,axiom,
    ( X1 = X3
    | hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).

cnf(cls_dB_Osimps_I2_J_0,axiom,
    ( X1 = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

cnf(cls_type_Osimps_I2_J_1,axiom,
    ( X2 = X4
    | hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).

cnf(cls_dB_Osimps_I2_J_1,axiom,
    ( X2 = X4
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_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/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

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

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

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

cnf(cls_subst__eq_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).

cnf(cls_linorder__neqE__nat_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

cnf(cls_nat__neq__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

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

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
    hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

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

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

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

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

cnf(cls_linorder__neq__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

cnf(cls_order__less__irrefl_0,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

cnf(cls_order__less__le_1,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).

cnf(cls_neq0__conv_1,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

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

cnf(cls_gr__implies__not0_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

cnf(cls_not__less0_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).

cnf(cls_less__not__refl_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

cnf(cls_nat__less__le_1,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

cnf(cls_Lambda_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).

cnf(cls_double__eq__0__iff_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

cnf(cls_add__is__0_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).

cnf(cls_add__is__0_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).

cnf(cls_add__eq__self__zero_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

cnf(cls_natgb_Oadd__r0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

cnf(cls_zero__less__one_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

cnf(cls_class__ringb_Osubr0__iff_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

cnf(cls_comm__monoid__add_Omult__1_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

cnf(cls_class__semiring_Oadd__0_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

cnf(cls_add__0__left_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).

cnf(cls_diff__0__right_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

cnf(cls_eq__iff__diff__eq__0_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

cnf(cls_right__minus__eq_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

cnf(cls_diff__self_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).

cnf(cls_conversep__eq_0,axiom,
    c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__eq_0) ).

cnf(cls_dB_Osimps_I8_J_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).

cnf(cls_dB_Osimps_I5_J_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

cnf(cls_dB_Osimps_I9_J_0,axiom,
    c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).

cnf(cls_dB_Osimps_I4_J_0,axiom,
    c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).

cnf(cls_listsp_ONil_0,axiom,
    c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).

cnf(cls_gr0I_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).

cnf(cls_diff__0__eq__0_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

cnf(cls_add__is__0_2,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).

cnf(cls_minus__nat_Odiff__0_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

cnf(cls_diff__self__eq__0_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

cnf(cls_rtranclp__idemp_0,axiom,
    c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).

cnf(cls_of__nat__eq__iff_0,axiom,
    ( X2 = X3
    | ~ class_Nat_Osemiring__char__0(X1)
    | c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

cnf(cls_plus__nat_Oadd__0_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

cnf(cls_Nat_Oadd__0__right_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

cnf(cls_natgb_Oadd__r0__iff_1,axiom,
    X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

cnf(cls_Var__IT_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).

cnf(clsarity_fun__Orderings_Opreorder,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

cnf(clsarity_fun__Orderings_Oorder,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

cnf(cls_of__nat__1_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__1_0) ).

cnf(cls_of__nat__0_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

cnf(cls_Var_I3_J_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).

cnf(cls_uIT_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).

cnf(cls_dB_Osize_I4_J_0,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).

cnf(cls_zero__neq__one_0,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

cnf(cls_dB_Osimps_I3_J_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

cnf(cls_dB_Osize_I1_J_0,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).

cnf(clsarity_nat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

cnf(clsarity_bool__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

cnf(clsarity_nat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

cnf(clsarity_bool__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

cnf(clsarity_nat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).

cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

cnf(cls_conjecture_0,negated_conjecture,
    ~ v_thesis____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_False_0,axiom,
    v_n____ != v_i____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_False_0) ).

cnf(i_0_393,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Olift(X2,X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
    | ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    cls_subst__subst_0 ).

cnf(i_0_394,axiom,
    c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
    cls_Suc__eq__plus1_0 ).

cnf(i_0_395,axiom,
    hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4)),c_HOL_Ozero__class_Ozero(tc_nat)),X5) = hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X5)),c_Suc(X3)),X4),
    cls_shift__commute_0 ).

cnf(i_0_396,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_add__eq__if_1 ).

cnf(i_0_397,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_398,axiom,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_type_Osize_I4_J_0 ).

cnf(i_0_399,axiom,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_dB_Osize_I5_J_0 ).

cnf(i_0_400,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_401,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
    cls_less__add__Suc1_0 ).

cnf(i_0_402,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
    cls_less__iff__Suc__add_1 ).

cnf(i_0_403,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
    cls_less__add__Suc2_0 ).

cnf(i_0_404,axiom,
    c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_type_Osize_I2_J_0 ).

cnf(i_0_405,axiom,
    c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_dB_Osize_I2_J_0 ).

cnf(i_0_406,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
    cls_add__Suc_0 ).

cnf(i_0_407,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_408,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_409,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,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    cls_lift__lift_0 ).

cnf(i_0_410,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
    cls_add__Suc__shift_0 ).

cnf(i_0_411,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
    cls_add__Suc__right_0 ).

cnf(i_0_412,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_413,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_414,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_415,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_416,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_add__is__1_4 ).

cnf(i_0_417,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_one__is__add_4 ).

cnf(i_0_418,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_419,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_420,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_421,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_422,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_423,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_424,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_425,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_426,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_427,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    cls_one__is__add_1 ).

cnf(i_0_428,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_1 ).

cnf(i_0_429,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_430,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_431,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_432,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    cls_one__is__add_0 ).

cnf(i_0_433,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    cls_one__is__add_3 ).

cnf(i_0_434,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_0 ).

cnf(i_0_435,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_3 ).

cnf(i_0_436,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_dB_Osize_I6_J_0 ).

cnf(i_0_437,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_add__is__1_5 ).

cnf(i_0_438,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_one__is__add_5 ).

cnf(i_0_439,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_Oof__nat(X2,X1))
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__Suc_0 ).

cnf(i_0_440,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_441,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_442,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    cls_dB_Osize_I3_J_0 ).

cnf(i_0_443,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    cls_one__is__add_2 ).

cnf(i_0_444,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    cls_add__is__1_2 ).

cnf(i_0_445,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_446,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_Suc__inject_0 ).

cnf(i_0_447,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_nat_Oinject_0 ).

cnf(i_0_448,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_449,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_450,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_451,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_less__Suc__eq_2 ).

cnf(i_0_452,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_lessI_0 ).

cnf(i_0_453,axiom,
    c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
    cls_Suc__eq__plus1__left_0 ).

cnf(i_0_454,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_Suc__neq__Zero_0 ).

cnf(i_0_455,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_nat_Osimps_I3_J_0 ).

cnf(i_0_456,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_nat_Osimps_I2_J_0 ).

cnf(i_0_457,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_Zero__neq__Suc_0 ).

cnf(i_0_458,axiom,
    c_Suc(X1) != X1,
    cls_Suc__n__not__n_0 ).

cnf(i_0_459,axiom,
    X1 != c_Suc(X1),
    cls_n__not__Suc__n_0 ).

cnf(i_0_460,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_461,axiom,
    c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_as____,tc_Lambda_OdB),
    cls_CHAINED_0_01,
    [final] ).

cnf(i_0_462,axiom,
    ( X1 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X2,X1,X3,X4),X2,tc_Type_Otype,tc_Type_Otype)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X1))
    | ~ c_Type_Otypings(X3,X6,X7)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X2)) ),
    cls_var__app__types_0,
    [final] ).

cnf(i_0_463,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
    | ~ c_Type_Otypings(X1,X6,X7)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_var__app__types_1,
    [final] ).

cnf(i_0_464,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X1)) ),
    cls_var__app__type__eq_0,
    [final] ).

cnf(i_0_465,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_var__app__typesE_0,
    [final] ).

cnf(i_0_466,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_list__app__typeD_0,
    [final] ).

cnf(i_0_467,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_list__app__typeE_0,
    [final] ).

cnf(i_0_468,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
    | ~ c_Type_Otypings(X1,X3,X5)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype))) ),
    cls_list__app__typeI_0,
    [final] ).

cnf(i_0_469,axiom,
    ( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X1)) ),
    cls_head__Var__reduction_1,
    [final] ).

cnf(i_0_470,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_var__app__typesE_1,
    [final] ).

cnf(i_0_471,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_list__app__typeD_1,
    [final] ).

cnf(i_0_472,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_list__app__typeE_1,
    [final] ).

cnf(i_0_473,axiom,
    ( c_ListOrder_Ostep1(c_Lambda_Obeta,X1,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X1,X3),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_head__Var__reduction_0,
    [final] ).

cnf(i_0_474,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X2,X3,tc_Lambda_OdB) ),
    cls_apps__preserves__betas_0,
    [final] ).

cnf(i_0_475,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    cls_apps__preserves__beta2_0,
    [final] ).

cnf(i_0_476,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
    cls_apps__preserves__beta_0,
    [final] ).

cnf(i_0_477,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    cls_Beta_0,
    [final] ).

cnf(i_0_478,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
    cls_nT_0,
    [final] ).

cnf(i_0_479,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
    cls_Var_I2_J_0,
    [final] ).

cnf(i_0_480,axiom,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB) ),
    cls_double__induction__lemma_0,
    [final] ).

cnf(i_0_481,axiom,
    c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
    cls_CHAINED_0,
    [final] ).

cnf(i_0_482,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)),X3)) ),
    cls_typing__elims_I2_J_0,
    [final] ).

cnf(i_0_483,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB) ),
    cls_IT_OVar_0,
    [final] ).

cnf(i_0_484,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X2,X1,X3))),X3),c_Type_Osko__Type__Xtyping__elims__3__2(X2,X1,X3)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X3)),X2)) ),
    cls_typing__elims_I3_J_1,
    [final] ).

cnf(i_0_485,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X6))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X3)),X5),X6)) ),
    cls_subst__lemma_0,
    [final] ).

cnf(i_0_486,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Abs__apps__eq__Abs__apps__conv_0,
    [final] ).

cnf(i_0_487,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Var__apps__eq__Var__apps__conv_0,
    [final] ).

cnf(i_0_488,axiom,
    ( X2 = X4
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Abs__apps__eq__Abs__apps__conv_1,
    [final] ).

cnf(i_0_489,axiom,
    ( X2 = X4
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Var__apps__eq__Var__apps__conv_1,
    [final] ).

cnf(i_0_490,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    cls_foldl__assoc_0,
    [final] ).

cnf(i_0_491,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
    cls_Var__apps__neq__Abs__apps_0,
    [final] ).

cnf(i_0_492,axiom,
    ( X1 = X3
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_apps__eq__tail__conv_0,
    [final] ).

cnf(i_0_493,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_foldl__absorb0_0,
    [final] ).

cnf(i_0_494,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1))
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_foldl__foldr1__lemma_0,
    [final] ).

cnf(i_0_495,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X5)))
    | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X6),X4),X1))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X6),X5),X1)),X3),X7))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    cls_MI1_0,
    [final] ).

cnf(i_0_496,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X5)))
    | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X6),X4),X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X6),X5),X2)),X3),X7))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    cls_MI2_0,
    [final] ).

cnf(i_0_497,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_a____),X4)) ),
    cls_CHAINED_0_02,
    [final] ).

cnf(i_0_498,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_a____),X4)) ),
    cls_Cons_I1_J_0,
    [final] ).

cnf(i_0_499,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_a____),X4)) ),
    cls_I_0,
    [final] ).

cnf(i_0_500,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X3)),X2),X4)) ),
    cls_Abs_0,
    [final] ).

cnf(i_0_501,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Olift(X2,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
    | ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_393,c_0_394]),
    [final] ).

cnf(i_0_502,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2))),X2),c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
    cls_abs__typeE_0,
    [final] ).

cnf(i_0_503,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_sko__CHAINED__1(v_T____,v_a____,v_e____,v_i____))),
    cls_CHAINED_1,
    [final] ).

cnf(i_0_504,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_a____,v_e____,v_i____))),
    cls_Cons_Ohyps_I1_J_1,
    [final] ).

cnf(i_0_505,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_sko__local__XCons__1__1(v_T____,v_a____,v_e____,v_i____))),
    cls_Cons_I1_J_1,
    [final] ).

cnf(i_0_506,negated_conjecture,
    ( v_thesis____
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),X1)) ),
    cls_conjecture_1,
    [final] ).

cnf(i_0_507,axiom,
    ( v_thesis____
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),X1)) ),
    cls_that_0,
    [final] ).

cnf(i_0_508,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_foldl__foldr1_0,
    [final] ).

cnf(i_0_509,axiom,
    ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    cls_foldr__conv__foldl_0,
    [final] ).

cnf(i_0_510,plain,
    hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4)),c_HOL_Ozero__class_Ozero(tc_nat)),X5) = hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat))),X4),
    inference(rw,[status(thm)],[i_0_395,c_0_394]),
    [final] ).

cnf(i_0_511,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),X3)),c_Lambda_Olift(X4,X2)),X5))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X5)) ),
    cls_lift__type_0,
    [final] ).

cnf(i_0_512,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_App__eq__foldl__conv_0,
    [final] ).

cnf(i_0_513,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
    cls_Abs__App__neq__Var__apps_0,
    [final] ).

cnf(i_0_514,axiom,
    ( c_Lambda_OdB_OAbs(X1) = X2
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Abs__eq__apps__conv_0,
    [final] ).

cnf(i_0_515,axiom,
    ( c_Lambda_OdB_OVar(X1) = X2
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Var__eq__apps__conv_0,
    [final] ).

cnf(i_0_516,axiom,
    ( X1 = c_Lambda_OdB_OAbs(X3)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    cls_apps__eq__Abs__conv_0,
    [final] ).

cnf(i_0_517,axiom,
    ( X2 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    cls_apps__eq__Abs__conv_1,
    [final] ).

cnf(i_0_518,axiom,
    ( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Abs__eq__apps__conv_1,
    [final] ).

cnf(i_0_519,axiom,
    ( X3 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    cls_Var__eq__apps__conv_1,
    [final] ).

cnf(i_0_520,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2)),X3)) ),
    cls_typing__elims_I2_J_1,
    [final] ).

cnf(i_0_521,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3)) ),
    cls_rtranclp__converseD_0,
    [final] ).

cnf(i_0_522,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4)) ),
    cls_subst__preserves__beta2_H_0,
    [final] ).

cnf(i_0_523,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X4)) ),
    cls_subst__preserves__beta_H_0,
    [final] ).

cnf(i_0_524,axiom,
    ( c_Lambda_Olift(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Olift(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)))),c_Lambda_Olift(X2,X4)),X3)
    | ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    cls_lift__subst_0,
    [final] ).

cnf(i_0_525,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3)) ),
    cls_rtranclp__converseI_0,
    [final] ).

cnf(i_0_526,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    cls_App__eq__foldl__conv_4,
    [final] ).

cnf(i_0_527,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
    cls_subst__preserves__beta2_0,
    [final] ).

cnf(i_0_528,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),X5))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X5),X4))) ),
    cls_App_0,
    [final] ).

cnf(i_0_529,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X4)) ),
    cls_subst__preserves__beta_0,
    [final] ).

cnf(i_0_530,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
    cls_apps__eq__Abs__conv_2,
    [final] ).

cnf(i_0_531,axiom,
    c_Lambda_OdB_OAbs(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    cls_Abs__eq__apps__conv_2,
    [final] ).

cnf(i_0_532,axiom,
    c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    cls_Var__eq__apps__conv_2,
    [final] ).

cnf(i_0_533,axiom,
    c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
    cls_foldr_Osimps_I1_J_0,
    [final] ).

cnf(i_0_534,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
    cls_foldl__Nil_0,
    [final] ).

cnf(i_0_535,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[i_0_396,c_0_394]),
    [final] ).

cnf(i_0_536,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    cls_rtrancl__beta__App_0,
    [final] ).

cnf(i_0_537,axiom,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat))) ),
    cls_nat__diff__split_1,
    [final] ).

cnf(i_0_538,axiom,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat))) ),
    cls_nat__diff__split__asm_1,
    [final] ).

cnf(i_0_539,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),
    cls_subst__App_0,
    [final] ).

cnf(i_0_540,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
    cls_conversepD_0,
    [final] ).

cnf(i_0_541,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
    cls_conversep_Ocases_0,
    [final] ).

cnf(i_0_542,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X3)) ),
    cls_rtrancl__beta__AppR_0,
    [final] ).

cnf(i_0_543,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    cls_rtrancl__beta__AppL_0,
    [final] ).

cnf(i_0_544,axiom,
    hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
    cls_beta_0,
    [final] ).

cnf(i_0_545,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Oone__class_Oone(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_397,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_546,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
    cls_rtranclp__trans_0,
    [final] ).

cnf(i_0_547,axiom,
    ( c_Lambda_Olift(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Olift(X1,X4)),c_Lambda_Olift(X2,X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    cls_lift__subst__lt_0,
    [final] ).

cnf(i_0_548,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I20_J_0,
    [final] ).

cnf(i_0_549,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X4),X2)) ),
    cls_subject__reduction_H_0,
    [final] ).

cnf(i_0_550,plain,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[i_0_398,c_0_394]),
    [final] ).

cnf(i_0_551,plain,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[i_0_399,c_0_394]),
    [final] ).

cnf(i_0_552,axiom,
    ( X1 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X1,X2,X3)),c_Type_Osko__Type__Xtyping__elims__3__2(X1,X2,X3))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),c_Lambda_OdB_OAbs(X3)),X1)) ),
    cls_typing__elims_I3_J_0,
    [final] ).

cnf(i_0_553,axiom,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
    cls_conversep__iff_1,
    [final] ).

cnf(i_0_554,axiom,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
    cls_conversep_Ointros_0,
    [final] ).

cnf(i_0_555,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X3)) ),
    cls_appR_0,
    [final] ).

cnf(i_0_556,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
    cls_appL_0,
    [final] ).

cnf(i_0_557,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X5),X4))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X5)) ),
    cls_converse__rtranclp__into__rtranclp_0,
    [final] ).

cnf(i_0_558,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
    cls_rtranclp_Ortrancl__into__rtrancl_0,
    [final] ).

cnf(i_0_559,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    cls_subst__Abs_0,
    [final] ).

cnf(i_0_560,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(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_400,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_561,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X2)),c_Lambda_Olift(X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    cls_lift__preserves__beta_H_0,
    [final] ).

cnf(i_0_562,axiom,
    ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3)) ),
    cls_subject__reduction_0,
    [final] ).

cnf(i_0_563,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I23_J_0,
    [final] ).

cnf(i_0_564,plain,
    c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_401,c_0_394]),
    [final] ).

cnf(i_0_565,plain,
    c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_402,c_0_394]),
    [final] ).

cnf(i_0_566,plain,
    c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_403,c_0_394]),
    [final] ).

cnf(i_0_567,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))) ),
    cls_nat__diff__split_0,
    [final] ).

cnf(i_0_568,plain,
    c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[i_0_404,c_0_394]),
    [final] ).

cnf(i_0_569,plain,
    c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[i_0_405,c_0_394]),
    [final] ).

cnf(i_0_570,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
    cls_add__less__cancel__right_0,
    [final] ).

cnf(i_0_571,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
    cls_add__less__cancel__left_0,
    [final] ).

cnf(i_0_572,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_406,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_573,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_subst__Var__IT_0,
    [final] ).

cnf(i_0_574,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    cls_rtrancl__beta__Abs_0,
    [final] ).

cnf(i_0_575,axiom,
    ( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X5) = hAPP(X2,c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X3,X5,tc_nat) ),
    cls_shift__lt_0,
    [final] ).

cnf(i_0_576,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_407,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_577,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__strict__mono_0,
    [final] ).

cnf(i_0_578,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[i_0_408,c_0_394]),
    [final] ).

cnf(i_0_579,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X3) ),
    cls_accp__downwards_0,
    [final] ).

cnf(i_0_580,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X4)) ),
    cls_accp__downwards__aux_0,
    [final] ).

cnf(i_0_581,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_582,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
    cls_nat__add__left__cancel__less_0,
    [final] ).

cnf(i_0_583,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__assoc_0,
    [final] ).

cnf(i_0_584,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I21_J_0,
    [final] ).

cnf(i_0_585,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
    [final] ).

cnf(i_0_586,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I25_J_0,
    [final] ).

cnf(i_0_587,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__a_0,
    [final] ).

cnf(i_0_588,plain,
    ( c_Lambda_Olift(c_Lambda_Olift(X1,X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Olift(c_Lambda_Olift(X1,X3),X2)
    | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_409,c_0_394]),
    [final] ).

cnf(i_0_589,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_add__less__mono_0,
    [final] ).

cnf(i_0_590,axiom,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
    cls_not__Nil__step1_0,
    [final] ).

cnf(i_0_591,axiom,
    ~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
    cls_not__step1__Nil_0,
    [final] ).

cnf(i_0_592,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),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_593,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
    cls_add__cancel__21_0,
    [final] ).

cnf(i_0_594,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
    cls_less__diff__conv_1,
    [final] ).

cnf(i_0_595,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_410,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_596,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_411,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_597,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
    cls_nat__add__assoc_0,
    [final] ).

cnf(i_0_598,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__neg__neg_0,
    [final] ).

cnf(i_0_599,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__pos__pos_0,
    [final] ).

cnf(i_0_600,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[i_0_412,c_0_394]),
    [final] ).

cnf(i_0_601,plain,
    ( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(rw,[status(thm)],[i_0_413,c_0_394]),
    [final] ).

cnf(i_0_602,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_add__less__cancel__left_1,
    [final] ).

cnf(i_0_603,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_add__strict__left__mono_0,
    [final] ).

cnf(i_0_604,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__less__cancel__right_1,
    [final] ).

cnf(i_0_605,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__strict__right__mono_0,
    [final] ).

cnf(i_0_606,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X2)),c_Lambda_Olift(X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
    cls_lift__preserves__beta_0,
    [final] ).

cnf(i_0_607,axiom,
    ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_pos__add__strict_0,
    [final] ).

cnf(i_0_608,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    cls_add__gr__0_0,
    [final] ).

cnf(i_0_609,axiom,
    ( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X5) = hAPP(X2,X5)
    | ~ c_HOL_Oord__class_Oless(X5,X3,tc_nat) ),
    cls_shift__gt_0,
    [final] ).

cnf(i_0_610,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_611,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_414,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_612,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_415,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_613,axiom,
    ( hAPP(X1,X2) = X3
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),X3)) ),
    cls_typing__elims_I1_J_0,
    [final] ).

cnf(i_0_614,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_615,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
    cls_zero__less__double__add__iff__zero__less__single__add_0,
    [final] ).

cnf(i_0_616,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_even__less__0__iff_0,
    [final] ).

cnf(i_0_617,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__less__zero__iff__single__less__zero_0,
    [final] ).

cnf(i_0_618,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_416,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_619,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_417,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_620,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_621,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_622,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_418,c_0_394]),
    [final] ).

cnf(i_0_623,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(rw,[status(thm)],[i_0_419,c_0_394]),
    [final] ).

cnf(i_0_624,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    cls_nat__add__left__cancel__less_1,
    [final] ).

cnf(i_0_625,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_add__less__mono1_0,
    [final] ).

cnf(i_0_626,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__left__commute_0,
    [final] ).

cnf(i_0_627,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I22_J_0,
    [final] ).

cnf(i_0_628,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_add__cancel__21_1,
    [final] ).

cnf(i_0_629,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
    cls_r__into__rtranclp_0,
    [final] ).

cnf(i_0_630,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_631,plain,
    c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(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_420,c_0_394]),
    [final] ).

cnf(i_0_632,axiom,
    ( hAPP(hAPP(hAPP(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_633,axiom,
    ( hAPP(hAPP(hAPP(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_634,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_635,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
    cls_diff__diff__left_0,
    [final] ).

cnf(i_0_636,plain,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_421,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_637,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_422,c_0_394]),
    [final] ).

cnf(i_0_638,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_423,c_0_394]),
    [final] ).

cnf(i_0_639,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_424,c_0_394]),
    [final] ).

cnf(i_0_640,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_425,c_0_394]),
    [final] ).

cnf(i_0_641,axiom,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
    cls_diff__cancel_0,
    [final] ).

cnf(i_0_642,axiom,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
    cls_diff__cancel2_0,
    [final] ).

cnf(i_0_643,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = X2
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_426,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_644,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
    | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    cls_less__add__eq__less_0,
    [final] ).

cnf(i_0_645,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
    cls_add__lessD1_0,
    [final] ).

cnf(i_0_646,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_diff__add__cancel_0,
    [final] ).

cnf(i_0_647,plain,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_427,c_0_394]),c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_648,plain,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_428,c_0_394]),c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_649,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
    cls_nat__add__left__commute_0,
    [final] ).

cnf(i_0_650,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X3) ),
    cls_accp__downward_0,
    [final] ).

cnf(i_0_651,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X3) ),
    cls_accp_Ocases_0,
    [final] ).

cnf(i_0_652,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_even__less__0__iff_1,
    [final] ).

cnf(i_0_653,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__less__zero__iff__single__less__zero_1,
    [final] ).

cnf(i_0_654,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_zero__less__double__add__iff__zero__less__single__add_1,
    [final] ).

cnf(i_0_655,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
    cls_termi__implies__IT_0,
    [final] ).

cnf(i_0_656,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_657,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_429,c_0_394]),
    [final] ).

cnf(i_0_658,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_430,c_0_394]),
    [final] ).

cnf(i_0_659,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),hAPP(X1,X2))),
    cls_typing_OVar_0,
    [final] ).

cnf(i_0_660,axiom,
    hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X3) = X4,
    cls_shift__eq_0,
    [final] ).

cnf(i_0_661,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_662,axiom,
    c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X2) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),
    cls_lift_Osimps_I3_J_0,
    [final] ).

cnf(i_0_663,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1)),c_Nat_Osemiring__1__class_Oof__nat(X3,X1))
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__add_0,
    [final] ).

cnf(i_0_664,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_665,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_app__Var__IT_0,
    [final] ).

cnf(i_0_666,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    cls_add__gr__0_1,
    [final] ).

cnf(i_0_667,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_add__gr__0_2,
    [final] ).

cnf(i_0_668,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_669,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_670,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(rw,[status(thm)],[i_0_431,c_0_394]),
    [final] ).

cnf(i_0_671,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    cls_abs_0,
    [final] ).

cnf(i_0_672,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
    cls_of__nat__less__iff_0,
    [final] ).

cnf(i_0_673,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_termination__basic__simps_I1_J_0,
    [final] ).

cnf(i_0_674,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_trans__less__add1_0,
    [final] ).

cnf(i_0_675,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_termination__basic__simps_I2_J_0,
    [final] ).

cnf(i_0_676,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_trans__less__add2_0,
    [final] ).

cnf(i_0_677,axiom,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
    cls_not__add__less1_0,
    [final] ).

cnf(i_0_678,axiom,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
    cls_not__add__less2_0,
    [final] ).

cnf(i_0_679,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_432,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_680,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_433,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_681,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_434,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_682,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_435,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_683,plain,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[i_0_436,c_0_394]),
    [final] ).

cnf(i_0_684,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_437,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_685,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_438,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_686,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_Oof__nat(X2,X1))
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(rw,[status(thm)],[i_0_439,c_0_394]),
    [final] ).

cnf(i_0_687,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_zero__less__two_0,
    [final] ).

cnf(i_0_688,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    cls_add__diff__inverse_0,
    [final] ).

cnf(i_0_689,plain,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_440,c_0_394]),
    [final] ).

cnf(i_0_690,plain,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(rw,[status(thm)],[i_0_441,c_0_394]),
    [final] ).

cnf(i_0_691,axiom,
    c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)),
    cls_lift_Osimps_I2_J_0,
    [final] ).

cnf(i_0_692,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
    cls_of__nat__0__less__iff_0,
    [final] ).

cnf(i_0_693,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_subst__lt_0,
    [final] ).

cnf(i_0_694,axiom,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    cls_of__nat__less__iff_1,
    [final] ).

cnf(i_0_695,axiom,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_IT__implies__termi_0,
    [final] ).

cnf(i_0_696,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | X3 = X2
    | c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
    cls_nat__less__cases_0,
    [final] ).

cnf(i_0_697,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Olift(X1,X2)),X3),X2) = X1,
    cls_subst__lift_0,
    [final] ).

cnf(i_0_698,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    cls_rtranclp_Ortrancl__refl_0,
    [final] ).

cnf(i_0_699,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    cls_Nitpick_Ortranclp__def_1,
    [final] ).

cnf(i_0_700,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_of__nat__0__less__iff_1,
    [final] ).

cnf(i_0_701,axiom,
    ( X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    cls_class__ringb_Oadd__cancel_0,
    [final] ).

cnf(i_0_702,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_703,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_704,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_705,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_706,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_707,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_708,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_709,plain,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(rw,[status(thm)],[i_0_442,c_0_394]),
    [final] ).

cnf(i_0_710,axiom,
    ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_less__add__one_0,
    [final] ).

cnf(i_0_711,axiom,
    ( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_lift_Osimps_I1_J_1,
    [final] ).

cnf(i_0_712,axiom,
    ( X2 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
    cls_add__right__cancel_0,
    [final] ).

cnf(i_0_713,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    cls_add__left__cancel_0,
    [final] ).

cnf(i_0_714,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    cls_add__imp__eq_0,
    [final] ).

cnf(i_0_715,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2)) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0,
    [final] ).

cnf(i_0_716,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
    | X1 = X3
    | c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    cls_subst__Var_2,
    [final] ).

cnf(i_0_717,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    inference(rw,[status(thm)],[i_0_443,c_0_394]),
    [final] ).

cnf(i_0_718,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[i_0_444,c_0_394]),
    [final] ).

cnf(i_0_719,axiom,
    ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
    | ~ class_OrderedGroup_Ogroup__add(X1) ),
    cls_add__diff__cancel_0,
    [final] ).

cnf(i_0_720,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2 ),
    cls_subst__Var_1,
    [final] ).

cnf(i_0_721,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_445,c_0_394]),
    [final] ).

cnf(i_0_722,axiom,
    c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
    cls_conversep__conversep_0,
    [final] ).

cnf(i_0_723,axiom,
    ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
    cls_beta__cases_I1_J_0,
    [final] ).

cnf(i_0_724,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_446,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_725,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_447,c_0_394]),c_0_394]),
    [final] ).

cnf(i_0_726,plain,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    inference(rw,[status(thm)],[i_0_448,c_0_394]),
    [final] ).

cnf(i_0_727,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_449,c_0_394]),
    [final] ).

cnf(i_0_728,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_450,c_0_394]),
    [final] ).

cnf(i_0_729,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
    cls_uT_0,
    [final] ).

cnf(i_0_730,axiom,
    hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
    cls_Var_I4_J_0,
    [final] ).

cnf(i_0_731,plain,
    c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_451,c_0_394]),
    [final] ).

cnf(i_0_732,plain,
    c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(rw,[status(thm)],[i_0_452,c_0_394]),
    [final] ).

cnf(i_0_733,axiom,
    ( X1 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    cls_nat__add__right__cancel_0,
    [final] ).

cnf(i_0_734,axiom,
    ( X2 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
    cls_nat__add__left__cancel_0,
    [final] ).

cnf(i_0_735,axiom,
    ( X2 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
    cls_natgb_Oadd__cancel_0,
    [final] ).

cnf(i_0_736,axiom,
    c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_diff__add__0_0,
    [final] ).

cnf(i_0_737,axiom,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
    cls_diff__add__inverse_0,
    [final] ).

cnf(i_0_738,axiom,
    c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
    cls_diff__add__inverse2_0,
    [final] ).

cnf(i_0_739,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_of__nat__less__0__iff_0,
    [final] ).

cnf(i_0_740,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_lift__IT_0,
    [final] ).

cnf(i_0_741,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_742,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_743,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_744,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_745,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_746,axiom,
    ( X1 = X3
    | hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
    cls_type_Osimps_I2_J_0,
    [final] ).

cnf(i_0_747,axiom,
    ( X1 = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
    cls_dB_Osimps_I2_J_0,
    [final] ).

cnf(i_0_748,axiom,
    ( X2 = X4
    | hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
    cls_type_Osimps_I2_J_1,
    [final] ).

cnf(i_0_749,axiom,
    ( X2 = X4
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
    cls_dB_Osimps_I2_J_1,
    [final] ).

cnf(i_0_750,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_751,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__commute_0,
    [final] ).

cnf(i_0_752,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I24_J_0,
    [final] ).

cnf(i_0_753,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__c_0,
    [final] ).

cnf(i_0_754,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
    cls_subst__eq_0,
    [final] ).

cnf(i_0_755,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_756,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_757,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_758,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_759,axiom,
    hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
    cls_ATP__Linkup_Oequal__imp__fequal_0,
    [final] ).

cnf(i_0_760,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
    cls_class__ringb_Oadd__r0__iff_0,
    [final] ).

cnf(i_0_761,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_762,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_763,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
    inference(rw,[status(thm)],[i_0_453,c_0_394]),
    [final] ).

cnf(i_0_764,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_double__eq__0__iff_0,
    [final] ).

cnf(i_0_765,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__neq__iff_1,
    [final] ).

cnf(i_0_766,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__irrefl_0,
    [final] ).

cnf(i_0_767,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__le_1,
    [final] ).

cnf(i_0_768,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_769,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
    cls_nat__add__commute_0,
    [final] ).

cnf(i_0_770,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_771,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_not__less0_0,
    [final] ).

cnf(i_0_772,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_less__not__refl_0,
    [final] ).

cnf(i_0_773,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_nat__less__le_1,
    [final] ).

cnf(i_0_774,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_Lambda_0,
    [final] ).

cnf(i_0_775,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_double__eq__0__iff_1,
    [final] ).

cnf(i_0_776,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rw,[status(thm)],[i_0_454,c_0_394]),
    [final] ).

cnf(i_0_777,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(rw,[status(thm)],[i_0_455,c_0_394]),
    [final] ).

cnf(i_0_778,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[i_0_456,c_0_394]),
    [final] ).

cnf(i_0_779,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[i_0_457,c_0_394]),
    [final] ).

cnf(i_0_780,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_add__is__0_0,
    [final] ).

cnf(i_0_781,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_add__is__0_1,
    [final] ).

cnf(i_0_782,plain,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != X1,
    inference(rw,[status(thm)],[i_0_458,c_0_394]),
    [final] ).

cnf(i_0_783,plain,
    X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[i_0_459,c_0_394]),
    [final] ).

cnf(i_0_784,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ),
    cls_add__eq__self__zero_0,
    [final] ).

cnf(i_0_785,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    cls_natgb_Oadd__r0__iff_0,
    [final] ).

cnf(i_0_786,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_787,axiom,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Oadd__r0__iff_1,
    [final] ).

cnf(i_0_788,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_789,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__1_0,
    [final] ).

cnf(i_0_790,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I5_J_0,
    [final] ).

cnf(i_0_791,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__0_0,
    [final] ).

cnf(i_0_792,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_add__0__left_0,
    [final] ).

cnf(i_0_793,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_794,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__1__right_0,
    [final] ).

cnf(i_0_795,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I6_J_0,
    [final] ).

cnf(i_0_796,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_monoid__add__class_Oadd__0__right_0,
    [final] ).

cnf(i_0_797,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_798,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_799,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_800,axiom,
    c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
    cls_conversep__eq_0,
    [final] ).

cnf(i_0_801,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
    cls_dB_Osimps_I8_J_0,
    [final] ).

cnf(i_0_802,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
    cls_dB_Osimps_I5_J_0,
    [final] ).

cnf(i_0_803,axiom,
    c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    cls_dB_Osimps_I9_J_0,
    [final] ).

cnf(i_0_804,axiom,
    c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    cls_dB_Osimps_I4_J_0,
    [final] ).

cnf(i_0_805,axiom,
    c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
    cls_listsp_ONil_0,
    [final] ).

cnf(i_0_806,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_807,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_808,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_add__is__0_2,
    [final] ).

cnf(i_0_809,plain,
    c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(rw,[status(thm)],[i_0_460,c_0_394]),
    [final] ).

cnf(i_0_810,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_811,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_812,axiom,
    c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
    cls_rtranclp__idemp_0,
    [final] ).

cnf(i_0_813,axiom,
    ( X2 = X3
    | ~ class_Nat_Osemiring__char__0(X1)
    | c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
    cls_of__nat__eq__iff_0,
    [final] ).

cnf(i_0_814,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
    cls_plus__nat_Oadd__0_0,
    [final] ).

cnf(i_0_815,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
    cls_Nat_Oadd__0__right_0,
    [final] ).

cnf(i_0_816,axiom,
    X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_natgb_Oadd__r0__iff_1,
    [final] ).

cnf(i_0_817,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
    cls_Var__IT_0,
    [final] ).

cnf(i_0_818,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_819,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_820,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__1_0,
    [final] ).

cnf(i_0_821,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__0_0,
    [final] ).

cnf(i_0_822,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
    cls_Var_I3_J_0,
    [final] ).

cnf(i_0_823,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    cls_uIT_0,
    [final] ).

cnf(i_0_824,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_dB_Osize_I4_J_0,
    [final] ).

cnf(i_0_825,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_826,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_827,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    cls_dB_Osimps_I3_J_0,
    [final] ).

cnf(i_0_828,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    cls_dB_Osimps_I1_J_0,
    [final] ).

cnf(i_0_829,axiom,
    c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
    cls_dB_Osimps_I7_J_0,
    [final] ).

cnf(i_0_830,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    cls_dB_Osimps_I6_J_0,
    [final] ).

cnf(i_0_831,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_dB_Osize_I1_J_0,
    [final] ).

cnf(i_0_832,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_833,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_834,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_835,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_836,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_837,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
    [final] ).

cnf(i_0_838,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
    [final] ).

cnf(i_0_839,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__add,
    [final] ).

cnf(i_0_840,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
    [final] ).

cnf(i_0_841,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Osemigroup__add,
    [final] ).

cnf(i_0_842,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    clsarity_nat__Nat_Osemiring__char__0,
    [final] ).

cnf(i_0_843,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__add,
    [final] ).

cnf(i_0_844,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
    [final] ).

cnf(i_0_845,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Osemiring__1,
    [final] ).

cnf(i_0_846,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    [final] ).

cnf(i_0_847,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semidom,
    [final] ).

cnf(i_0_848,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__add,
    [final] ).

cnf(i_0_849,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
    [final] ).

cnf(i_0_850,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    clsarity_nat__Ring__and__Field_Ozero__neq__one,
    [final] ).

cnf(i_0_851,negated_conjecture,
    ~ v_thesis____,
    cls_conjecture_0,
    [final] ).

cnf(i_0_852,axiom,
    v_n____ != v_i____,
    cls_False_0,
    [final] ).

cnf(i_0_853,axiom,
    X1 = X1 ).

cnf(i_0_854,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_855,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_856,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_857,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_858,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).

cnf(i_0_859,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).

cnf(i_0_860,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).

cnf(i_0_861,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).

cnf(i_0_862,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).

cnf(i_0_863,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_864,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X1,X3) = c_Transitive__Closure_Ortranclp(X2,X3) ) ).

cnf(i_0_865,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X3,X1) = c_Transitive__Closure_Ortranclp(X3,X2) ) ).

cnf(i_0_866,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_867,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_868,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_869,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_870,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_871,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X1,X3) = c_Lambda_Olift(X2,X3) ) ).

cnf(i_0_872,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X3,X1) = c_Lambda_Olift(X3,X2) ) ).

cnf(i_0_873,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_874,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_875,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_876,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_877,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_878,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_879,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_880,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__size(X1) = c_Type_Otype_Otype__size(X2) ) ).

cnf(i_0_881,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__size(X1) = c_Lambda_OdB_OdB__size(X2) ) ).

cnf(i_0_882,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_883,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_884,axiom,
    ( X1 != X2
    | c_fequal(X1) = c_fequal(X2) ) ).

cnf(i_0_885,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X1,X3,X4,X5,X6) = c_List_Ofoldr(X2,X3,X4,X5,X6) ) ).

cnf(i_0_886,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X1,X4,X5,X6) = c_List_Ofoldr(X3,X2,X4,X5,X6) ) ).

cnf(i_0_887,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X1,X5,X6) = c_List_Ofoldr(X3,X4,X2,X5,X6) ) ).

cnf(i_0_888,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X1,X6) = c_List_Ofoldr(X3,X4,X5,X2,X6) ) ).

cnf(i_0_889,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X6,X1) = c_List_Ofoldr(X3,X4,X5,X6,X2) ) ).

cnf(i_0_890,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X1,X3,X4)
    | c_List_Olistsp(X2,X3,X4) ) ).

cnf(i_0_891,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X1,X4)
    | c_List_Olistsp(X3,X2,X4) ) ).

cnf(i_0_892,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X4,X1)
    | c_List_Olistsp(X3,X4,X2) ) ).

cnf(i_0_893,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_894,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_895,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_896,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_897,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_898,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_899,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_900,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_901,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_902,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_903,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_904,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_905,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_906,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_907,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_908,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_909,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_910,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_911,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_912,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_913,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_914,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X1,X3,X4)
    | c_Type_Otypings(X2,X3,X4) ) ).

cnf(i_0_915,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X1,X4)
    | c_Type_Otypings(X3,X2,X4) ) ).

cnf(i_0_916,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X4,X1)
    | c_Type_Otypings(X3,X4,X2) ) ).

cnf(i_0_917,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_918,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_919,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X1,X3,X4,X5)
    | c_ListOrder_Ostep1(X2,X3,X4,X5) ) ).

cnf(i_0_920,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X1,X4,X5)
    | c_ListOrder_Ostep1(X3,X2,X4,X5) ) ).

cnf(i_0_921,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X1,X5)
    | c_ListOrder_Ostep1(X3,X4,X2,X5) ) ).

cnf(i_0_922,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X5,X1)
    | c_ListOrder_Ostep1(X3,X4,X5,X2) ) ).

cnf(i_0_923,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X1,X3,X4)
    | c_Wellfounded_Oaccp(X2,X3,X4) ) ).

cnf(i_0_924,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X1,X4)
    | c_Wellfounded_Oaccp(X3,X2,X4) ) ).

cnf(i_0_925,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X4,X1)
    | c_Wellfounded_Oaccp(X3,X4,X2) ) ).

cnf(i_0_926,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Osemigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X2) ) ).

cnf(i_0_927,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_928,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_929,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_930,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_853_001,axiom,
    X1 = X1 ).

cnf(i_0_854_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_855_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_856_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_857_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_858_006,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).

cnf(i_0_859_007,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).

cnf(i_0_860_008,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).

cnf(i_0_861_009,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).

cnf(i_0_862_010,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).

cnf(i_0_863_011,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_864_012,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X1,X3) = c_Transitive__Closure_Ortranclp(X2,X3) ) ).

cnf(i_0_865_013,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X3,X1) = c_Transitive__Closure_Ortranclp(X3,X2) ) ).

cnf(i_0_866_014,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_867_015,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_868_016,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_869_017,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_870_018,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_871_019,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X1,X3) = c_Lambda_Olift(X2,X3) ) ).

cnf(i_0_872_020,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X3,X1) = c_Lambda_Olift(X3,X2) ) ).

cnf(i_0_873_021,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_874_022,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_875_023,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_876_024,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_877_025,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_878_026,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_879_027,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_880_028,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__size(X1) = c_Type_Otype_Otype__size(X2) ) ).

cnf(i_0_881_029,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__size(X1) = c_Lambda_OdB_OdB__size(X2) ) ).

cnf(i_0_882_030,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_883_031,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_884_032,axiom,
    ( X1 != X2
    | c_fequal(X1) = c_fequal(X2) ) ).

cnf(i_0_885_033,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X1,X3,X4,X5,X6) = c_List_Ofoldr(X2,X3,X4,X5,X6) ) ).

cnf(i_0_886_034,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X1,X4,X5,X6) = c_List_Ofoldr(X3,X2,X4,X5,X6) ) ).

cnf(i_0_887_035,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X1,X5,X6) = c_List_Ofoldr(X3,X4,X2,X5,X6) ) ).

cnf(i_0_888_036,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X1,X6) = c_List_Ofoldr(X3,X4,X5,X2,X6) ) ).

cnf(i_0_889_037,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X6,X1) = c_List_Ofoldr(X3,X4,X5,X6,X2) ) ).

cnf(i_0_890_038,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X1,X3,X4)
    | c_List_Olistsp(X2,X3,X4) ) ).

cnf(i_0_891_039,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X1,X4)
    | c_List_Olistsp(X3,X2,X4) ) ).

cnf(i_0_892_040,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X4,X1)
    | c_List_Olistsp(X3,X4,X2) ) ).

cnf(i_0_893_041,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_894_042,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_895_043,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_896_044,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_897_045,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_898_046,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_899_047,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_900_048,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_901_049,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_902_050,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_903_051,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_904_052,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_905_053,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_906_054,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_907_055,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_908_056,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_909_057,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_910_058,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_911_059,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_912_060,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_913_061,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_914_062,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X1,X3,X4)
    | c_Type_Otypings(X2,X3,X4) ) ).

cnf(i_0_915_063,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X1,X4)
    | c_Type_Otypings(X3,X2,X4) ) ).

cnf(i_0_916_064,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X4,X1)
    | c_Type_Otypings(X3,X4,X2) ) ).

cnf(i_0_917_065,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_918_066,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_919_067,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X1,X3,X4,X5)
    | c_ListOrder_Ostep1(X2,X3,X4,X5) ) ).

cnf(i_0_920_068,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X1,X4,X5)
    | c_ListOrder_Ostep1(X3,X2,X4,X5) ) ).

cnf(i_0_921_069,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X1,X5)
    | c_ListOrder_Ostep1(X3,X4,X2,X5) ) ).

cnf(i_0_922_070,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X5,X1)
    | c_ListOrder_Ostep1(X3,X4,X5,X2) ) ).

cnf(i_0_923_071,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X1,X3,X4)
    | c_Wellfounded_Oaccp(X2,X3,X4) ) ).

cnf(i_0_924_072,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X1,X4)
    | c_Wellfounded_Oaccp(X3,X2,X4) ) ).

cnf(i_0_925_073,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X4,X1)
    | c_Wellfounded_Oaccp(X3,X4,X2) ) ).

cnf(i_0_926_074,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Osemigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X2) ) ).

cnf(i_0_927_075,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_928_076,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_929_077,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_930_078,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_931,plain,
    X1 = X1,
    inference(equality_inference,[],[486]) ).

cnf(i_0_932,plain,
    X1 = X1,
    inference(equality_inference,[],[487]) ).

cnf(i_0_933,plain,
    X1 = X1,
    inference(equality_inference,[],[488]) ).

cnf(i_0_934,plain,
    X1 = X1,
    inference(equality_inference,[],[489]) ).

cnf(i_0_935,plain,
    X1 = X1,
    inference(equality_inference,[],[492]) ).

cnf(i_0_936,plain,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
    inference(equality_inference,[],[593]) ).

cnf(i_0_937,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[647]) ).

cnf(i_0_938,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
    | c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[648]) ).

cnf(i_0_939,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[679]) ).

cnf(i_0_940,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[680]) ).

cnf(i_0_941,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[681]) ).

cnf(i_0_942,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(equality_inference,[],[682]) ).

cnf(i_0_943,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[701]) ).

cnf(i_0_944,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[702]) ).

cnf(i_0_945,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[703]) ).

cnf(i_0_946,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[712]) ).

cnf(i_0_947,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[713]) ).

cnf(i_0_948,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[714]) ).

cnf(i_0_949,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,[],[717]) ).

cnf(i_0_950,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,[],[718]) ).

cnf(i_0_951,plain,
    X1 = X1,
    inference(equality_inference,[],[733]) ).

cnf(i_0_952,plain,
    X1 = X1,
    inference(equality_inference,[],[735]) ).

cnf(i_0_953,plain,
    X1 = X1,
    inference(equality_inference,[],[746]) ).

cnf(i_0_954,plain,
    X1 = X1,
    inference(equality_inference,[],[747]) ).

cnf(i_0_955,plain,
    X1 = X1,
    inference(equality_inference,[],[748]) ).

cnf(i_0_956,plain,
    X1 = X1,
    inference(equality_inference,[],[749]) ).

cnf(i_0_957,plain,
    ( X1 = X1
    | ~ class_Nat_Osemiring__char__0(X2) ),
    inference(equality_inference,[],[813]) ).

cnf(i_0_958,plain,
    X1 = X1,
    inference(equality_inference,[],[827]) ).

cnf(i_0_959,plain,
    X1 = X1,
    inference(equality_inference,[],[828]) ).

cnf(i_0_960,plain,
    $false,
    inference(scs_inference,[],[i_0_851,i_0_505,i_0_507]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : LCL827-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.31  % Computer : n011.cluster.edu
% 0.14/0.31  % Model    : x86_64 x86_64
% 0.14/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31  % Memory   : 8042.1875MB
% 0.14/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31  % CPULimit   : 300
% 0.14/0.31  % WCLimit    : 300
% 0.14/0.31  % DateTime   : Mon May  4 23:11:17 EDT 2026
% 0.14/0.32  % CPUTime    : 
% 0.14/0.33  % start to proof: theBenchmark
% 0.40/1.65  % Version  : CSE_E---1.7
% 0.40/1.65  % Problem  : theBenchmark.p
% 0.40/1.65  % SZS status Unsatisfiable for theBenchmark.p
% 0.40/1.65  % SZS output start CNFRefutation
% See solution above
% 0.45/1.71  % Total time : 1.323s
%------------------------------------------------------------------------------