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CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : LCL814-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n016.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 04:45:08 PM UTC 2026

% Result   : Unsatisfiable 5.47s 5.67s
% Output   : CNFRefutation 5.60s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_682)

% Comments : 
%------------------------------------------------------------------------------
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)
    | ~ 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)
    | ~ 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/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).

cnf(cls_foldr__foldl_0,axiom,
    c_List_Ofoldr(X1,X2,X3,X4,X5) = c_List_Ofoldl(c_COMBC(X1,X4,X5,X5),X3,c_List_Orev(X2,X4),X5,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).

cnf(cls_calculation_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_0) ).

cnf(cls_var__app__typesE_0,axiom,
    ( 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))
    | ~ 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/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).

cnf(cls_list__app__typeE_0,axiom,
    ( 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))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).

cnf(cls_list__app__typeD_0,axiom,
    ( 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))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).

cnf(cls_list__app__typeI_0,axiom,
    ( 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)
    | ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).

cnf(cls_varT_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_varT_0) ).

cnf(cls_foldr__append_0,axiom,
    c_List_Ofoldr(X1,c_List_Oappend(X2,X3,X4),X5,X4,X6) = c_List_Ofoldr(X1,X2,c_List_Ofoldr(X1,X3,X5,X4,X6),X4,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__append_0) ).

cnf(cls_uT_H_0,axiom,
    c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_H_0) ).

cnf(cls_foldr_Osimps_I2_J_0,axiom,
    c_List_Ofoldr(X1,c_List_Olist_OCons(X2,X3,X4),X5,X4,X6) = hAPP(hAPP(X1,X2),c_List_Ofoldr(X1,X3,X5,X4,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_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/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).

cnf(cls_headT_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_headT_0) ).

cnf(cls_foldl__foldr_0,axiom,
    c_List_Ofoldl(X1,X2,X3,X4,X5) = c_List_Ofoldr(c_COMBC(X1,X4,X5,X4),c_List_Orev(X3,X5),X2,X5,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr_0) ).

cnf(cls_T_0,axiom,
    v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).

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

cnf(cls_add__nonneg__eq__0__iff_2,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_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

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

cnf(cls_conjecture_0,negated_conjecture,
    ~ c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_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/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).

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))
    | ~ 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)
    | ~ 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/sandbox/benchmark/theBenchmark.p',cls_var__app__types_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).

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

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

cnf(cls_map__eq__conv_2,axiom,
    ( c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5)
    | hAPP(X1,c_List_Osko__List__Xmap__eq__conv__1__1(X1,X2,X3,X4,X5)) != hAPP(X2,c_List_Osko__List__Xmap__eq__conv__1__1(X1,X2,X3,X4,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__conv_2) ).

cnf(cls_map__cong_1,axiom,
    ( c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5)
    | hAPP(X1,c_List_Osko__List__Xmap__cong__1__1(X1,X2,X3,X4,X5)) != hAPP(X2,c_List_Osko__List__Xmap__cong__1__1(X1,X2,X3,X4,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__cong_1) ).

cnf(cls_map__ext_1,axiom,
    ( c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5)
    | hAPP(X1,c_List_Osko__List__Xmap__ext__1__1(X1,X2,X3,X4,X5)) != hAPP(X2,c_List_Osko__List__Xmap__ext__1__1(X1,X2,X3,X4,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__ext_1) ).

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

cnf(cls_o__assoc_0,axiom,
    c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).

cnf(cls_comp__cong_0,axiom,
    ( hAPP(c_Fun_Ocomp(X1,X2,X7,X8,X9),X3) = hAPP(c_Fun_Ocomp(X4,X5,X10,X8,X11),X6)
    | hAPP(X1,hAPP(X2,X3)) != hAPP(X4,hAPP(X5,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).

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

cnf(cls_foldl__append_0,axiom,
    c_List_Ofoldl(X1,X2,c_List_Oappend(X3,X4,X5),X6,X5) = c_List_Ofoldl(X1,c_List_Ofoldl(X1,X2,X3,X6,X5),X4,X6,X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).

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))
    | ~ 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/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_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))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_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))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).

cnf(cls_o__eq__dest_0,axiom,
    ( hAPP(X1,hAPP(X2,X9)) = hAPP(X6,hAPP(X7,X9))
    | c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(X6,X7,X8,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).

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

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

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

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

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

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

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

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

cnf(cls_map__map_0,axiom,
    c_List_Omap(X1,c_List_Omap(X2,X3,X4,X5),X5,X6) = c_List_Omap(c_Fun_Ocomp(X1,X2,X5,X6,X4),X3,X4,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__map_0) ).

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

cnf(cls_nT_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),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/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).

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

cnf(cls_foldl__Cons_0,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_OCons(X3,X4,X5),X6,X5) = c_List_Ofoldl(X1,hAPP(hAPP(X1,X2),X3),X4,X6,X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).

cnf(cls_o__apply_0,axiom,
    hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).

cnf(cls_o__eq__dest__lhs_0,axiom,
    hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).

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

cnf(cls_append__eq__append__conv__if_6,axiom,
    ( c_List_Oappend(X3,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)),X1,X2),X4,X2),X2) = c_List_Oappend(X1,X4,X2)
    | c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2),c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)),X1,X2),X4,X2),X2) != X4
    | c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2) != X1
    | X3 != c_List_Otake(c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)),X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).

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

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

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

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

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

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

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

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

cnf(cls_Snoc__step1__SnocD_1,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_ListOrder_Ostep1(X1,X4,X5,X6)
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(X6),X6),X6),c_List_Oappend(X5,c_List_Olist_OCons(X3,c_List_Olist_ONil(X6),X6),X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).

cnf(cls_Snoc__step1__SnocD_0,axiom,
    ( X1 = X2
    | c_ListOrder_Ostep1(X3,X1,X2,X4)
    | ~ c_ListOrder_Ostep1(X3,c_List_Oappend(X1,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).

cnf(cls_Snoc__step1__SnocD_3,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X2 = X3
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(X5),X5),X5),c_List_Oappend(X6,c_List_Olist_OCons(X3,c_List_Olist_ONil(X5),X5),X5),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).

cnf(cls_map__update_0,axiom,
    c_List_Omap(X1,c_List_Olist__update(X2,X3,X4,X5),X5,X6) = c_List_Olist__update(c_List_Omap(X1,X2,X5,X6),X3,hAPP(X1,X4),X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__update_0) ).

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

cnf(cls_list__update__swap_0,axiom,
    ( c_List_Olist__update(c_List_Olist__update(X1,X2,X3,X4),X5,X6,X4) = c_List_Olist__update(c_List_Olist__update(X1,X5,X6,X4),X2,X3,X4)
    | X2 = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).

cnf(cls_Snoc__step1__SnocD_2,axiom,
    ( X1 = X2
    | X3 = X4
    | ~ c_ListOrder_Ostep1(X5,c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X6),X6),X6),c_List_Oappend(X2,c_List_Olist_OCons(X4,c_List_Olist_ONil(X6),X6),X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).

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)
    | ~ c_Type_Otyping(X6,X4,X1)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X6,X5,X1,tc_Type_Otype),X3,X7)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    file('/export/starexec/sandbox/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)
    | ~ c_Type_Otyping(X6,X4,X2)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X6,X5,X2,tc_Type_Otype),X3,X7)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).

cnf(cls_map__append_0,axiom,
    c_List_Omap(X1,c_List_Oappend(X2,X3,X4),X4,X5) = c_List_Oappend(c_List_Omap(X1,X2,X4,X5),c_List_Omap(X1,X3,X4,X5),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__append_0) ).

cnf(cls_rev__update_0,axiom,
    ( c_List_Orev(c_List_Olist__update(X1,X2,X3,X4),X4) = c_List_Olist__update(c_List_Orev(X1,X4),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,X4)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__update_0) ).

cnf(cls_list__update__append_1,axiom,
    ( c_List_Olist__update(c_List_Oappend(X1,X2,X3),X4,X5,X3) = c_List_Oappend(X1,c_List_Olist__update(X2,c_HOL_Ominus__class_Ominus(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat),X5,X3),X3)
    | c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_1) ).

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).

cnf(cls_rotate__rev_0,axiom,
    c_List_Orotate(X1,c_List_Orev(X2,X3),X3) = c_List_Orev(c_List_Orotate(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),c_Divides_Odiv__class_Omod(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),tc_nat),X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__rev_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).

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

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

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).

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

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

cnf(cls_Cons__step1__Cons_1,axiom,
    ( c_ListOrder_Ostep1(X1,X2,X3,X4)
    | hBOOL(hAPP(hAPP(X1,X5),X6))
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X6,X3,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).

cnf(cls_list__update__append_0,axiom,
    ( c_List_Olist__update(c_List_Oappend(X1,X2,X3),X4,X5,X3) = c_List_Oappend(c_List_Olist__update(X1,X4,X5,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_0) ).

cnf(cls_list__update__append1_0,axiom,
    ( c_List_Olist__update(c_List_Oappend(X1,X2,X3),X4,X5,X3) = c_List_Oappend(c_List_Olist__update(X1,X4,X5,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append1_0) ).

cnf(cls_rotate__drop__take_0,axiom,
    c_List_Orotate(X1,X2,X3) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),X2,X3),c_List_Otake(c_Divides_Odiv__class_Omod(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__drop__take_0) ).

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

cnf(cls_list__update__overwrite_0,axiom,
    c_List_Olist__update(c_List_Olist__update(X1,X2,X3,X4),X2,X5,X4) = c_List_Olist__update(X1,X2,X5,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).

cnf(cls_Cons__step1__Cons_3,axiom,
    ( c_ListOrder_Ostep1(X1,X2,X3,X4)
    | X3 = X2
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X6,X3,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).

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

cnf(cls_append__eq__append__conv__if_5,axiom,
    ( c_List_Oappend(X1,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2),X4,X2),X2) = c_List_Oappend(X3,X4,X2)
    | X1 != c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2)
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_5) ).

cnf(cls_Cons__eq__map__conv_3,axiom,
    c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5) = c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).

cnf(cls_map_Osimps_I2_J_0,axiom,
    c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).

cnf(cls_map__eq__Cons__conv_3,axiom,
    c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).

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

cnf(cls_list__update__code_I3_J_0,axiom,
    c_List_Olist__update(c_List_Olist_OCons(X1,X2,X3),c_Suc(X4),X5,X3) = c_List_Olist_OCons(X1,c_List_Olist__update(X2,X4,X5,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).

cnf(cls_rotate__map_0,axiom,
    c_List_Orotate(X1,c_List_Omap(X2,X3,X4,X5),X5) = c_List_Omap(X2,c_List_Orotate(X1,X3,X4),X4,X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__map_0) ).

cnf(cls_take__map_0,axiom,
    c_List_Otake(X1,c_List_Omap(X2,X3,X4,X5),X5) = c_List_Omap(X2,c_List_Otake(X1,X3,X4),X4,X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__map_0) ).

cnf(cls_drop__map_0,axiom,
    c_List_Odrop(X1,c_List_Omap(X2,X3,X4,X5),X5) = c_List_Omap(X2,c_List_Odrop(X1,X3,X4),X4,X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__map_0) ).

cnf(cls_upd__conv__take__nth__drop_0,axiom,
    ( c_List_Olist__update(X1,X2,X3,X4) = c_List_Oappend(c_List_Otake(X2,X1,X4),c_List_Olist_OCons(X3,c_List_Odrop(c_Suc(X2),X1,X4),X4),X4)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upd__conv__take__nth__drop_0) ).

cnf(cls_id__take__nth__drop_0,axiom,
    ( X1 = c_List_Oappend(c_List_Otake(X2,X1,X3),c_List_Olist_OCons(c_List_Onth(X1,X2,X3),c_List_Odrop(c_Suc(X2),X1,X3),X3),X3)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__take__nth__drop_0) ).

cnf(cls_append__eq__append__conv__if_4,axiom,
    ( c_lessequals(c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | c_List_Oappend(X3,X4,X2) = c_List_Oappend(X1,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2),X4,X2),X2)
    | c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2) != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_4) ).

cnf(cls_Cons__step1__Cons_5,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X2,X5,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X3,X5,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).

cnf(cls_append__step1I_1,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X2,X5,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X3,X5,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_1) ).

cnf(cls_append__step1I_0,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X5,X4),c_List_Oappend(X3,X5,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_0) ).

cnf(cls_lift__preserves__beta_H_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X2)),hAPP(hAPP(c_Lambda_Olift,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).

cnf(cls_map__eq__imp__length__eq_0,axiom,
    ( c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)) = c_Nat_Osize__class_Osize(X5,tc_List_Olist(X3))
    | c_List_Omap(X1,X2,X3,X4) != c_List_Omap(X1,X5,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).

cnf(cls_nth__map_0,axiom,
    ( c_List_Onth(c_List_Omap(X1,X2,X3,X4),X5,X4) = hAPP(X1,c_List_Onth(X2,X5,X3))
    | ~ c_HOL_Oord__class_Oless(X5,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__map_0) ).

cnf(cls_distinct__map_0,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Omap(X3,X1,X2,X4),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__map_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/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

cnf(cls_Cons__step1__Cons_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ c_ListOrder_Ostep1(X3,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X1,X6,X5),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).

cnf(cls_take__append_0,axiom,
    c_List_Otake(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Otake(X1,X2,X4),c_List_Otake(c_HOL_Ominus__class_Ominus(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X4)),tc_nat),X3,X4),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__append_0) ).

cnf(cls_drop__append_0,axiom,
    c_List_Odrop(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Odrop(X1,X2,X4),c_List_Odrop(c_HOL_Ominus__class_Ominus(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X4)),tc_nat),X3,X4),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__append_0) ).

cnf(cls_rev__map_0,axiom,
    c_List_Orev(c_List_Omap(X1,X2,X3,X4),X4) = c_List_Omap(X1,c_List_Orev(X2,X3),X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__map_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/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).

cnf(cls_list__update__length_0,axiom,
    c_List_Olist__update(c_List_Oappend(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),X5,X4) = c_List_Oappend(X1,c_List_Olist_OCons(X5,X3,X4),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__length_0) ).

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

cnf(cls_nth__list__update_1,axiom,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X5,X4) = c_List_Onth(X1,X5,X4)
    | X2 = X5
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update_1) ).

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

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

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

cnf(cls_Cons__step1__Cons_2,axiom,
    ( X1 = X2
    | X3 = X4
    | ~ c_ListOrder_Ostep1(X5,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X1,X3,X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).

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

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

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

cnf(cls_take__Suc__conv__app__nth_0,axiom,
    ( c_List_Otake(c_Suc(X1),X2,X3) = c_List_Oappend(c_List_Otake(X1,X2,X3),c_List_Olist_OCons(c_List_Onth(X2,X1,X3),c_List_Olist_ONil(X3),X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__conv__app__nth_0) ).

cnf(cls_nth__list__update__eq_0,axiom,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X2,X4) = X3
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update__eq_0) ).

cnf(cls_nth__list__update_0,axiom,
    ( c_List_Onth(c_List_Olist__update(X2,X1,X4,X3),X1,X3) = X4
    | ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update_0) ).

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

cnf(cls_take__Cons__number__of_1,axiom,
    ( c_List_Otake(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,X4),X4)
    | c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_1) ).

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

cnf(cls_replicate__app__Cons__same_0,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,X4,X3),X3) = c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X1,X2,X3),X4,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).

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

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

cnf(cls_lift__preserves__beta_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X2)),hAPP(hAPP(c_Lambda_Olift,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).

cnf(cls_append__eq__append__conv__if_1,axiom,
    ( X2 = c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),X4,X3),X5,X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X5,X3)
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_1) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).

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

cnf(cls_nth__list__update__neq_0,axiom,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X5,X4) = c_List_Onth(X1,X5,X4)
    | X2 = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update__neq_0) ).

cnf(cls_Cons__step1__Cons_4,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X3,X4,X5),X5)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).

cnf(cls_list__update__same__conv_0,axiom,
    ( c_List_Onth(X1,X2,X4) = X3
    | c_List_Olist__update(X1,X2,X3,X4) != X1
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__same__conv_0) ).

cnf(cls_append1__eq__conv_0,axiom,
    ( X1 = X4
    | c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X4,c_List_Olist_OCons(X5,c_List_Olist_ONil(X3),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

cnf(cls_append1__eq__conv_1,axiom,
    ( X2 = X5
    | c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X4,c_List_Olist_OCons(X5,c_List_Olist_ONil(X3),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

cnf(cls_take__Cons_H_1,axiom,
    ( c_List_Otake(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,X4),X4)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_1) ).

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

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

cnf(cls_append__eq__append__conv__if_3,axiom,
    ( c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),X1,X3),X2,X3) = X5
    | c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),tc_nat)
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_3) ).

cnf(cls_impossible__Cons_0,axiom,
    ~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).

cnf(cls_append__replicate__commute_0,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X2,X3),X3) = c_List_Oappend(c_List_Oreplicate(X4,X2,X3),c_List_Oreplicate(X1,X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).

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

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

cnf(cls_length__map_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Omap(X1,X2,X3,X4),tc_List_Olist(X4)) = c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__map_0) ).

cnf(cls_length__list__update_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist__update(X1,X2,X3,X4),tc_List_Olist(X4)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__list__update_0) ).

cnf(cls_CHAINED_0,axiom,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

cnf(cls_argsT_0,axiom,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argsT_0) ).

cnf(cls_argT_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argT_0) ).

cnf(cls_map__idI_1,axiom,
    ( c_List_Omap(X1,X2,X3,X3) = X2
    | hAPP(X1,c_List_Osko__List__Xmap__idI__1__1(X1,X2,X3)) != c_List_Osko__List__Xmap__idI__1__1(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__idI_1) ).

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

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

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

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

cnf(cls_list__update__same__conv_1,axiom,
    ( c_List_Olist__update(X2,X1,c_List_Onth(X2,X1,X3),X3) = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__same__conv_1) ).

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

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

cnf(cls_nth__append_1,axiom,
    ( c_List_Onth(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Onth(X2,c_HOL_Ominus__class_Ominus(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat),X3)
    | c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append_1) ).

cnf(cls_nth__eq__iff__index__eq_0,axiom,
    ( X2 = X4
    | c_List_Onth(X1,X2,X3) != c_List_Onth(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_List_Odistinct(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__eq__iff__index__eq_0) ).

cnf(cls_distinct__conv__nth_0,axiom,
    ( X2 = X4
    | c_List_Onth(X1,X2,X3) != c_List_Onth(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_List_Odistinct(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__conv__nth_0) ).

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

cnf(cls_nth__drop_H_0,axiom,
    ( c_List_Olist_OCons(c_List_Onth(X1,X2,X3),c_List_Odrop(c_Suc(X2),X1,X3),X3) = c_List_Odrop(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__drop_H_0) ).

cnf(cls_rev__nth_0,axiom,
    ( c_List_Onth(c_List_Orev(X1,X2),X3,X2) = c_List_Onth(X1,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_Suc(X3),tc_nat),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__nth_0) ).

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

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

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

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

cnf(cls_append__eq__append__conv__if_0,axiom,
    ( X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),X4,X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X5,X3)
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_0) ).

cnf(cls_rev__eq__Cons__iff_1,axiom,
    c_List_Orev(c_List_Oappend(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).

cnf(cls_map__replicate__const_0,axiom,
    c_List_Omap(c_COMBK(X1,X2,X3),X4,X3,X2) = c_List_Oreplicate(c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__replicate__const_0) ).

cnf(cls_replicate__append__same_0,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).

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

cnf(cls_add__less__le__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(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_lessequals(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

cnf(cls_add__le__less__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(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_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

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

cnf(cls_map__replicate_0,axiom,
    c_List_Omap(X1,c_List_Oreplicate(X2,X3,X4),X4,X5) = c_List_Oreplicate(X2,hAPP(X1,X3),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__replicate_0) ).

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

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

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

cnf(cls_drop__take_0,axiom,
    c_List_Odrop(X1,c_List_Otake(X2,X3,X4),X4) = c_List_Otake(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_List_Odrop(X1,X3,X4),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__take_0) ).

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

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

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

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

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

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

cnf(cls_nth__append__length_0,axiom,
    c_List_Onth(c_List_Oappend(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),X4) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append__length_0) ).

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

cnf(cls_list__update__code_I2_J_0,axiom,
    c_List_Olist__update(c_List_Olist_OCons(X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat),X4,X3) = c_List_Olist_OCons(X4,X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).

cnf(cls_nth__Cons__number__of_1,axiom,
    ( c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,tc_nat),X3) = c_List_Onth(X2,c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3)
    | c_Int_Onumber__class_Onumber__of(X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__number__of_1) ).

cnf(cls_drop__Cons__number__of_1,axiom,
    ( c_List_Odrop(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,X4)
    | c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_1) ).

cnf(cls_list__update__nonempty_0,axiom,
    ( X1 = c_List_Olist_ONil(X4)
    | c_List_Olist__update(X1,X2,X3,X4) != c_List_Olist_ONil(X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).

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

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

cnf(cls_not__Nil__step1_0,axiom,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).

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

cnf(cls_append__eq__append__conv__if_2,axiom,
    ( c_List_Otake(c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),X1,X3) = X4
    | c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),tc_nat)
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_2) ).

cnf(cls_list__update__beyond_0,axiom,
    ( c_List_Olist__update(X1,X2,X3,X4) = X1
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).

cnf(cls_append__eq__conv__conj_2,axiom,
    ( c_List_Oappend(X1,c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2),X2) = X3
    | X1 != c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).

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

cnf(cls_rev__take_0,axiom,
    c_List_Orev(c_List_Otake(X1,X2,X3),X3) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),c_List_Orev(X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__take_0) ).

cnf(cls_rev__drop_0,axiom,
    c_List_Orev(c_List_Odrop(X1,X2,X3),X3) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),c_List_Orev(X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__drop_0) ).

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

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

cnf(cls_add__neg__nonpos_0,axiom,
    ( c_HOL_Oord__class_Oless(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_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

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

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

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

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

cnf(cls_add__nonneg__pos_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),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_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

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

cnf(cls_nth__append_0,axiom,
    ( c_List_Onth(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Onth(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append_0) ).

cnf(cls_list__update__id_0,axiom,
    c_List_Olist__update(X1,X2,c_List_Onth(X1,X2,X3),X3) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__id_0) ).

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

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

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

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

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

cnf(cls_add__le__cancel__left_1,axiom,
    ( c_lessequals(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_lessequals(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

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

cnf(cls_add__le__cancel__right_1,axiom,
    ( c_lessequals(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_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

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

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

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

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

cnf(cls_le__number__of__eq__not__less_0,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
    | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).

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

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

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

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

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

cnf(cls_append__in__listsp__conv_2,axiom,
    ( c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)
    | ~ c_List_Olistsp(X1,X3,X4)
    | ~ c_List_Olistsp(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).

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

cnf(cls_nth__Cons_H_1,axiom,
    ( c_List_Onth(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Onth(X2,c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3)
    | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons_H_1) ).

cnf(cls_drop__Cons_H_1,axiom,
    ( c_List_Odrop(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,X4)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_1) ).

cnf(cls_take__Suc__Cons_0,axiom,
    c_List_Otake(c_Suc(X1),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(X1,X3,X4),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).

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

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

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

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

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

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

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

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

cnf(cls_append__Cons_0,axiom,
    c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).

cnf(cls_append__eq__Cons__conv_5,axiom,
    c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).

cnf(cls_append__eq__append__conv2_4,axiom,
    c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).

cnf(cls_append__assoc_0,axiom,
    c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).

cnf(cls_Cons__eq__appendI_0,axiom,
    c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

cnf(cls_Cons__eq__append__conv_5,axiom,
    c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).

cnf(cls_append__eq__append__conv2_5,axiom,
    c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).

cnf(cls_append__eq__appendI_0,axiom,
    c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

cnf(cls_rev_Osimps_I2_J_0,axiom,
    c_List_Orev(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).

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

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

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

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

cnf(cls_drop__replicate_0,axiom,
    c_List_Odrop(X1,c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__replicate_0) ).

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

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

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

cnf(cls_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

cnf(cls_append__in__listsp__conv_0,axiom,
    ( c_List_Olistsp(X1,X2,X3)
    | ~ c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).

cnf(cls_append__in__listsp__conv_1,axiom,
    ( c_List_Olistsp(X1,X2,X3)
    | ~ c_List_Olistsp(X1,c_List_Oappend(X4,X2,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).

cnf(cls_rev__eq__Cons__iff_0,axiom,
    ( X1 = c_List_Oappend(c_List_Orev(X4,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2),X2)
    | c_List_Orev(X1,X2) != c_List_Olist_OCons(X3,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

cnf(cls_nth__take_0,axiom,
    ( c_List_Onth(c_List_Otake(X1,X2,X3),X4,X3) = c_List_Onth(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__take_0) ).

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

cnf(cls_expand__Suc_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_expand__Suc_0) ).

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

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

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

cnf(cls_rotate__conv__mod_0,axiom,
    c_List_Orotate(X1,X2,X3) = c_List_Orotate(c_Divides_Odiv__class_Omod(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__conv__mod_0) ).

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

cnf(cls_append__take__drop__id_0,axiom,
    c_List_Oappend(c_List_Otake(X1,X2,X3),c_List_Odrop(X1,X2,X3),X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).

cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
    ( c_lessequals(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_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

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

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

cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
    ( c_lessequals(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_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

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

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

cnf(cls_drop__Cons__number__of_0,axiom,
    ( c_List_Odrop(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,X3,X4)
    | c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_0) ).

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

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

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

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

cnf(cls_list__update_Osimps_I1_J_0,axiom,
    c_List_Olist__update(c_List_Olist_ONil(X1),X2,X3,X1) = c_List_Olist_ONil(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).

cnf(cls_list__update__code_I1_J_0,axiom,
    c_List_Olist__update(c_List_Olist_ONil(X1),X2,X3,X1) = c_List_Olist_ONil(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).

cnf(cls_list__update__nonempty_1,axiom,
    c_List_Olist__update(c_List_Olist_ONil(X1),X2,X3,X1) = c_List_Olist_ONil(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).

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

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

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

cnf(cls_nth__replicate_0,axiom,
    ( c_List_Onth(c_List_Oreplicate(X1,X2,X3),X4,X3) = X2
    | ~ c_HOL_Oord__class_Oless(X4,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__replicate_0) ).

cnf(cls_mod__le__divisor_0,axiom,
    ( c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).

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

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

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

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

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

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

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

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

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

cnf(cls_order__le__less__trans_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

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

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

cnf(cls_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/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

cnf(cls_le__number__of__eq__not__less_1,axiom,
    ( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).

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

cnf(cls_rev__append_0,axiom,
    c_List_Orev(c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Orev(X1,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).

cnf(cls_nth__via__drop_0,axiom,
    ( c_List_Onth(X2,X1,X3) = X4
    | c_List_Odrop(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__via__drop_0) ).

cnf(cls_take__1__Cons_0,axiom,
    c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).

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

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

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

cnf(cls_nth__Cons__Suc_0,axiom,
    c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Suc(X4),X3) = c_List_Onth(X2,X4,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__Suc_0) ).

cnf(cls_drop__Suc__Cons_0,axiom,
    c_List_Odrop(c_Suc(X1),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(X1,X3,X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).

cnf(cls_append__eq__Cons__conv_4,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_OCons(X2,X3,X1),X1) = c_List_Olist_OCons(X2,X3,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).

cnf(cls_replicate__Suc_0,axiom,
    c_List_Oreplicate(c_Suc(X1),X2,X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).

cnf(cls_Cons__eq__append__conv_4,axiom,
    c_List_Olist_OCons(X1,X2,X3) = c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X1,X2,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

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

cnf(cls_drop__Cons_H_0,axiom,
    c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_OCons(X1,X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).

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

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

cnf(cls_length__drop_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Odrop(X1,X2,X3),tc_List_Olist(X3)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__drop_0) ).

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

cnf(cls_take__Cons__number__of_0,axiom,
    ( c_List_Otake(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_ONil(X4)
    | c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_0) ).

cnf(cls_nth__Cons__number__of_0,axiom,
    ( c_List_Onth(c_List_Olist_OCons(X2,X3,X4),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) = X2
    | c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__number__of_0) ).

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

cnf(cls_distinct__rotate_0,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orotate(X3,X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).

cnf(cls_distinct_Osimps_I2_J_1,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Olist_OCons(X3,X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).

cnf(cls_distinct__append_0,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Oappend(X1,X3,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_0) ).

cnf(cls_distinct__append_1,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Oappend(X3,X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_1) ).

cnf(cls_rotate__length01_0,axiom,
    ( c_List_Orotate(X1,X2,X3) = X2
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__length01_0) ).

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

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

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

cnf(cls_rotate__id_0,axiom,
    ( c_List_Orotate(X1,X2,X3) = X2
    | c_Divides_Odiv__class_Omod(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__id_0) ).

cnf(cls_drop__all_0,axiom,
    ( c_List_Odrop(X1,X2,X3) = c_List_Olist_ONil(X3)
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__all_0) ).

cnf(cls_append__eq__conv__conj_0,axiom,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).

cnf(cls_append__eq__conv__conj_1,axiom,
    X1 = c_List_Odrop(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),c_List_Oappend(X2,X1,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).

cnf(cls_take__all_0,axiom,
    ( c_List_Otake(X1,X2,X3) = X2
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__all_0) ).

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

cnf(cls_rev__singleton__conv_1,axiom,
    c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).

cnf(cls_singleton__rev__conv_1,axiom,
    c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).

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

cnf(cls_rtranclp_Ortrancl__refl_0,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).

cnf(cls_drop__eq__Nil_0,axiom,
    ( c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat)
    | c_List_Odrop(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_singleton__rev__conv_0,axiom,
    ( X3 = c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2)
    | c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) != c_List_Orev(X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).

cnf(cls_rev__singleton__conv_0,axiom,
    ( X1 = c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2)
    | c_List_Orev(X1,X2) != c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).

cnf(cls_replicate__eq__replicate_1,axiom,
    ( X2 = X5
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).

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

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

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

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

cnf(cls_rev__replicate_0,axiom,
    c_List_Orev(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(X1,X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).

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

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

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

cnf(cls_replicate__eq__replicate_0,axiom,
    ( X1 = X4
    | c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).

cnf(cls_list_Oinject_0,axiom,
    ( X1 = X4
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

cnf(cls_append__same__eq_0,axiom,
    ( X1 = X4
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).

cnf(cls_same__append__eq_0,axiom,
    ( X2 = X4
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

cnf(cls_list_Oinject_1,axiom,
    ( X2 = X5
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

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

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

cnf(cls_length__Suc__conv_2,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)) = c_Suc(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).

cnf(cls_Suc__length__conv_2,axiom,
    c_Suc(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2))) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(X3,X1,X2),tc_List_Olist(X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).

cnf(cls_take__Cons_H_0,axiom,
    c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_ONil(X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).

cnf(cls_length__greater__0__conv_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).

cnf(cls_nth__Cons_H_0,axiom,
    c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat),X3) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons_H_0) ).

cnf(cls_drop__1__Cons_0,axiom,
    c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X1,X2,X3),X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_length__rotate_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Orotate(X1,X2,X3),tc_List_Olist(X3)) = c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate_0) ).

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

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

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

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

cnf(cls_less__Suc__eq__le_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

cnf(cls_distinct__rotate_1,axiom,
    ( c_List_Odistinct(c_List_Orotate(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).

cnf(cls_distinct__take_0,axiom,
    ( c_List_Odistinct(c_List_Otake(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__take_0) ).

cnf(cls_distinct__drop_0,axiom,
    ( c_List_Odistinct(c_List_Odrop(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__drop_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_length__replicate_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Oreplicate(X1,X2,X3),tc_List_Olist(X3)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__replicate_0) ).

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

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

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

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

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

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

cnf(cls_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

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

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

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

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

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

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

cnf(cls_replicate__eq__replicate_2,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_take__eq__Nil_0,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Otake(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).

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

cnf(cls_length__greater__0__conv_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | X1 = c_List_Olist_ONil(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).

cnf(cls_append__is__Nil__conv_0,axiom,
    ( X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

cnf(cls_rotate__is__Nil__conv_0,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Orotate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).

cnf(cls_append__is__Nil__conv_1,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).

cnf(cls_Nil__is__append__conv_0,axiom,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Oappend(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).

cnf(cls_Nil__is__append__conv_1,axiom,
    ( X3 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Oappend(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

cnf(cls_replicate__empty_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_0) ).

cnf(cls_empty__replicate_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Olist_ONil(X1) != c_List_Oreplicate(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_0) ).

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

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

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

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

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

cnf(cls_append__self__conv2_0,axiom,
    ( X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).

cnf(cls_append__self__conv_0,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).

cnf(cls_self__append__conv_0,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 != c_List_Oappend(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).

cnf(cls_self__append__conv2_0,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 != c_List_Oappend(X2,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

cnf(cls_le__0__eq_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).

cnf(cls_list_Osimps_I3_J_0,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

cnf(cls_neq__Nil__conv_1,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

cnf(cls_list_Osimps_I2_J_0,axiom,
    c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).

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

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

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

cnf(cls_not__Cons__self2_0,axiom,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

cnf(cls_not__Cons__self_0,axiom,
    X1 != c_List_Olist_OCons(X2,X1,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

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

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

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

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

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

cnf(cls_distinct__rev_0,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orev(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_0) ).

cnf(cls_zero__le__one_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

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

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

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

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

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

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

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

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

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

cnf(cls_append__is__Nil__conv_2,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).

cnf(cls_Nil__is__append__conv_2,axiom,
    c_List_Olist_ONil(X1) = c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

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

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

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

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

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

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

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

cnf(cls_length__rev_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rev_0) ).

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

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

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

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

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

cnf(cls_rotate__is__Nil__conv_1,axiom,
    c_List_Orotate(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).

cnf(cls_take__eq__Nil_2,axiom,
    c_List_Otake(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).

cnf(cls_drop__Nil_0,axiom,
    c_List_Odrop(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Nil_0) ).

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

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

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

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

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

cnf(cls_distinct__rev_1,axiom,
    ( c_List_Odistinct(c_List_Orev(X1,X2),X2)
    | ~ c_List_Odistinct(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_1) ).

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

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

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

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

cnf(cls_replicate__empty_1,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).

cnf(cls_take__0_0,axiom,
    c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__0_0) ).

cnf(cls_empty__replicate_1,axiom,
    c_List_Olist_ONil(X1) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_1) ).

cnf(cls_append__Nil_0,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),X2,X1) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).

cnf(cls_append__Nil2_0,axiom,
    c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

cnf(cls_self__append__conv2_1,axiom,
    X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).

cnf(cls_eq__Nil__appendI_0,axiom,
    X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).

cnf(cls_self__append__conv_1,axiom,
    X1 = c_List_Oappend(X1,c_List_Olist_ONil(X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).

cnf(cls_eq__number__of_0,axiom,
    ( X2 = X3
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).

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

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

cnf(cls_le__0__eq_1,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).

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

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

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

cnf(cls_drop__0_0,axiom,
    c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__0_0) ).

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

cnf(cls_le0_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).

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

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

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

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

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

cnf(cls_CHAINED_0_01,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

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

cnf(cls_rev__is__rev__conv_0,axiom,
    ( X1 = X3
    | c_List_Orev(X1,X2) != c_List_Orev(X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).

cnf(cls_length__0__conv_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_0) ).

cnf(cls_rev__rev__ident_0,axiom,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).

cnf(cls_rev__swap_1,axiom,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_1) ).

cnf(cls_rev__swap_0,axiom,
    X1 = c_List_Orev(c_List_Orev(X1,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_0) ).

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

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

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

cnf(cls_rev__is__Nil__conv_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Orev(X1,X2) != c_List_Olist_ONil(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).

cnf(cls_Nil__is__rev__conv_0,axiom,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Orev(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).

cnf(cls_length__0__conv_1,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_1) ).

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

cnf(cls_rev__is__Nil__conv_1,axiom,
    c_List_Orev(c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).

cnf(cls_Nil__is__rev__conv_1,axiom,
    c_List_Olist_ONil(X1) = c_List_Orev(c_List_Olist_ONil(X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).

cnf(cls_distinct_Osimps_I1_J_0,axiom,
    c_List_Odistinct(c_List_Olist_ONil(X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(clsarity_Int__Oint__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).

cnf(clsarity_Int__Oint__Int_Onumber,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).

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

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

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

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).

cnf(clsarity_Int__Oint__Divides_Oring__div,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Oring__div) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).

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

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

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

cnf(clsarity_Int__Oint__OrderedGroup_Oab__group__add,axiom,
    class_OrderedGroup_Oab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom,
    class_OrderedGroup_Ogroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).

cnf(clsarity_Int__Oint__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oidom,axiom,
    class_Ring__and__Field_Oidom(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).

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

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

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

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

cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,axiom,
    class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__idom,axiom,
    class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).

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

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

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

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

cnf(cls_True_0,axiom,
    v_n____ = v_i____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).

cnf(i_0_681,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)
    | ~ 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)
    | ~ 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 ).

cnf(i_0_682,axiom,
    c_List_Ofoldr(X1,X2,X3,X4,X5) = c_List_Ofoldl(c_COMBC(X1,X4,X5,X5),X3,c_List_Orev(X2,X4),X5,X4),
    cls_foldr__foldl_0 ).

cnf(i_0_683,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    cls_calculation_0 ).

cnf(i_0_684,axiom,
    ( 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))
    | ~ 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 ).

cnf(i_0_685,axiom,
    ( 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))
    | ~ 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 ).

cnf(i_0_686,axiom,
    ( 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))
    | ~ 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 ).

cnf(i_0_687,axiom,
    ( 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)
    | ~ 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 ).

cnf(i_0_688,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
    cls_varT_0 ).

cnf(i_0_689,axiom,
    c_List_Ofoldr(X1,c_List_Oappend(X2,X3,X4),X5,X4,X6) = c_List_Ofoldr(X1,X2,c_List_Ofoldr(X1,X3,X5,X4,X6),X4,X6),
    cls_foldr__append_0 ).

cnf(i_0_690,axiom,
    c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
    cls_uT_H_0 ).

cnf(i_0_691,axiom,
    c_List_Ofoldr(X1,c_List_Olist_OCons(X2,X3,X4),X5,X4,X6) = hAPP(hAPP(X1,X2),c_List_Ofoldr(X1,X3,X5,X4,X6)),
    cls_foldr_Osimps_I2_J_0 ).

cnf(i_0_692,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 ).

cnf(i_0_693,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    cls_headT_0 ).

cnf(i_0_694,axiom,
    c_List_Ofoldl(X1,X2,X3,X4,X5) = c_List_Ofoldr(c_COMBC(X1,X4,X5,X4),c_List_Orev(X3,X5),X2,X5,X4),
    cls_foldl__foldr_0 ).

cnf(i_0_695,axiom,
    v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    cls_T_0 ).

cnf(i_0_696,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 ).

cnf(i_0_697,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 ).

cnf(i_0_698,axiom,
    c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
    cls_foldr_Osimps_I1_J_0 ).

cnf(i_0_699,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_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__nonneg__eq__0__iff_2 ).

cnf(i_0_700,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X3),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    cls_subst__map_0,
    [final] ).

cnf(i_0_701,plain,
    ( X1 = c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X2,c_List_Orev(c_Type_Osko__Type__Xvar__app__types__1__1(X2,X1,X3,X4),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)
    | ~ c_Type_Otypings(X3,X6,X7)
    | ~ 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_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) ),
    inference(rw,[status(thm)],[i_0_681,c_0_682]),
    [final] ).

cnf(i_0_702,negated_conjecture,
    ~ c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
    cls_conjecture_0,
    [final] ).

cnf(i_0_703,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_704,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))
    | ~ 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)
    | ~ 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_705,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_706,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_707,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_708,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_709,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_710,axiom,
    ( c_Type_Otypings(X1,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X2),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X3,X6,tc_Type_Otype),X4,X5)
    | ~ c_Type_Otyping(X1,X2,X6) ),
    cls_substs__lemma_0,
    [final] ).

cnf(i_0_711,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_683,c_0_682]),c_0_682]),
    [final] ).

cnf(i_0_712,plain,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X3,c_List_Orev(c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    inference(rw,[status(thm)],[i_0_684,c_0_682]),
    [final] ).

cnf(i_0_713,plain,
    ( c_Type_Otyping(X1,X2,c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X3,c_List_Orev(c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X2,X4),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    inference(rw,[status(thm)],[i_0_685,c_0_682]),
    [final] ).

cnf(i_0_714,plain,
    ( c_Type_Otyping(X1,X2,c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X3,c_List_Orev(c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    inference(rw,[status(thm)],[i_0_686,c_0_682]),
    [final] ).

cnf(i_0_715,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X3),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    cls_lift__map_0,
    [final] ).

cnf(i_0_716,axiom,
    ( c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5)
    | hAPP(X1,c_List_Osko__List__Xmap__eq__conv__1__1(X1,X2,X3,X4,X5)) != hAPP(X2,c_List_Osko__List__Xmap__eq__conv__1__1(X1,X2,X3,X4,X5)) ),
    cls_map__eq__conv_2,
    [final] ).

cnf(i_0_717,axiom,
    ( c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5)
    | hAPP(X1,c_List_Osko__List__Xmap__cong__1__1(X1,X2,X3,X4,X5)) != hAPP(X2,c_List_Osko__List__Xmap__cong__1__1(X1,X2,X3,X4,X5)) ),
    cls_map__cong_1,
    [final] ).

cnf(i_0_718,axiom,
    ( c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5)
    | hAPP(X1,c_List_Osko__List__Xmap__ext__1__1(X1,X2,X3,X4,X5)) != hAPP(X2,c_List_Osko__List__Xmap__ext__1__1(X1,X2,X3,X4,X5)) ),
    cls_map__ext_1,
    [final] ).

cnf(i_0_719,plain,
    ( 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)
    | ~ c_Type_Otyping(X1,X2,c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X4,c_List_Orev(X5,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)) ),
    inference(rw,[status(thm)],[i_0_687,c_0_682]),
    [final] ).

cnf(i_0_720,axiom,
    ( X1 = X2
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X1) ),
    cls_var__app__type__eq_0,
    [final] ).

cnf(i_0_721,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))),
    inference(rw,[status(thm)],[i_0_688,c_0_682]),
    [final] ).

cnf(i_0_722,axiom,
    c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
    cls_o__assoc_0,
    [final] ).

cnf(i_0_723,plain,
    c_List_Ofoldl(c_COMBC(X1,X4,X6,X6),X5,c_List_Orev(c_List_Oappend(X2,X3,X4),X4),X6,X4) = c_List_Ofoldl(c_COMBC(X1,X4,X6,X6),c_List_Ofoldl(c_COMBC(X1,X4,X6,X6),X5,c_List_Orev(X3,X4),X6,X4),c_List_Orev(X2,X4),X6,X4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_689,c_0_682]),c_0_682]),c_0_682]),
    [final] ).

cnf(i_0_724,plain,
    c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))),
    inference(rw,[status(thm)],[i_0_690,c_0_682]),
    [final] ).

cnf(i_0_725,plain,
    c_List_Ofoldl(c_COMBC(X1,X4,X6,X6),X5,c_List_Orev(c_List_Olist_OCons(X2,X3,X4),X4),X6,X4) = hAPP(hAPP(X1,X2),c_List_Ofoldl(c_COMBC(X1,X4,X6,X6),X5,c_List_Orev(X3,X4),X6,X4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_691,c_0_682]),c_0_682]),
    [final] ).

cnf(i_0_726,axiom,
    ( hAPP(c_Fun_Ocomp(X1,X2,X7,X8,X9),X3) = hAPP(c_Fun_Ocomp(X4,X5,X10,X8,X11),X6)
    | hAPP(X1,hAPP(X2,X3)) != hAPP(X4,hAPP(X5,X6)) ),
    cls_comp__cong_0,
    [final] ).

cnf(i_0_727,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_728,axiom,
    c_List_Ofoldl(X1,X2,c_List_Oappend(X3,X4,X5),X6,X5) = c_List_Ofoldl(X1,c_List_Ofoldl(X1,X2,X3,X6,X5),X4,X6,X5),
    cls_foldl__append_0,
    [final] ).

cnf(i_0_729,plain,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_COMBC(c_HOL_Oplus__class_Oplus(X1),X1,X1,X1),c_HOL_Ozero__class_Ozero(X1),c_List_Orev(X3,X1),X1,X1))
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(rw,[status(thm)],[i_0_692,c_0_682]),
    [final] ).

cnf(i_0_730,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))
    | ~ 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_731,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))
    | ~ 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_732,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))
    | ~ 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_733,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)),
    inference(rw,[status(thm)],[i_0_693,c_0_682]),
    [final] ).

cnf(i_0_734,plain,
    c_List_Ofoldl(X1,X2,X3,X4,X5) = c_List_Ofoldl(c_COMBC(c_COMBC(X1,X4,X5,X4),X5,X4,X4),X2,c_List_Orev(c_List_Orev(X3,X5),X5),X4,X5),
    inference(rw,[status(thm)],[i_0_694,c_0_682]),
    [final] ).

cnf(i_0_735,axiom,
    ( hAPP(X1,hAPP(X2,X9)) = hAPP(X6,hAPP(X7,X9))
    | c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(X6,X7,X8,X4,X5) ),
    cls_o__eq__dest_0,
    [final] ).

cnf(i_0_736,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_737,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_738,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_739,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_740,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_741,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_742,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_743,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_744,plain,
    v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(v_Ts____,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)),
    inference(rw,[status(thm)],[i_0_695,c_0_682]),
    [final] ).

cnf(i_0_745,axiom,
    c_List_Omap(X1,c_List_Omap(X2,X3,X4,X5),X5,X6) = c_List_Omap(c_Fun_Ocomp(X1,X2,X5,X6,X4),X3,X4,X6),
    cls_map__map_0,
    [final] ).

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

cnf(i_0_747,plain,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) = c_List_Ofoldl(c_COMBC(c_HOL_Oplus__class_Oplus(X1),X1,X1,X1),c_HOL_Ozero__class_Ozero(X1),c_List_Orev(X2,X1),X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(rw,[status(thm)],[i_0_696,c_0_682]),
    [final] ).

cnf(i_0_748,plain,
    ( c_List_Ofoldl(c_COMBC(c_HOL_Oplus__class_Oplus(X1),X1,X1,X1),X3,c_List_Orev(X2,X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(rw,[status(thm)],[i_0_697,c_0_682]),
    [final] ).

cnf(i_0_749,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),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_750,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    cls_lifts__IT_0,
    [final] ).

cnf(i_0_751,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_OCons(X3,X4,X5),X6,X5) = c_List_Ofoldl(X1,hAPP(hAPP(X1,X2),X3),X4,X6,X5),
    cls_foldl__Cons_0,
    [final] ).

cnf(i_0_752,axiom,
    hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    cls_o__apply_0,
    [final] ).

cnf(i_0_753,axiom,
    hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
    cls_o__eq__dest__lhs_0,
    [final] ).

cnf(i_0_754,axiom,
    ( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4),X3) ),
    cls_typing__elims_I2_J_0,
    [final] ).

cnf(i_0_755,axiom,
    ( c_List_Oappend(X3,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)),X1,X2),X4,X2),X2) = c_List_Oappend(X1,X4,X2)
    | c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2),c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)),X1,X2),X4,X2),X2) != X4
    | c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2) != X1
    | X3 != c_List_Otake(c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)),X1,X2) ),
    cls_append__eq__append__conv__if_6,
    [final] ).

cnf(i_0_756,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_757,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_758,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_759,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_760,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_761,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_762,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_763,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_764,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_ListOrder_Ostep1(X1,X4,X5,X6)
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(X6),X6),X6),c_List_Oappend(X5,c_List_Olist_OCons(X3,c_List_Olist_ONil(X6),X6),X6),X6) ),
    cls_Snoc__step1__SnocD_1,
    [final] ).

cnf(i_0_765,plain,
    c_List_Ofoldl(c_COMBC(X1,X2,X4,X4),X3,c_List_Orev(c_List_Olist_ONil(X2),X2),X4,X2) = X3,
    inference(rw,[status(thm)],[i_0_698,c_0_682]),
    [final] ).

cnf(i_0_766,axiom,
    ( X1 = X2
    | c_ListOrder_Ostep1(X3,X1,X2,X4)
    | ~ c_ListOrder_Ostep1(X3,c_List_Oappend(X1,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    cls_Snoc__step1__SnocD_0,
    [final] ).

cnf(i_0_767,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X2 = X3
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(X5),X5),X5),c_List_Oappend(X6,c_List_Olist_OCons(X3,c_List_Olist_ONil(X5),X5),X5),X5) ),
    cls_Snoc__step1__SnocD_3,
    [final] ).

cnf(i_0_768,axiom,
    c_List_Omap(X1,c_List_Olist__update(X2,X3,X4,X5),X5,X6) = c_List_Olist__update(c_List_Omap(X1,X2,X5,X6),X3,hAPP(X1,X4),X6),
    cls_map__update_0,
    [final] ).

cnf(i_0_769,axiom,
    c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4) = c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4),
    cls_shift__commute_0,
    [final] ).

cnf(i_0_770,axiom,
    ( c_List_Olist__update(c_List_Olist__update(X1,X2,X3,X4),X5,X6,X4) = c_List_Olist__update(c_List_Olist__update(X1,X5,X6,X4),X2,X3,X4)
    | X2 = X5 ),
    cls_list__update__swap_0,
    [final] ).

cnf(i_0_771,axiom,
    ( X1 = X2
    | X3 = X4
    | ~ c_ListOrder_Ostep1(X5,c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X6),X6),X6),c_List_Oappend(X2,c_List_Olist_OCons(X4,c_List_Olist_ONil(X6),X6),X6),X6) ),
    cls_Snoc__step1__SnocD_2,
    [final] ).

cnf(i_0_772,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)
    | ~ c_Type_Otyping(X6,X4,X1)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X6,X5,X1,tc_Type_Otype),X3,X7)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    cls_MI1_0,
    [final] ).

cnf(i_0_773,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)
    | ~ c_Type_Otyping(X6,X4,X2)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X6,X5,X2,tc_Type_Otype),X3,X7)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    cls_MI2_0,
    [final] ).

cnf(i_0_774,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_775,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_776,axiom,
    c_List_Omap(X1,c_List_Oappend(X2,X3,X4),X4,X5) = c_List_Oappend(c_List_Omap(X1,X2,X4,X5),c_List_Omap(X1,X3,X4,X5),X5),
    cls_map__append_0,
    [final] ).

cnf(i_0_777,axiom,
    ( c_List_Orev(c_List_Olist__update(X1,X2,X3,X4),X4) = c_List_Olist__update(c_List_Orev(X1,X4),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),X2,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,X4)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    cls_rev__update_0,
    [final] ).

cnf(i_0_778,axiom,
    ( c_List_Olist__update(c_List_Oappend(X1,X2,X3),X4,X5,X3) = c_List_Oappend(X1,c_List_Olist__update(X2,c_HOL_Ominus__class_Ominus(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat),X5,X3),X3)
    | c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    cls_list__update__append_1,
    [final] ).

cnf(i_0_779,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_780,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_781,axiom,
    c_List_Orotate(X1,c_List_Orev(X2,X3),X3) = c_List_Orev(c_List_Orotate(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),c_Divides_Odiv__class_Omod(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),tc_nat),X2,X3),X3),
    cls_rotate__rev_0,
    [final] ).

cnf(i_0_782,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_783,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_784,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_785,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_786,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
    cls_foldl__Nil_0,
    [final] ).

cnf(i_0_787,axiom,
    ( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    cls_subst__lemma_0,
    [final] ).

cnf(i_0_788,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_789,axiom,
    hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
    cls_ATP__Linkup_OCOMBC__def_0,
    [final] ).

cnf(i_0_790,axiom,
    hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
    cls_COMBC__def_0,
    [final] ).

cnf(i_0_791,axiom,
    ( c_ListOrder_Ostep1(X1,X2,X3,X4)
    | hBOOL(hAPP(hAPP(X1,X5),X6))
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X6,X3,X4),X4) ),
    cls_Cons__step1__Cons_1,
    [final] ).

cnf(i_0_792,axiom,
    ( c_List_Olist__update(c_List_Oappend(X1,X2,X3),X4,X5,X3) = c_List_Oappend(c_List_Olist__update(X1,X4,X5,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    cls_list__update__append_0,
    [final] ).

cnf(i_0_793,axiom,
    ( c_List_Olist__update(c_List_Oappend(X1,X2,X3),X4,X5,X3) = c_List_Oappend(c_List_Olist__update(X1,X4,X5,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    cls_list__update__append1_0,
    [final] ).

cnf(i_0_794,axiom,
    c_List_Orotate(X1,X2,X3) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),X2,X3),c_List_Otake(c_Divides_Odiv__class_Omod(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),X2,X3),X3),
    cls_rotate__drop__take_0,
    [final] ).

cnf(i_0_795,axiom,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_Type_Otype),X2,X4) ),
    cls_Abs_0,
    [final] ).

cnf(i_0_796,axiom,
    c_List_Olist__update(c_List_Olist__update(X1,X2,X3,X4),X2,X5,X4) = c_List_Olist__update(X1,X2,X5,X4),
    cls_list__update__overwrite_0,
    [final] ).

cnf(i_0_797,axiom,
    ( c_ListOrder_Ostep1(X1,X2,X3,X4)
    | X3 = X2
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X6,X3,X4),X4) ),
    cls_Cons__step1__Cons_3,
    [final] ).

cnf(i_0_798,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__eq_0,
    [final] ).

cnf(i_0_799,axiom,
    ( c_List_Oappend(X1,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2),X4,X2),X2) = c_List_Oappend(X3,X4,X2)
    | X1 != c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2)
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)),tc_nat) ),
    cls_append__eq__append__conv__if_5,
    [final] ).

cnf(i_0_800,axiom,
    c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5) = c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5),
    cls_Cons__eq__map__conv_3,
    [final] ).

cnf(i_0_801,axiom,
    c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
    cls_map_Osimps_I2_J_0,
    [final] ).

cnf(i_0_802,axiom,
    c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
    cls_map__eq__Cons__conv_3,
    [final] ).

cnf(i_0_803,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_804,axiom,
    c_List_Olist__update(c_List_Olist_OCons(X1,X2,X3),c_Suc(X4),X5,X3) = c_List_Olist_OCons(X1,c_List_Olist__update(X2,X4,X5,X3),X3),
    cls_list__update__code_I3_J_0,
    [final] ).

cnf(i_0_805,axiom,
    c_List_Orotate(X1,c_List_Omap(X2,X3,X4,X5),X5) = c_List_Omap(X2,c_List_Orotate(X1,X3,X4),X4,X5),
    cls_rotate__map_0,
    [final] ).

cnf(i_0_806,axiom,
    c_List_Otake(X1,c_List_Omap(X2,X3,X4,X5),X5) = c_List_Omap(X2,c_List_Otake(X1,X3,X4),X4,X5),
    cls_take__map_0,
    [final] ).

cnf(i_0_807,axiom,
    c_List_Odrop(X1,c_List_Omap(X2,X3,X4,X5),X5) = c_List_Omap(X2,c_List_Odrop(X1,X3,X4),X4,X5),
    cls_drop__map_0,
    [final] ).

cnf(i_0_808,axiom,
    ( c_List_Olist__update(X1,X2,X3,X4) = c_List_Oappend(c_List_Otake(X2,X1,X4),c_List_Olist_OCons(X3,c_List_Odrop(c_Suc(X2),X1,X4),X4),X4)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    cls_upd__conv__take__nth__drop_0,
    [final] ).

cnf(i_0_809,axiom,
    ( X1 = c_List_Oappend(c_List_Otake(X2,X1,X3),c_List_Olist_OCons(c_List_Onth(X1,X2,X3),c_List_Odrop(c_Suc(X2),X1,X3),X3),X3)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    cls_id__take__nth__drop_0,
    [final] ).

cnf(i_0_810,axiom,
    ( c_lessequals(c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | c_List_Oappend(X3,X4,X2) = c_List_Oappend(X1,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2),X4,X2),X2)
    | c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2) != X1 ),
    cls_append__eq__append__conv__if_4,
    [final] ).

cnf(i_0_811,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X2,X5,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X3,X5,X4) ),
    cls_Cons__step1__Cons_5,
    [final] ).

cnf(i_0_812,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X2,X5,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X3,X5,X4) ),
    cls_append__step1I_1,
    [final] ).

cnf(i_0_813,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X5,X4),c_List_Oappend(X3,X5,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
    cls_append__step1I_0,
    [final] ).

cnf(i_0_814,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X2)),hAPP(hAPP(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_815,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_816,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_817,axiom,
    ( c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)) = c_Nat_Osize__class_Osize(X5,tc_List_Olist(X3))
    | c_List_Omap(X1,X2,X3,X4) != c_List_Omap(X1,X5,X3,X4) ),
    cls_map__eq__imp__length__eq_0,
    [final] ).

cnf(i_0_818,axiom,
    ( c_List_Onth(c_List_Omap(X1,X2,X3,X4),X5,X4) = hAPP(X1,c_List_Onth(X2,X5,X3))
    | ~ c_HOL_Oord__class_Oless(X5,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    cls_nth__map_0,
    [final] ).

cnf(i_0_819,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Omap(X3,X1,X2,X4),X4) ),
    cls_distinct__map_0,
    [final] ).

cnf(i_0_820,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_821,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ c_ListOrder_Ostep1(X3,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X1,X6,X5),X5) ),
    cls_Cons__step1__Cons_0,
    [final] ).

cnf(i_0_822,axiom,
    c_List_Otake(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Otake(X1,X2,X4),c_List_Otake(c_HOL_Ominus__class_Ominus(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X4)),tc_nat),X3,X4),X4),
    cls_take__append_0,
    [final] ).

cnf(i_0_823,axiom,
    c_List_Odrop(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Odrop(X1,X2,X4),c_List_Odrop(c_HOL_Ominus__class_Ominus(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X4)),tc_nat),X3,X4),X4),
    cls_drop__append_0,
    [final] ).

cnf(i_0_824,axiom,
    c_List_Orev(c_List_Omap(X1,X2,X3,X4),X4) = c_List_Omap(X1,c_List_Orev(X2,X3),X3,X4),
    cls_rev__map_0,
    [final] ).

cnf(i_0_825,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_826,axiom,
    c_List_Olist__update(c_List_Oappend(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),X5,X4) = c_List_Oappend(X1,c_List_Olist_OCons(X5,X3,X4),X4),
    cls_list__update__length_0,
    [final] ).

cnf(i_0_827,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    cls_mod__diff__eq_0,
    [final] ).

cnf(i_0_828,axiom,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X5,X4) = c_List_Onth(X1,X5,X4)
    | X2 = X5
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    cls_nth__list__update_1,
    [final] ).

cnf(i_0_829,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_zmod__simps_I1_J_0,
    [final] ).

cnf(i_0_830,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__left__eq_0,
    [final] ).

cnf(i_0_831,axiom,
    ( c_Type_Otyping(X1,X2,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2),X3) ),
    cls_typing__elims_I2_J_1,
    [final] ).

cnf(i_0_832,axiom,
    ( X1 = X2
    | X3 = X4
    | ~ c_ListOrder_Ostep1(X5,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X1,X3,X6),X6) ),
    cls_Cons__step1__Cons_2,
    [final] ).

cnf(i_0_833,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_834,axiom,
    ( hAPP(c_Type_Oshift(X1,X2,X3,X4),X5) = hAPP(X1,c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X2,X5,tc_nat) ),
    cls_shift__lt_0,
    [final] ).

cnf(i_0_835,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X4),X2),X5)
    | ~ c_Type_Otyping(X1,X4,X5) ),
    cls_lift__type_0,
    [final] ).

cnf(i_0_836,axiom,
    ( c_List_Otake(c_Suc(X1),X2,X3) = c_List_Oappend(c_List_Otake(X1,X2,X3),c_List_Olist_OCons(c_List_Onth(X2,X1,X3),c_List_Olist_ONil(X3),X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    cls_take__Suc__conv__app__nth_0,
    [final] ).

cnf(i_0_837,axiom,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X2,X4) = X3
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    cls_nth__list__update__eq_0,
    [final] ).

cnf(i_0_838,axiom,
    ( c_List_Onth(c_List_Olist__update(X2,X1,X4,X3),X1,X3) = X4
    | ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    cls_nth__list__update_0,
    [final] ).

cnf(i_0_839,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X4,X1),X3,X1)
    | ~ class_Divides_Oring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
    | c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
    cls_mod__diff__cong_0,
    [final] ).

cnf(i_0_840,axiom,
    ( c_List_Otake(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,X4),X4)
    | c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_take__Cons__number__of_1,
    [final] ).

cnf(i_0_841,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X2),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X6),X4),X3,X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X2,X3,X1) != c_Divides_Odiv__class_Omod(X4,X3,X1)
    | c_Divides_Odiv__class_Omod(X5,X3,X1) != c_Divides_Odiv__class_Omod(X6,X3,X1) ),
    cls_mod__add__cong_0,
    [final] ).

cnf(i_0_842,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,X4,X3),X3) = c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X1,X2,X3),X4,X3),X3),
    cls_replicate__app__Cons__same_0,
    [final] ).

cnf(i_0_843,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    cls_le__diff__iff_0,
    [final] ).

cnf(i_0_844,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    cls_less__diff__iff_0,
    [final] ).

cnf(i_0_845,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X2)),hAPP(hAPP(c_Lambda_Olift,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
    cls_lift__preserves__beta_0,
    [final] ).

cnf(i_0_846,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_847,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_848,axiom,
    ( X2 = c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),X4,X3),X5,X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X5,X3)
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),tc_nat) ),
    cls_append__eq__append__conv__if_1,
    [final] ).

cnf(i_0_849,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_850,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_851,axiom,
    ( hAPP(c_Type_Oshift(X1,X2,X3,X4),X5) = hAPP(X1,X5)
    | ~ c_HOL_Oord__class_Oless(X5,X2,tc_nat) ),
    cls_shift__gt_0,
    [final] ).

cnf(i_0_852,axiom,
    ( c_List_Onth(c_List_Olist__update(X1,X2,X3,X4),X5,X4) = c_List_Onth(X1,X5,X4)
    | X2 = X5 ),
    cls_nth__list__update__neq_0,
    [final] ).

cnf(i_0_853,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X3,X4,X5),X5)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    cls_Cons__step1__Cons_4,
    [final] ).

cnf(i_0_854,axiom,
    ( c_List_Onth(X1,X2,X4) = X3
    | c_List_Olist__update(X1,X2,X3,X4) != X1
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),tc_nat) ),
    cls_list__update__same__conv_0,
    [final] ).

cnf(i_0_855,axiom,
    ( X1 = X4
    | c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X4,c_List_Olist_OCons(X5,c_List_Olist_ONil(X3),X3),X3) ),
    cls_append1__eq__conv_0,
    [final] ).

cnf(i_0_856,axiom,
    ( X2 = X5
    | c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X4,c_List_Olist_OCons(X5,c_List_Olist_ONil(X3),X3),X3) ),
    cls_append1__eq__conv_1,
    [final] ).

cnf(i_0_857,axiom,
    ( c_List_Otake(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,X4),X4)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_take__Cons_H_1,
    [final] ).

cnf(i_0_858,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X4,X1),X3,X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    cls_mod__diff__left__eq_0,
    [final] ).

cnf(i_0_859,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X3,X4,X1),X1),X4,X1)
    | ~ class_Divides_Oring__div(X1) ),
    cls_mod__diff__right__eq_0,
    [final] ).

cnf(i_0_860,axiom,
    ( c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),X1,X3),X2,X3) = X5
    | c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),tc_nat)
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    cls_append__eq__append__conv__if_3,
    [final] ).

cnf(i_0_861,axiom,
    ~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),
    cls_impossible__Cons_0,
    [final] ).

cnf(i_0_862,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X2,X3),X3) = c_List_Oappend(c_List_Oreplicate(X4,X2,X3),c_List_Oreplicate(X1,X2,X3),X3),
    cls_append__replicate__commute_0,
    [final] ).

cnf(i_0_863,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_zmod__simps_I2_J_0,
    [final] ).

cnf(i_0_864,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__right__eq_0,
    [final] ).

cnf(i_0_865,axiom,
    c_Nat_Osize__class_Osize(c_List_Omap(X1,X2,X3,X4),tc_List_Olist(X4)) = c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),
    cls_length__map_0,
    [final] ).

cnf(i_0_866,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist__update(X1,X2,X3,X4),tc_List_Olist(X4)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),
    cls_length__list__update_0,
    [final] ).

cnf(i_0_867,axiom,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
    cls_CHAINED_0,
    [final] ).

cnf(i_0_868,axiom,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
    cls_argsT_0,
    [final] ).

cnf(i_0_869,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
    cls_argT_0,
    [final] ).

cnf(i_0_870,axiom,
    ( c_List_Omap(X1,X2,X3,X3) = X2
    | hAPP(X1,c_List_Osko__List__Xmap__idI__1__1(X1,X2,X3)) != c_List_Osko__List__Xmap__idI__1__1(X1,X2,X3) ),
    cls_map__idI_1,
    [final] ).

cnf(i_0_871,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_872,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_le__diff__iff_1,
    [final] ).

cnf(i_0_873,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_less__diff__iff_1,
    [final] ).

cnf(i_0_874,axiom,
    hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
    cls_shift__eq_0,
    [final] ).

cnf(i_0_875,axiom,
    ( c_List_Olist__update(X2,X1,c_List_Onth(X2,X1,X3),X3) = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    cls_list__update__same__conv_1,
    [final] ).

cnf(i_0_876,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X5,X4,X1)
    | ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5),X1) ),
    cls_le__add__right__mono_0,
    [final] ).

cnf(i_0_877,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_878,axiom,
    ( c_List_Onth(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Onth(X2,c_HOL_Ominus__class_Ominus(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat),X3)
    | c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    cls_nth__append_1,
    [final] ).

cnf(i_0_879,axiom,
    ( X2 = X4
    | c_List_Onth(X1,X2,X3) != c_List_Onth(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_List_Odistinct(X1,X3) ),
    cls_nth__eq__iff__index__eq_0,
    [final] ).

cnf(i_0_880,axiom,
    ( X2 = X4
    | c_List_Onth(X1,X2,X3) != c_List_Onth(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat)
    | ~ c_List_Odistinct(X1,X3) ),
    cls_distinct__conv__nth_0,
    [final] ).

cnf(i_0_881,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_Nat_Odiff__diff__eq_0,
    [final] ).

cnf(i_0_882,axiom,
    ( c_List_Olist_OCons(c_List_Onth(X1,X2,X3),c_List_Odrop(c_Suc(X2),X1,X3),X3) = c_List_Odrop(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    cls_nth__drop_H_0,
    [final] ).

cnf(i_0_883,axiom,
    ( c_List_Onth(c_List_Orev(X1,X2),X3,X2) = c_List_Onth(X1,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_Suc(X3),tc_nat),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
    cls_rev__nth_0,
    [final] ).

cnf(i_0_884,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
    cls_add__le__cancel__right_0,
    [final] ).

cnf(i_0_885,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
    cls_add__le__cancel__left_0,
    [final] ).

cnf(i_0_886,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_887,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_888,axiom,
    ( X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),X4,X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X5,X3)
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),tc_nat) ),
    cls_append__eq__append__conv__if_0,
    [final] ).

cnf(i_0_889,axiom,
    c_List_Orev(c_List_Oappend(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    cls_rev__eq__Cons__iff_1,
    [final] ).

cnf(i_0_890,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_891,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_892,axiom,
    c_List_Omap(c_COMBK(X1,X2,X3),X4,X3,X2) = c_List_Oreplicate(c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),X1,X2),
    cls_map__replicate__const_0,
    [final] ).

cnf(i_0_893,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
    cls_replicate__append__same_0,
    [final] ).

cnf(i_0_894,axiom,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ c_lessequals(X3,X5,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_add__mono_0,
    [final] ).

cnf(i_0_895,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_lessequals(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__less__le__mono_0,
    [final] ).

cnf(i_0_896,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_lessequals(X2,X4,X1) ),
    cls_add__le__less__mono_0,
    [final] ).

cnf(i_0_897,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_898,axiom,
    c_List_Omap(X1,c_List_Oreplicate(X2,X3,X4),X4,X5) = c_List_Oreplicate(X2,hAPP(X1,X3),X5),
    cls_map__replicate_0,
    [final] ).

cnf(i_0_899,axiom,
    hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)),
    cls_lift_Osimps_I2_J_0,
    [final] ).

cnf(i_0_900,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_901,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_diff__less__mono_0,
    [final] ).

cnf(i_0_902,axiom,
    c_List_Odrop(X1,c_List_Otake(X2,X3,X4),X4) = c_List_Otake(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_List_Odrop(X1,X3,X4),X4),
    cls_drop__take_0,
    [final] ).

cnf(i_0_903,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    cls_split__mod_0,
    [final] ).

cnf(i_0_904,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_905,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_906,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_907,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_908,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_909,axiom,
    c_List_Onth(c_List_Oappend(X1,c_List_Olist_OCons(X2,X3,X4),X4),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),X4) = X2,
    cls_nth__append__length_0,
    [final] ).

cnf(i_0_910,axiom,
    ( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
    | ~ c_Type_Otyping(X1,X3,X5)
    | ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X5),X4)) ),
    cls_App_0,
    [final] ).

cnf(i_0_911,axiom,
    c_List_Olist__update(c_List_Olist_OCons(X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat),X4,X3) = c_List_Olist_OCons(X4,X2,X3),
    cls_list__update__code_I2_J_0,
    [final] ).

cnf(i_0_912,axiom,
    ( c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X4,tc_nat),X3) = c_List_Onth(X2,c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3)
    | c_Int_Onumber__class_Onumber__of(X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_nth__Cons__number__of_1,
    [final] ).

cnf(i_0_913,axiom,
    ( c_List_Odrop(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,X4)
    | c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_drop__Cons__number__of_1,
    [final] ).

cnf(i_0_914,axiom,
    ( X1 = c_List_Olist_ONil(X4)
    | c_List_Olist__update(X1,X2,X3,X4) != c_List_Olist_ONil(X4) ),
    cls_list__update__nonempty_0,
    [final] ).

cnf(i_0_915,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Omap(X1,X2,X3,X4) != c_List_Olist_ONil(X4) ),
    cls_map__is__Nil__conv_0,
    [final] ).

cnf(i_0_916,axiom,
    ( X3 = c_List_Olist_ONil(X4)
    | c_List_Olist_ONil(X1) != c_List_Omap(X2,X3,X4,X1) ),
    cls_Nil__is__map__conv_0,
    [final] ).

cnf(i_0_917,axiom,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
    cls_not__Nil__step1_0,
    [final] ).

cnf(i_0_918,axiom,
    ~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
    cls_not__step1__Nil_0,
    [final] ).

cnf(i_0_919,axiom,
    ( c_Type_Otyping(X1,X2,X3)
    | ~ 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_920,axiom,
    ( c_List_Otake(c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),X1,X3) = X4
    | c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X4,tc_List_Olist(X3)),tc_nat)
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    cls_append__eq__append__conv__if_2,
    [final] ).

cnf(i_0_921,axiom,
    ( c_List_Olist__update(X1,X2,X3,X4) = X1
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),X2,tc_nat) ),
    cls_list__update__beyond_0,
    [final] ).

cnf(i_0_922,axiom,
    ( c_List_Oappend(X1,c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2),X2) = X3
    | X1 != c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X3,X2) ),
    cls_append__eq__conv__conj_2,
    [final] ).

cnf(i_0_923,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_924,axiom,
    c_List_Orev(c_List_Otake(X1,X2,X3),X3) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),c_List_Orev(X2,X3),X3),
    cls_rev__take_0,
    [final] ).

cnf(i_0_925,axiom,
    c_List_Orev(c_List_Odrop(X1,X2,X3),X3) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),c_List_Orev(X2,X3),X3),
    cls_rev__drop_0,
    [final] ).

cnf(i_0_926,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
    cls_subst__lift_0,
    [final] ).

cnf(i_0_927,axiom,
    ( c_lessequals(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_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__nonpos__nonpos_0,
    [final] ).

cnf(i_0_928,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_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__neg__nonpos_0,
    [final] ).

cnf(i_0_929,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_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__nonpos__neg_0,
    [final] ).

cnf(i_0_930,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_931,axiom,
    ( c_lessequals(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_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__nonneg_0,
    [final] ).

cnf(i_0_932,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_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__pos__nonneg_0,
    [final] ).

cnf(i_0_933,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_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__pos_0,
    [final] ).

cnf(i_0_934,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_935,axiom,
    ( c_List_Onth(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Onth(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),tc_nat) ),
    cls_nth__append_0,
    [final] ).

cnf(i_0_936,axiom,
    c_List_Olist__update(X1,X2,c_List_Onth(X1,X2,X3),X3) = X1,
    cls_list__update__id_0,
    [final] ).

cnf(i_0_937,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
    cls_add__increasing2_0,
    [final] ).

cnf(i_0_938,axiom,
    ( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_add__increasing_0,
    [final] ).

cnf(i_0_939,axiom,
    ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_add__strict__increasing_0,
    [final] ).

cnf(i_0_940,axiom,
    ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_add__strict__increasing2_0,
    [final] ).

cnf(i_0_941,axiom,
    ( c_lessequals(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(X1)
    | ~ c_lessequals(X3,X4,X1) ),
    cls_add__left__mono_0,
    [final] ).

cnf(i_0_942,axiom,
    ( c_lessequals(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_lessequals(X3,X4,X1) ),
    cls_add__le__cancel__left_1,
    [final] ).

cnf(i_0_943,axiom,
    ( c_lessequals(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(X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_add__right__mono_0,
    [final] ).

cnf(i_0_944,axiom,
    ( c_lessequals(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_lessequals(X2,X4,X1) ),
    cls_add__le__cancel__right_1,
    [final] ).

cnf(i_0_945,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_946,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_947,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_948,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_949,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
    | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
    cls_le__number__of__eq__not__less_0,
    [final] ).

cnf(i_0_950,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_951,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    cls_diff__le__mono2_0,
    [final] ).

cnf(i_0_952,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_diff__le__mono_0,
    [final] ).

cnf(i_0_953,axiom,
    ( X1 = X3
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_eq__diff__iff_0,
    [final] ).

cnf(i_0_954,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_955,axiom,
    ( c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)
    | ~ c_List_Olistsp(X1,X3,X4)
    | ~ c_List_Olistsp(X1,X2,X4) ),
    cls_append__in__listsp__conv_2,
    [final] ).

cnf(i_0_956,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,
    [final] ).

cnf(i_0_957,axiom,
    ( c_List_Onth(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Onth(X2,c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3)
    | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_nth__Cons_H_1,
    [final] ).

cnf(i_0_958,axiom,
    ( c_List_Odrop(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,X4)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_drop__Cons_H_1,
    [final] ).

cnf(i_0_959,axiom,
    c_List_Otake(c_Suc(X1),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Otake(X1,X3,X4),X4),
    cls_take__Suc__Cons_0,
    [final] ).

cnf(i_0_960,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_le__iff__diff__le__0_1,
    [final] ).

cnf(i_0_961,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_962,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat),
    cls_mod__Suc__eq__Suc__mod_0,
    [final] ).

cnf(i_0_963,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
    cls_zero__le__double__add__iff__zero__le__single__add_0,
    [final] ).

cnf(i_0_964,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_965,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__le__zero__iff__single__add__le__zero_0,
    [final] ).

cnf(i_0_966,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_967,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_968,axiom,
    c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3),
    cls_append__Cons_0,
    [final] ).

cnf(i_0_969,axiom,
    c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3),
    cls_append__eq__Cons__conv_5,
    [final] ).

cnf(i_0_970,axiom,
    c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3),
    cls_append__eq__append__conv2_4,
    [final] ).

cnf(i_0_971,axiom,
    c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3),
    cls_append__assoc_0,
    [final] ).

cnf(i_0_972,axiom,
    c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
    cls_Cons__eq__appendI_0,
    [final] ).

cnf(i_0_973,axiom,
    c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
    cls_Cons__eq__append__conv_5,
    [final] ).

cnf(i_0_974,axiom,
    c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
    cls_append__eq__append__conv2_5,
    [final] ).

cnf(i_0_975,axiom,
    c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
    cls_append__eq__appendI_0,
    [final] ).

cnf(i_0_976,axiom,
    c_List_Orev(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),
    cls_rev_Osimps_I2_J_0,
    [final] ).

cnf(i_0_977,axiom,
    ( c_lessequals(X3,X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X5,X4,X1) ),
    cls_le__eqI_1,
    [final] ).

cnf(i_0_978,axiom,
    ( c_lessequals(X5,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_le__eqI_0,
    [final] ).

cnf(i_0_979,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_980,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_981,axiom,
    c_List_Odrop(X1,c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,X4),
    cls_drop__replicate_0,
    [final] ).

cnf(i_0_982,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_983,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_984,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_985,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_986,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_987,axiom,
    ( c_List_Olistsp(X1,X2,X3)
    | ~ c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3) ),
    cls_append__in__listsp__conv_0,
    [final] ).

cnf(i_0_988,axiom,
    ( c_List_Olistsp(X1,X2,X3)
    | ~ c_List_Olistsp(X1,c_List_Oappend(X4,X2,X3),X3) ),
    cls_append__in__listsp__conv_1,
    [final] ).

cnf(i_0_989,axiom,
    ( X1 = c_List_Oappend(c_List_Orev(X4,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2),X2)
    | c_List_Orev(X1,X2) != c_List_Olist_OCons(X3,X4,X2) ),
    cls_rev__eq__Cons__iff_0,
    [final] ).

cnf(i_0_990,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_991,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_992,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_993,axiom,
    ( c_List_Onth(c_List_Otake(X1,X2,X3),X4,X3) = c_List_Onth(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,tc_nat) ),
    cls_nth__take_0,
    [final] ).

cnf(i_0_994,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    cls_split__mod_5,
    [final] ).

cnf(i_0_995,axiom,
    ( c_Int_Onumber__class_Onumber__of(X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(X1,tc_nat),tc_nat) ),
    cls_expand__Suc_0,
    [final] ).

cnf(i_0_996,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_le__mod__geq_0,
    [final] ).

cnf(i_0_997,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__eq__0__iff_0,
    [final] ).

cnf(i_0_998,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__nonneg__eq__0__iff_1,
    [final] ).

cnf(i_0_999,axiom,
    c_List_Orotate(X1,X2,X3) = c_List_Orotate(c_Divides_Odiv__class_Omod(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),X2,X3),
    cls_rotate__conv__mod_0,
    [final] ).

cnf(i_0_1000,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat))
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2 ),
    cls_mod__Suc_1,
    [final] ).

cnf(i_0_1001,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_1002,axiom,
    c_List_Oappend(c_List_Otake(X1,X2,X3),c_List_Odrop(X1,X2,X3),X3) = X2,
    cls_append__take__drop__id_0,
    [final] ).

cnf(i_0_1003,axiom,
    ( c_lessequals(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_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__le__zero__iff__single__add__le__zero_1,
    [final] ).

cnf(i_0_1004,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_1005,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_1006,axiom,
    ( c_lessequals(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_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_zero__le__double__add__iff__zero__le__single__add_1,
    [final] ).

cnf(i_0_1007,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_1008,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_mod__if_1,
    [final] ).

cnf(i_0_1009,axiom,
    ( c_List_Odrop(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,X3,X4)
    | c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_drop__Cons__number__of_0,
    [final] ).

cnf(i_0_1010,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_le__iff__diff__le__0_0,
    [final] ).

cnf(i_0_1011,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_1012,axiom,
    ( c_Type_Otyping(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2))
    | ~ c_Type_Otyping(X1,X4,X3) ),
    cls_subject__reduction_0,
    [final] ).

cnf(i_0_1013,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,
    [final] ).

cnf(i_0_1014,axiom,
    c_List_Olist__update(c_List_Olist_ONil(X1),X2,X3,X1) = c_List_Olist_ONil(X1),
    cls_list__update_Osimps_I1_J_0,
    [final] ).

cnf(i_0_1015,axiom,
    c_List_Olist__update(c_List_Olist_ONil(X1),X2,X3,X1) = c_List_Olist_ONil(X1),
    cls_list__update__code_I1_J_0,
    [final] ).

cnf(i_0_1016,axiom,
    c_List_Olist__update(c_List_Olist_ONil(X1),X2,X3,X1) = c_List_Olist_ONil(X1),
    cls_list__update__nonempty_1,
    [final] ).

cnf(i_0_1017,axiom,
    c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
    cls_map__is__Nil__conv_1,
    [final] ).

cnf(i_0_1018,axiom,
    c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
    cls_Nil__is__map__conv_1,
    [final] ).

cnf(i_0_1019,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat))
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_Suc__diff__le_0,
    [final] ).

cnf(i_0_1020,axiom,
    ( c_List_Onth(c_List_Oreplicate(X1,X2,X3),X4,X3) = X2
    | ~ c_HOL_Oord__class_Oless(X4,X1,tc_nat) ),
    cls_nth__replicate_0,
    [final] ).

cnf(i_0_1021,axiom,
    ( c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_mod__le__divisor_0,
    [final] ).

cnf(i_0_1022,axiom,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_mod__less__divisor_0,
    [final] ).

cnf(i_0_1023,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_1024,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_diff__diff__cancel_0,
    [final] ).

cnf(i_0_1025,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_1026,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_1027,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    cls_xt1_I6_J_0,
    [final] ).

cnf(i_0_1028,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_order__trans_0,
    [final] ).

cnf(i_0_1029,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    cls_xt1_I8_J_0,
    [final] ).

cnf(i_0_1030,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
    cls_xt1_I7_J_0,
    [final] ).

cnf(i_0_1031,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_1032,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X4,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_order__less__le__trans_0,
    [final] ).

cnf(i_0_1033,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X4,X3,X1)
    | ~ c_lessequals(X2,X4,X1) ),
    cls_order__le__less__trans_0,
    [final] ).

cnf(i_0_1034,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_1035,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
    cls_mod__Suc_0,
    [final] ).

cnf(i_0_1036,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_1037,axiom,
    ( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1) ),
    cls_le__number__of__eq__not__less_1,
    [final] ).

cnf(i_0_1038,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,
    [final] ).

cnf(i_0_1039,axiom,
    c_List_Orev(c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Orev(X1,X3),X3),
    cls_rev__append_0,
    [final] ).

cnf(i_0_1040,axiom,
    ( c_List_Onth(X2,X1,X3) = X4
    | c_List_Odrop(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    cls_nth__via__drop_0,
    [final] ).

cnf(i_0_1041,axiom,
    c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),
    cls_take__1__Cons_0,
    [final] ).

cnf(i_0_1042,axiom,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X3,X1),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__mod__trivial_0,
    [final] ).

cnf(i_0_1043,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,
    [final] ).

cnf(i_0_1044,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,
    [final] ).

cnf(i_0_1045,axiom,
    c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_Suc(X4),X3) = c_List_Onth(X2,X4,X3),
    cls_nth__Cons__Suc_0,
    [final] ).

cnf(i_0_1046,axiom,
    c_List_Odrop(c_Suc(X1),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Odrop(X1,X3,X4),
    cls_drop__Suc__Cons_0,
    [final] ).

cnf(i_0_1047,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_OCons(X2,X3,X1),X1) = c_List_Olist_OCons(X2,X3,X1),
    cls_append__eq__Cons__conv_4,
    [final] ).

cnf(i_0_1048,axiom,
    c_List_Oreplicate(c_Suc(X1),X2,X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
    cls_replicate__Suc_0,
    [final] ).

cnf(i_0_1049,axiom,
    c_List_Olist_OCons(X1,X2,X3) = c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X1,X2,X3),X3),
    cls_Cons__eq__append__conv_4,
    [final] ).

cnf(i_0_1050,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    cls_le__trans_0,
    [final] ).

cnf(i_0_1051,axiom,
    c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_OCons(X1,X2,X3),
    cls_drop__Cons_H_0,
    [final] ).

cnf(i_0_1052,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__self1_0,
    [final] ).

cnf(i_0_1053,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__add__self2_0,
    [final] ).

cnf(i_0_1054,axiom,
    c_Nat_Osize__class_Osize(c_List_Odrop(X1,X2,X3),tc_List_Olist(X3)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat),
    cls_length__drop_0,
    [final] ).

cnf(i_0_1055,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_lift__IT_0,
    [final] ).

cnf(i_0_1056,axiom,
    ( c_List_Otake(c_Int_Onumber__class_Onumber__of(X1,tc_nat),c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_ONil(X4)
    | c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_take__Cons__number__of_0,
    [final] ).

cnf(i_0_1057,axiom,
    ( c_List_Onth(c_List_Olist_OCons(X2,X3,X4),c_Int_Onumber__class_Onumber__of(X1,tc_nat),X4) = X2
    | c_Int_Onumber__class_Onumber__of(X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_nth__Cons__number__of_0,
    [final] ).

cnf(i_0_1058,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_1059,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orotate(X3,X1,X2),X2) ),
    cls_distinct__rotate_0,
    [final] ).

cnf(i_0_1060,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Olist_OCons(X3,X1,X2),X2) ),
    cls_distinct_Osimps_I2_J_1,
    [final] ).

cnf(i_0_1061,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Oappend(X1,X3,X2),X2) ),
    cls_distinct__append_0,
    [final] ).

cnf(i_0_1062,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Oappend(X3,X1,X2),X2) ),
    cls_distinct__append_1,
    [final] ).

cnf(i_0_1063,axiom,
    ( c_List_Orotate(X1,X2,X3) = X2
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    cls_rotate__length01_0,
    [final] ).

cnf(i_0_1064,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,
    [final] ).

cnf(i_0_1065,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,
    [final] ).

cnf(i_0_1066,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_less__le__not__le_2,
    [final] ).

cnf(i_0_1067,axiom,
    ( c_List_Orotate(X1,X2,X3) = X2
    | c_Divides_Odiv__class_Omod(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_rotate__id_0,
    [final] ).

cnf(i_0_1068,axiom,
    ( c_List_Odrop(X1,X2,X3) = c_List_Olist_ONil(X3)
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat) ),
    cls_drop__all_0,
    [final] ).

cnf(i_0_1069,axiom,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    cls_append__eq__conv__conj_0,
    [final] ).

cnf(i_0_1070,axiom,
    X1 = c_List_Odrop(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),c_List_Oappend(X2,X1,X3),X3),
    cls_append__eq__conv__conj_1,
    [final] ).

cnf(i_0_1071,axiom,
    ( c_List_Otake(X1,X2,X3) = X2
    | ~ c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat) ),
    cls_take__all_0,
    [final] ).

cnf(i_0_1072,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_1073,axiom,
    c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),
    cls_rev__singleton__conv_1,
    [final] ).

cnf(i_0_1074,axiom,
    c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2),
    cls_singleton__rev__conv_1,
    [final] ).

cnf(i_0_1075,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_1076,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_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(cn,[status(thm)],[i_0_699]),
    [final] ).

cnf(i_0_1077,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    cls_rtranclp_Ortrancl__refl_0,
    [final] ).

cnf(i_0_1078,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    cls_Nitpick_Ortranclp__def_1,
    [final] ).

cnf(i_0_1079,axiom,
    ( c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat)
    | c_List_Odrop(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    cls_drop__eq__Nil_0,
    [final] ).

cnf(i_0_1080,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_order__antisym__conv_0,
    [final] ).

cnf(i_0_1081,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__antisym_0,
    [final] ).

cnf(i_0_1082,axiom,
    ( X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X3,X2,X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__eq__iff_2,
    [final] ).

cnf(i_0_1083,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_1084,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_1085,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_1086,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__antisym__conv2_1,
    [final] ).

cnf(i_0_1087,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ c_lessequals(X3,X2,X1) ),
    cls_linorder__not__less_1,
    [final] ).

cnf(i_0_1088,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_linorder__not__le_1,
    [final] ).

cnf(i_0_1089,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_1090,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_1091,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_less__le__not__le_1,
    [final] ).

cnf(i_0_1092,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_1093,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_1094,axiom,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    cls_le__less__Suc__eq_0,
    [final] ).

cnf(i_0_1095,axiom,
    ( X3 = c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2)
    | c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) != c_List_Orev(X3,X2) ),
    cls_singleton__rev__conv_0,
    [final] ).

cnf(i_0_1096,axiom,
    ( X1 = c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2)
    | c_List_Orev(X1,X2) != c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2) ),
    cls_rev__singleton__conv_0,
    [final] ).

cnf(i_0_1097,axiom,
    ( X2 = X5
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
    cls_replicate__eq__replicate_1,
    [final] ).

cnf(i_0_1098,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    cls_not__less__eq__eq_1,
    [final] ).

cnf(i_0_1099,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,
    [final] ).

cnf(i_0_1100,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_1101,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_1102,axiom,
    c_List_Orev(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(X1,X2,X3),
    cls_rev__replicate_0,
    [final] ).

cnf(i_0_1103,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_1104,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_1105,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_1106,axiom,
    ( X1 = X4
    | c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
    cls_replicate__eq__replicate_0,
    [final] ).

cnf(i_0_1107,axiom,
    ( X1 = X4
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    cls_list_Oinject_0,
    [final] ).

cnf(i_0_1108,axiom,
    ( X1 = X4
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X2,X3) ),
    cls_append__same__eq_0,
    [final] ).

cnf(i_0_1109,axiom,
    ( X2 = X4
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X1,X4,X3) ),
    cls_same__append__eq_0,
    [final] ).

cnf(i_0_1110,axiom,
    ( X2 = X5
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    cls_list_Oinject_1,
    [final] ).

cnf(i_0_1111,axiom,
    ( X1 = X2
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__antisym_0,
    [final] ).

cnf(i_0_1112,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_1113,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)) = c_Suc(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3))),
    cls_length__Suc__conv_2,
    [final] ).

cnf(i_0_1114,axiom,
    c_Suc(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2))) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(X3,X1,X2),tc_List_Olist(X2)),
    cls_Suc__length__conv_2,
    [final] ).

cnf(i_0_1115,axiom,
    c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_ONil(X3),
    cls_take__Cons_H_0,
    [final] ).

cnf(i_0_1116,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1)),tc_nat),
    cls_length__greater__0__conv_0,
    [final] ).

cnf(i_0_1117,axiom,
    c_List_Onth(c_List_Olist_OCons(X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat),X3) = X1,
    cls_nth__Cons_H_0,
    [final] ).

cnf(i_0_1118,axiom,
    c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X1,X2,X3),X3) = X2,
    cls_drop__1__Cons_0,
    [final] ).

cnf(i_0_1119,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_1120,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_1121,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,
    [final] ).

cnf(i_0_1122,axiom,
    ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
    cls_beta__cases_I1_J_0,
    [final] ).

cnf(i_0_1123,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
    cls_diff__le__self_0,
    [final] ).

cnf(i_0_1124,axiom,
    c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
    cls_mod__less__eq__dividend_0,
    [final] ).

cnf(i_0_1125,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    cls_Suc__le__mono_0,
    [final] ).

cnf(i_0_1126,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,
    [final] ).

cnf(i_0_1127,axiom,
    ( X1 = c_Suc(X2)
    | c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
    cls_le__SucE_0,
    [final] ).

cnf(i_0_1128,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_linorder__antisym__conv2_0,
    [final] ).

cnf(i_0_1129,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_linorder__antisym__conv1_0,
    [final] ).

cnf(i_0_1130,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__neq__le__trans_0,
    [final] ).

cnf(i_0_1131,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__le__neq__trans_0,
    [final] ).

cnf(i_0_1132,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X2 = X3
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__less__le_2,
    [final] ).

cnf(i_0_1133,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_order__le__less_0,
    [final] ).

cnf(i_0_1134,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_xt1_I12_J_0,
    [final] ).

cnf(i_0_1135,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | X3 = X2
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_xt1_I11_J_0,
    [final] ).

cnf(i_0_1136,axiom,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_Suc__le__mono_1,
    [final] ).

cnf(i_0_1137,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,
    [final] ).

cnf(i_0_1138,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,
    [final] ).

cnf(i_0_1139,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,
    [final] ).

cnf(i_0_1140,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,
    [final] ).

cnf(i_0_1141,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,
    [final] ).

cnf(i_0_1142,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,
    [final] ).

cnf(i_0_1143,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_order__le__less_1,
    [final] ).

cnf(i_0_1144,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
    cls_order__less__imp__le_0,
    [final] ).

cnf(i_0_1145,axiom,
    c_Nat_Osize__class_Osize(c_List_Orotate(X1,X2,X3),tc_List_Olist(X3)) = c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),
    cls_length__rotate_0,
    [final] ).

cnf(i_0_1146,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    cls_Suc__leD_0,
    [final] ).

cnf(i_0_1147,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    cls_Suc__le__eq_0,
    [final] ).

cnf(i_0_1148,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    cls_less__eq__Suc__le_1,
    [final] ).

cnf(i_0_1149,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,
    [final] ).

cnf(i_0_1150,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    cls_less__Suc__eq__le_0,
    [final] ).

cnf(i_0_1151,axiom,
    ( c_List_Odistinct(c_List_Orotate(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    cls_distinct__rotate_1,
    [final] ).

cnf(i_0_1152,axiom,
    ( c_List_Odistinct(c_List_Otake(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    cls_distinct__take_0,
    [final] ).

cnf(i_0_1153,axiom,
    ( c_List_Odistinct(c_List_Odrop(X1,X2,X3),X3)
    | ~ c_List_Odistinct(X2,X3) ),
    cls_distinct__drop_0,
    [final] ).

cnf(i_0_1154,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_Suc__leI_0,
    [final] ).

cnf(i_0_1155,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_less__eq__Suc__le_0,
    [final] ).

cnf(i_0_1156,axiom,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__SucI_0,
    [final] ).

cnf(i_0_1157,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | ~ c_lessequals(X1,X1,tc_nat) ),
    cls_le__less__Suc__eq_1,
    [final] ).

cnf(i_0_1158,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_less__Suc__eq__le_1,
    [final] ).

cnf(i_0_1159,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,
    [final] ).

cnf(i_0_1160,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_diff__is__0__eq_0,
    [final] ).

cnf(i_0_1161,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__neq__implies__less_0,
    [final] ).

cnf(i_0_1162,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_le__eq__less__or__eq_0,
    [final] ).

cnf(i_0_1163,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_nat__less__le_2,
    [final] ).

cnf(i_0_1164,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    cls_diff__is__0__eq_1,
    [final] ).

cnf(i_0_1165,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_mod__if_0,
    [final] ).

cnf(i_0_1166,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_lift_Osimps_I1_J_0,
    [final] ).

cnf(i_0_1167,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_nat__less__le_0,
    [final] ).

cnf(i_0_1168,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_termination__basic__simps_I5_J_0,
    [final] ).

cnf(i_0_1169,axiom,
    c_Nat_Osize__class_Osize(c_List_Oreplicate(X1,X2,X3),tc_List_Olist(X3)) = X1,
    cls_length__replicate_0,
    [final] ).

cnf(i_0_1170,axiom,
    hAPP(c_COMBK(X1,X2,X3),X4) = X1,
    cls_COMBK__def_0,
    [final] ).

cnf(i_0_1171,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_1172,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_1173,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_1174,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_1175,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_1176,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_1177,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_1178,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_1179,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_1180,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,
    [final] ).

cnf(i_0_1181,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__linear_0,
    [final] ).

cnf(i_0_1182,axiom,
    ( c_HOL_Oord__class_Oless(X2,X2,X1)
    | c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__antisym__conv1_1,
    [final] ).

cnf(i_0_1183,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__not__le_0,
    [final] ).

cnf(i_0_1184,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_not__leE_0,
    [final] ).

cnf(i_0_1185,axiom,
    ( c_lessequals(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_linorder__not__less_0,
    [final] ).

cnf(i_0_1186,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2),
    cls_replicate__eq__replicate_2,
    [final] ).

cnf(i_0_1187,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    cls_not__less__eq__eq_0,
    [final] ).

cnf(i_0_1188,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,
    [final] ).

cnf(i_0_1189,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,
    [final] ).

cnf(i_0_1190,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_not__one__le__zero_0,
    [final] ).

cnf(i_0_1191,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_1192,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_1193,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_1194,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_1195,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
    cls_subst__eq_0,
    [final] ).

cnf(i_0_1196,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    cls_typing__elims_I1_J_0,
    [final] ).

cnf(i_0_1197,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_1198,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_1199,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_1200,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,
    [final] ).

cnf(i_0_1201,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    cls_nat__le__linear_0,
    [final] ).

cnf(i_0_1202,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_1203,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_1204,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_1205,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Otake(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    cls_take__eq__Nil_0,
    [final] ).

cnf(i_0_1206,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_1207,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | X1 = c_List_Olist_ONil(X2) ),
    cls_length__greater__0__conv_1,
    [final] ).

cnf(i_0_1208,axiom,
    ( X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    cls_append__is__Nil__conv_0,
    [final] ).

cnf(i_0_1209,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Orotate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    cls_rotate__is__Nil__conv_0,
    [final] ).

cnf(i_0_1210,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    cls_append__is__Nil__conv_1,
    [final] ).

cnf(i_0_1211,axiom,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Oappend(X2,X3,X1) ),
    cls_Nil__is__append__conv_0,
    [final] ).

cnf(i_0_1212,axiom,
    ( X3 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Oappend(X2,X3,X1) ),
    cls_Nil__is__append__conv_1,
    [final] ).

cnf(i_0_1213,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    cls_replicate__empty_0,
    [final] ).

cnf(i_0_1214,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Olist_ONil(X1) != c_List_Oreplicate(X2,X3,X1) ),
    cls_empty__replicate_0,
    [final] ).

cnf(i_0_1215,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__neq__iff_1,
    [final] ).

cnf(i_0_1216,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__le_1,
    [final] ).

cnf(i_0_1217,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__irrefl_0,
    [final] ).

cnf(i_0_1218,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_1219,axiom,
    ~ c_lessequals(c_Suc(X1),X1,tc_nat),
    cls_Suc__n__not__le__n_0,
    [final] ).

cnf(i_0_1220,axiom,
    ( X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != X2 ),
    cls_append__self__conv2_0,
    [final] ).

cnf(i_0_1221,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != X1 ),
    cls_append__self__conv_0,
    [final] ).

cnf(i_0_1222,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 != c_List_Oappend(X1,X2,X3) ),
    cls_self__append__conv_0,
    [final] ).

cnf(i_0_1223,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 != c_List_Oappend(X2,X1,X3) ),
    cls_self__append__conv2_0,
    [final] ).

cnf(i_0_1224,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    cls_le__0__eq_0,
    [final] ).

cnf(i_0_1225,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    cls_list_Osimps_I3_J_0,
    [final] ).

cnf(i_0_1226,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    cls_neq__Nil__conv_1,
    [final] ).

cnf(i_0_1227,axiom,
    c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
    cls_list_Osimps_I2_J_0,
    [final] ).

cnf(i_0_1228,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_not__less0_0,
    [final] ).

cnf(i_0_1229,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_1230,axiom,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0,
    [final] ).

cnf(i_0_1231,axiom,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    cls_not__Cons__self2_0,
    [final] ).

cnf(i_0_1232,axiom,
    X1 != c_List_Olist_OCons(X2,X1,X3),
    cls_not__Cons__self_0,
    [final] ).

cnf(i_0_1233,axiom,
    c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
    cls_typing_OVar_0,
    [final] ).

cnf(i_0_1234,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_less__not__refl_0,
    [final] ).

cnf(i_0_1235,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_nat__less__le_1,
    [final] ).

cnf(i_0_1236,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_Lambda_0,
    [final] ).

cnf(i_0_1237,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_1238,axiom,
    ( c_List_Odistinct(X1,X2)
    | ~ c_List_Odistinct(c_List_Orev(X1,X2),X2) ),
    cls_distinct__rev_0,
    [final] ).

cnf(i_0_1239,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    cls_zero__le__one_0,
    [final] ).

cnf(i_0_1240,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_1241,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_1242,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_1243,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_1244,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_1245,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_1246,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_1247,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__0_0,
    [final] ).

cnf(i_0_1248,axiom,
    ( c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__by__1_0,
    [final] ).

cnf(i_0_1249,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    cls_append__is__Nil__conv_2,
    [final] ).

cnf(i_0_1250,axiom,
    c_List_Olist_ONil(X1) = c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1),
    cls_Nil__is__append__conv_2,
    [final] ).

cnf(i_0_1251,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_1252,axiom,
    ( c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__by__0_0,
    [final] ).

cnf(i_0_1253,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,
    [final] ).

cnf(i_0_1254,axiom,
    c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_mod__1_0,
    [final] ).

cnf(i_0_1255,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_1256,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_1257,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_1258,axiom,
    c_Nat_Osize__class_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),
    cls_length__rev_0,
    [final] ).

cnf(i_0_1259,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_1260,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_1261,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_1262,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    cls_mod__self_0,
    [final] ).

cnf(i_0_1263,axiom,
    c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
    cls_le__Suc__eq_2,
    [final] ).

cnf(i_0_1264,axiom,
    c_List_Orotate(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
    cls_rotate__is__Nil__conv_1,
    [final] ).

cnf(i_0_1265,axiom,
    c_List_Otake(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
    cls_take__eq__Nil_2,
    [final] ).

cnf(i_0_1266,axiom,
    c_List_Odrop(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
    cls_drop__Nil_0,
    [final] ).

cnf(i_0_1267,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
    cls_dB_Osimps_I8_J_0,
    [final] ).

cnf(i_0_1268,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
    cls_dB_Osimps_I5_J_0,
    [final] ).

cnf(i_0_1269,axiom,
    c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    cls_dB_Osimps_I9_J_0,
    [final] ).

cnf(i_0_1270,axiom,
    c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    cls_dB_Osimps_I4_J_0,
    [final] ).

cnf(i_0_1271,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    cls_diff__Suc__1_0,
    [final] ).

cnf(i_0_1272,axiom,
    ( c_List_Odistinct(c_List_Orev(X1,X2),X2)
    | ~ c_List_Odistinct(X1,X2) ),
    cls_distinct__rev_1,
    [final] ).

cnf(i_0_1273,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    cls_gr0__conv__Suc_1,
    [final] ).

cnf(i_0_1274,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    cls_zero__less__Suc_0,
    [final] ).

cnf(i_0_1275,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Oorder(X1) ),
    cls_order__eq__iff_0,
    [final] ).

cnf(i_0_1276,axiom,
    ( c_lessequals(X2,X2,X1)
    | ~ class_Orderings_Opreorder(X1) ),
    cls_order__eq__refl_0,
    [final] ).

cnf(i_0_1277,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
    cls_replicate__empty_1,
    [final] ).

cnf(i_0_1278,axiom,
    c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
    cls_take__0_0,
    [final] ).

cnf(i_0_1279,axiom,
    c_List_Olist_ONil(X1) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X2,X1),
    cls_empty__replicate_1,
    [final] ).

cnf(i_0_1280,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),X2,X1) = X2,
    cls_append__Nil_0,
    [final] ).

cnf(i_0_1281,axiom,
    c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
    cls_append__Nil2_0,
    [final] ).

cnf(i_0_1282,axiom,
    X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
    cls_self__append__conv2_1,
    [final] ).

cnf(i_0_1283,axiom,
    X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
    cls_eq__Nil__appendI_0,
    [final] ).

cnf(i_0_1284,axiom,
    X1 = c_List_Oappend(X1,c_List_Olist_ONil(X2),X2),
    cls_self__append__conv_1,
    [final] ).

cnf(i_0_1285,axiom,
    ( X2 = X3
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X3,X1) ),
    cls_eq__number__of_0,
    [final] ).

cnf(i_0_1286,axiom,
    c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
    cls_listsp_ONil_0,
    [final] ).

cnf(i_0_1287,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_1288,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_le__0__eq_1,
    [final] ).

cnf(i_0_1289,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_less__Suc__eq_2,
    [final] ).

cnf(i_0_1290,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    cls_lessI_0,
    [final] ).

cnf(i_0_1291,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_diff__0__eq__0_0,
    [final] ).

cnf(i_0_1292,axiom,
    c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
    cls_drop__0_0,
    [final] ).

cnf(i_0_1293,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    cls_minus__nat_Odiff__0_0,
    [final] ).

cnf(i_0_1294,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    cls_le0_0,
    [final] ).

cnf(i_0_1295,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_1296,axiom,
    c_fequal(X1,X1,X2),
    cls_ATP__Linkup_Oequal__imp__fequal_0,
    [final] ).

cnf(i_0_1297,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_1298,axiom,
    c_lessequals(X1,X1,tc_nat),
    cls_eq__imp__le_0,
    [final] ).

cnf(i_0_1299,axiom,
    c_lessequals(X1,X1,tc_nat),
    cls_le__refl_0,
    [final] ).

cnf(i_0_1300,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    cls_CHAINED_0_01,
    [final] ).

cnf(i_0_1301,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    cls_uT_0,
    [final] ).

cnf(i_0_1302,axiom,
    ( X1 = X3
    | c_List_Orev(X1,X2) != c_List_Orev(X3,X2) ),
    cls_rev__is__rev__conv_0,
    [final] ).

cnf(i_0_1303,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_length__0__conv_0,
    [final] ).

cnf(i_0_1304,axiom,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    cls_rev__rev__ident_0,
    [final] ).

cnf(i_0_1305,axiom,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    cls_rev__swap_1,
    [final] ).

cnf(i_0_1306,axiom,
    X1 = c_List_Orev(c_List_Orev(X1,X2),X2),
    cls_rev__swap_0,
    [final] ).

cnf(i_0_1307,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
    cls_Var__IT_0,
    [final] ).

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

cnf(i_0_1309,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_1310,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Orev(X1,X2) != c_List_Olist_ONil(X2) ),
    cls_rev__is__Nil__conv_0,
    [final] ).

cnf(i_0_1311,axiom,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Orev(X2,X1) ),
    cls_Nil__is__rev__conv_0,
    [final] ).

cnf(i_0_1312,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
    cls_length__0__conv_1,
    [final] ).

cnf(i_0_1313,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    cls_uIT_0,
    [final] ).

cnf(i_0_1314,axiom,
    c_List_Orev(c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    cls_rev__is__Nil__conv_1,
    [final] ).

cnf(i_0_1315,axiom,
    c_List_Olist_ONil(X1) = c_List_Orev(c_List_Olist_ONil(X1),X1),
    cls_Nil__is__rev__conv_1,
    [final] ).

cnf(i_0_1316,axiom,
    c_List_Odistinct(c_List_Olist_ONil(X1),X1),
    cls_distinct_Osimps_I1_J_0,
    [final] ).

cnf(i_0_1317,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_1318,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_1319,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    cls_dB_Osimps_I3_J_0,
    [final] ).

cnf(i_0_1320,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    cls_dB_Osimps_I1_J_0,
    [final] ).

cnf(i_0_1321,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_Suc__inject_0,
    [final] ).

cnf(i_0_1322,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    cls_nat_Oinject_0,
    [final] ).

cnf(i_0_1323,axiom,
    c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
    cls_dB_Osimps_I7_J_0,
    [final] ).

cnf(i_0_1324,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    cls_dB_Osimps_I6_J_0,
    [final] ).

cnf(i_0_1325,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_nat_Osimps_I2_J_0,
    [final] ).

cnf(i_0_1326,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    cls_Zero__neq__Suc_0,
    [final] ).

cnf(i_0_1327,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_Suc__neq__Zero_0,
    [final] ).

cnf(i_0_1328,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    cls_nat_Osimps_I3_J_0,
    [final] ).

cnf(i_0_1329,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    cls_One__nat__def_0,
    [final] ).

cnf(i_0_1330,axiom,
    c_Suc(X1) != X1,
    cls_Suc__n__not__n_0,
    [final] ).

cnf(i_0_1331,axiom,
    X1 != c_Suc(X1),
    cls_n__not__Suc__n_0,
    [final] ).

cnf(i_0_1332,axiom,
    class_OrderedGroup_Omonoid__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Omonoid__add,
    [final] ).

cnf(i_0_1333,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__add,
    [final] ).

cnf(i_0_1334,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add,
    [final] ).

cnf(i_0_1335,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
    [final] ).

cnf(i_0_1336,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1337,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1338,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    clsarity_Int__Oint__Int_Oring__char__0,
    [final] ).

cnf(i_0_1339,axiom,
    class_Int_Onumber(tc_Int_Oint),
    clsarity_Int__Oint__Int_Onumber,
    [final] ).

cnf(i_0_1340,axiom,
    class_Int_Onumber(tc_nat),
    clsarity_nat__Int_Onumber,
    [final] ).

cnf(i_0_1341,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1342,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
    [final] ).

cnf(i_0_1343,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,
    [final] ).

cnf(i_0_1344,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    clsarity_Int__Oint__Divides_Oring__div,
    [final] ).

cnf(i_0_1345,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    clsarity_Int__Oint__Orderings_Olinorder,
    [final] ).

cnf(i_0_1346,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_1347,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add,
    [final] ).

cnf(i_0_1348,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__add,
    [final] ).

cnf(i_0_1349,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    clsarity_Int__Oint__Orderings_Oorder,
    [final] ).

cnf(i_0_1350,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_1351,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_1352,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    clsarity_Int__Oint__Orderings_Opreorder,
    [final] ).

cnf(i_0_1353,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_1354,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_1355,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add,
    [final] ).

cnf(i_0_1356,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,
    [final] ).

cnf(i_0_1357,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    [final] ).

cnf(i_0_1358,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    [final] ).

cnf(i_0_1359,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add,
    [final] ).

cnf(i_0_1360,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__add,
    [final] ).

cnf(i_0_1361,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
    clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,
    [final] ).

cnf(i_0_1362,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
    [final] ).

cnf(i_0_1363,axiom,
    class_OrderedGroup_Osemigroup__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Osemigroup__add,
    [final] ).

cnf(i_0_1364,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Osemigroup__add,
    [final] ).

cnf(i_0_1365,axiom,
    class_OrderedGroup_Oab__group__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Oab__group__add,
    [final] ).

cnf(i_0_1366,axiom,
    class_OrderedGroup_Ogroup__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Ogroup__add,
    [final] ).

cnf(i_0_1367,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    clsarity_Int__Oint__Int_Onumber__ring,
    [final] ).

cnf(i_0_1368,axiom,
    class_Ring__and__Field_Oidom(tc_Int_Oint),
    clsarity_Int__Oint__Ring__and__Field_Oidom,
    [final] ).

cnf(i_0_1369,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add,
    [final] ).

cnf(i_0_1370,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
    [final] ).

cnf(i_0_1371,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    clsarity_Int__Oint__Divides_Osemiring__div,
    [final] ).

cnf(i_0_1372,axiom,
    class_Divides_Osemiring__div(tc_nat),
    clsarity_nat__Divides_Osemiring__div,
    [final] ).

cnf(i_0_1373,axiom,
    class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
    clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,
    [final] ).

cnf(i_0_1374,axiom,
    class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
    clsarity_Int__Oint__Ring__and__Field_Oordered__idom,
    [final] ).

cnf(i_0_1375,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
    clsarity_Int__Oint__Ring__and__Field_Oordered__semidom,
    [final] ).

cnf(i_0_1376,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semidom,
    [final] ).

cnf(i_0_1377,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
    clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one,
    [final] ).

cnf(i_0_1378,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    clsarity_nat__Ring__and__Field_Ozero__neq__one,
    [final] ).

cnf(i_0_1379,axiom,
    v_n____ = v_i____,
    cls_True_0,
    [final] ).

cnf(i_0_1380,axiom,
    X1 = X1 ).

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

cnf(i_0_1382,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1383,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1384,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1385,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X1,X3) = c_Transitive__Closure_Ortranclp(X2,X3) ) ).

cnf(i_0_1386,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X3,X1) = c_Transitive__Closure_Ortranclp(X3,X2) ) ).

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

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

cnf(i_0_1389,axiom,
    ( X1 != X2
    | c_Type_Oshift(X1,X3,X4,X5) = c_Type_Oshift(X2,X3,X4,X5) ) ).

cnf(i_0_1390,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X1,X4,X5) = c_Type_Oshift(X3,X2,X4,X5) ) ).

cnf(i_0_1391,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X4,X1,X5) = c_Type_Oshift(X3,X4,X2,X5) ) ).

cnf(i_0_1392,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X4,X5,X1) = c_Type_Oshift(X3,X4,X5,X2) ) ).

cnf(i_0_1393,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1394,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1395,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1396,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1397,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1398,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5,X6) = c_Fun_Ocomp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1399,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5,X6) = c_Fun_Ocomp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1400,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5,X6) = c_Fun_Ocomp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1401,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1,X6) = c_Fun_Ocomp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1402,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X6,X1) = c_Fun_Ocomp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1403,axiom,
    ( X1 != X2
    | c_List_Oappend(X1,X3,X4) = c_List_Oappend(X2,X3,X4) ) ).

cnf(i_0_1404,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X1,X4) = c_List_Oappend(X3,X2,X4) ) ).

cnf(i_0_1405,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X4,X1) = c_List_Oappend(X3,X4,X2) ) ).

cnf(i_0_1406,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X1,X3,X4) = c_List_Olist_OCons(X2,X3,X4) ) ).

cnf(i_0_1407,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X3,X1,X4) = c_List_Olist_OCons(X3,X2,X4) ) ).

cnf(i_0_1408,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X3,X4,X1) = c_List_Olist_OCons(X3,X4,X2) ) ).

cnf(i_0_1409,axiom,
    ( X1 != X2
    | c_List_Odrop(X1,X3,X4) = c_List_Odrop(X2,X3,X4) ) ).

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

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

cnf(i_0_1412,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_1413,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_1414,axiom,
    ( X1 != X2
    | c_List_Otake(X1,X3,X4) = c_List_Otake(X2,X3,X4) ) ).

cnf(i_0_1415,axiom,
    ( X1 != X2
    | c_List_Otake(X3,X1,X4) = c_List_Otake(X3,X2,X4) ) ).

cnf(i_0_1416,axiom,
    ( X1 != X2
    | c_List_Otake(X3,X4,X1) = c_List_Otake(X3,X4,X2) ) ).

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

cnf(i_0_1418,axiom,
    ( X1 != X2
    | c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_1419,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X1,X4,X5) = c_List_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_1420,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X4,X1,X5) = c_List_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_1421,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X4,X5,X1) = c_List_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_1422,axiom,
    ( X1 != X2
    | c_List_Olist__update(X1,X3,X4,X5) = c_List_Olist__update(X2,X3,X4,X5) ) ).

cnf(i_0_1423,axiom,
    ( X1 != X2
    | c_List_Olist__update(X3,X1,X4,X5) = c_List_Olist__update(X3,X2,X4,X5) ) ).

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

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

cnf(i_0_1426,axiom,
    ( X1 != X2
    | c_Suc(X1) = c_Suc(X2) ) ).

cnf(i_0_1427,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1428,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1429,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1430,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_1431,axiom,
    ( X1 != X2
    | c_List_Orotate(X1,X3,X4) = c_List_Orotate(X2,X3,X4) ) ).

cnf(i_0_1432,axiom,
    ( X1 != X2
    | c_List_Orotate(X3,X1,X4) = c_List_Orotate(X3,X2,X4) ) ).

cnf(i_0_1433,axiom,
    ( X1 != X2
    | c_List_Orotate(X3,X4,X1) = c_List_Orotate(X3,X4,X2) ) ).

cnf(i_0_1434,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_1435,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_1436,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_1437,axiom,
    ( X1 != X2
    | c_List_Onth(X1,X3,X4) = c_List_Onth(X2,X3,X4) ) ).

cnf(i_0_1438,axiom,
    ( X1 != X2
    | c_List_Onth(X3,X1,X4) = c_List_Onth(X3,X2,X4) ) ).

cnf(i_0_1439,axiom,
    ( X1 != X2
    | c_List_Onth(X3,X4,X1) = c_List_Onth(X3,X4,X2) ) ).

cnf(i_0_1440,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).

cnf(i_0_1441,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).

cnf(i_0_1442,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_1443,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_1444,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_1445,axiom,
    ( X1 != X2
    | c_List_Osko__List__Xmap__idI__1__1(X1,X3,X4) = c_List_Osko__List__Xmap__idI__1__1(X2,X3,X4) ) ).

cnf(i_0_1446,axiom,
    ( X1 != X2
    | c_List_Osko__List__Xmap__idI__1__1(X3,X1,X4) = c_List_Osko__List__Xmap__idI__1__1(X3,X2,X4) ) ).

cnf(i_0_1447,axiom,
    ( X1 != X2
    | c_List_Osko__List__Xmap__idI__1__1(X3,X4,X1) = c_List_Osko__List__Xmap__idI__1__1(X3,X4,X2) ) ).

cnf(i_0_1448,axiom,
    ( X1 != X2
    | c_List_Orev(X1,X3) = c_List_Orev(X2,X3) ) ).

cnf(i_0_1449,axiom,
    ( X1 != X2
    | c_List_Orev(X3,X1) = c_List_Orev(X3,X2) ) ).

cnf(i_0_1450,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_1451,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X1,X3,X4)
    | c_Type_Otypings(X2,X3,X4) ) ).

cnf(i_0_1452,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X1,X4)
    | c_Type_Otypings(X3,X2,X4) ) ).

cnf(i_0_1453,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X4,X1)
    | c_Type_Otypings(X3,X4,X2) ) ).

cnf(i_0_1454,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_1455,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1456,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1457,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1458,axiom,
    ( X1 != X2
    | ~ c_List_Odistinct(X1,X3)
    | c_List_Odistinct(X2,X3) ) ).

cnf(i_0_1459,axiom,
    ( X1 != X2
    | ~ c_List_Odistinct(X3,X1)
    | c_List_Odistinct(X3,X2) ) ).

cnf(i_0_1460,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_1461,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1462,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1463,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1464,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1465,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1466,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1467,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X1,X3,X4)
    | c_Type_Otyping(X2,X3,X4) ) ).

cnf(i_0_1468,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X1,X4)
    | c_Type_Otyping(X3,X2,X4) ) ).

cnf(i_0_1469,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X4,X1)
    | c_Type_Otyping(X3,X4,X2) ) ).

cnf(i_0_1470,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1471,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_1472,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1473,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_1474,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_1475,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1476,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_1477,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1478,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1479,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1480,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1481,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_1482,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_1483,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1484,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1485,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_1486,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_1487,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_1488,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_1489,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_1490,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X1,X3,X4,X5)
    | c_ListOrder_Ostep1(X2,X3,X4,X5) ) ).

cnf(i_0_1491,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X1,X4,X5)
    | c_ListOrder_Ostep1(X3,X2,X4,X5) ) ).

cnf(i_0_1492,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X1,X5)
    | c_ListOrder_Ostep1(X3,X4,X2,X5) ) ).

cnf(i_0_1493,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X5,X1)
    | c_ListOrder_Ostep1(X3,X4,X5,X2) ) ).

cnf(i_0_1494,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X1,X3,X4)
    | c_List_Olistsp(X2,X3,X4) ) ).

cnf(i_0_1495,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X1,X4)
    | c_List_Olistsp(X3,X2,X4) ) ).

cnf(i_0_1496,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X4,X1)
    | c_List_Olistsp(X3,X4,X2) ) ).

cnf(i_0_1497,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_1498,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Osemigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X2) ) ).

cnf(i_0_1499,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_1500,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_1501,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_1502,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_1380_001,axiom,
    X1 = X1 ).

cnf(i_0_1381_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_1382_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_1383_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_1384_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_1385_006,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X1,X3) = c_Transitive__Closure_Ortranclp(X2,X3) ) ).

cnf(i_0_1386_007,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X3,X1) = c_Transitive__Closure_Ortranclp(X3,X2) ) ).

cnf(i_0_1387_008,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_1388_009,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_1389_010,axiom,
    ( X1 != X2
    | c_Type_Oshift(X1,X3,X4,X5) = c_Type_Oshift(X2,X3,X4,X5) ) ).

cnf(i_0_1390_011,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X1,X4,X5) = c_Type_Oshift(X3,X2,X4,X5) ) ).

cnf(i_0_1391_012,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X4,X1,X5) = c_Type_Oshift(X3,X4,X2,X5) ) ).

cnf(i_0_1392_013,axiom,
    ( X1 != X2
    | c_Type_Oshift(X3,X4,X5,X1) = c_Type_Oshift(X3,X4,X5,X2) ) ).

cnf(i_0_1393_014,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1394_015,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1395_016,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1396_017,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1397_018,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1398_019,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5,X6) = c_Fun_Ocomp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_1399_020,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5,X6) = c_Fun_Ocomp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_1400_021,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5,X6) = c_Fun_Ocomp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_1401_022,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1,X6) = c_Fun_Ocomp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_1402_023,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X6,X1) = c_Fun_Ocomp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_1403_024,axiom,
    ( X1 != X2
    | c_List_Oappend(X1,X3,X4) = c_List_Oappend(X2,X3,X4) ) ).

cnf(i_0_1404_025,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X1,X4) = c_List_Oappend(X3,X2,X4) ) ).

cnf(i_0_1405_026,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X4,X1) = c_List_Oappend(X3,X4,X2) ) ).

cnf(i_0_1406_027,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X1,X3,X4) = c_List_Olist_OCons(X2,X3,X4) ) ).

cnf(i_0_1407_028,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X3,X1,X4) = c_List_Olist_OCons(X3,X2,X4) ) ).

cnf(i_0_1408_029,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X3,X4,X1) = c_List_Olist_OCons(X3,X4,X2) ) ).

cnf(i_0_1409_030,axiom,
    ( X1 != X2
    | c_List_Odrop(X1,X3,X4) = c_List_Odrop(X2,X3,X4) ) ).

cnf(i_0_1410_031,axiom,
    ( X1 != X2
    | c_List_Odrop(X3,X1,X4) = c_List_Odrop(X3,X2,X4) ) ).

cnf(i_0_1411_032,axiom,
    ( X1 != X2
    | c_List_Odrop(X3,X4,X1) = c_List_Odrop(X3,X4,X2) ) ).

cnf(i_0_1412_033,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_1413_034,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_1414_035,axiom,
    ( X1 != X2
    | c_List_Otake(X1,X3,X4) = c_List_Otake(X2,X3,X4) ) ).

cnf(i_0_1415_036,axiom,
    ( X1 != X2
    | c_List_Otake(X3,X1,X4) = c_List_Otake(X3,X2,X4) ) ).

cnf(i_0_1416_037,axiom,
    ( X1 != X2
    | c_List_Otake(X3,X4,X1) = c_List_Otake(X3,X4,X2) ) ).

cnf(i_0_1417_038,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_1418_039,axiom,
    ( X1 != X2
    | c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_1419_040,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X1,X4,X5) = c_List_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_1420_041,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X4,X1,X5) = c_List_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_1421_042,axiom,
    ( X1 != X2
    | c_List_Omap(X3,X4,X5,X1) = c_List_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_1422_043,axiom,
    ( X1 != X2
    | c_List_Olist__update(X1,X3,X4,X5) = c_List_Olist__update(X2,X3,X4,X5) ) ).

cnf(i_0_1423_044,axiom,
    ( X1 != X2
    | c_List_Olist__update(X3,X1,X4,X5) = c_List_Olist__update(X3,X2,X4,X5) ) ).

cnf(i_0_1424_045,axiom,
    ( X1 != X2
    | c_List_Olist__update(X3,X4,X1,X5) = c_List_Olist__update(X3,X4,X2,X5) ) ).

cnf(i_0_1425_046,axiom,
    ( X1 != X2
    | c_List_Olist__update(X3,X4,X5,X1) = c_List_Olist__update(X3,X4,X5,X2) ) ).

cnf(i_0_1426_047,axiom,
    ( X1 != X2
    | c_Suc(X1) = c_Suc(X2) ) ).

cnf(i_0_1427_048,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).

cnf(i_0_1428_049,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).

cnf(i_0_1429_050,axiom,
    ( X1 != X2
    | c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).

cnf(i_0_1430_051,axiom,
    ( X1 != X2
    | c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).

cnf(i_0_1431_052,axiom,
    ( X1 != X2
    | c_List_Orotate(X1,X3,X4) = c_List_Orotate(X2,X3,X4) ) ).

cnf(i_0_1432_053,axiom,
    ( X1 != X2
    | c_List_Orotate(X3,X1,X4) = c_List_Orotate(X3,X2,X4) ) ).

cnf(i_0_1433_054,axiom,
    ( X1 != X2
    | c_List_Orotate(X3,X4,X1) = c_List_Orotate(X3,X4,X2) ) ).

cnf(i_0_1434_055,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_1435_056,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_1436_057,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_1437_058,axiom,
    ( X1 != X2
    | c_List_Onth(X1,X3,X4) = c_List_Onth(X2,X3,X4) ) ).

cnf(i_0_1438_059,axiom,
    ( X1 != X2
    | c_List_Onth(X3,X1,X4) = c_List_Onth(X3,X2,X4) ) ).

cnf(i_0_1439_060,axiom,
    ( X1 != X2
    | c_List_Onth(X3,X4,X1) = c_List_Onth(X3,X4,X2) ) ).

cnf(i_0_1440_061,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).

cnf(i_0_1441_062,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).

cnf(i_0_1442_063,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_1443_064,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_1444_065,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_1445_066,axiom,
    ( X1 != X2
    | c_List_Osko__List__Xmap__idI__1__1(X1,X3,X4) = c_List_Osko__List__Xmap__idI__1__1(X2,X3,X4) ) ).

cnf(i_0_1446_067,axiom,
    ( X1 != X2
    | c_List_Osko__List__Xmap__idI__1__1(X3,X1,X4) = c_List_Osko__List__Xmap__idI__1__1(X3,X2,X4) ) ).

cnf(i_0_1447_068,axiom,
    ( X1 != X2
    | c_List_Osko__List__Xmap__idI__1__1(X3,X4,X1) = c_List_Osko__List__Xmap__idI__1__1(X3,X4,X2) ) ).

cnf(i_0_1448_069,axiom,
    ( X1 != X2
    | c_List_Orev(X1,X3) = c_List_Orev(X2,X3) ) ).

cnf(i_0_1449_070,axiom,
    ( X1 != X2
    | c_List_Orev(X3,X1) = c_List_Orev(X3,X2) ) ).

cnf(i_0_1450_071,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_1451_072,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X1,X3,X4)
    | c_Type_Otypings(X2,X3,X4) ) ).

cnf(i_0_1452_073,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X1,X4)
    | c_Type_Otypings(X3,X2,X4) ) ).

cnf(i_0_1453_074,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X4,X1)
    | c_Type_Otypings(X3,X4,X2) ) ).

cnf(i_0_1454_075,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_1455_076,axiom,
    ( X1 != X2
    | ~ c_lessequals(X1,X3,X4)
    | c_lessequals(X2,X3,X4) ) ).

cnf(i_0_1456_077,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X1,X4)
    | c_lessequals(X3,X2,X4) ) ).

cnf(i_0_1457_078,axiom,
    ( X1 != X2
    | ~ c_lessequals(X3,X4,X1)
    | c_lessequals(X3,X4,X2) ) ).

cnf(i_0_1458_079,axiom,
    ( X1 != X2
    | ~ c_List_Odistinct(X1,X3)
    | c_List_Odistinct(X2,X3) ) ).

cnf(i_0_1459_080,axiom,
    ( X1 != X2
    | ~ c_List_Odistinct(X3,X1)
    | c_List_Odistinct(X3,X2) ) ).

cnf(i_0_1460_081,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_1461_082,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_1462_083,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X2) ) ).

cnf(i_0_1463_084,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_1464_085,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).

cnf(i_0_1465_086,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1466_087,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_1467_088,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X1,X3,X4)
    | c_Type_Otyping(X2,X3,X4) ) ).

cnf(i_0_1468_089,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X1,X4)
    | c_Type_Otyping(X3,X2,X4) ) ).

cnf(i_0_1469_090,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X4,X1)
    | c_Type_Otyping(X3,X4,X2) ) ).

cnf(i_0_1470_091,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_1471_092,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_1472_093,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_1473_094,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_1474_095,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_1475_096,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_1476_097,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_1477_098,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ogroup__add(X1)
    | class_OrderedGroup_Ogroup__add(X2) ) ).

cnf(i_0_1478_099,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_1479_100,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_1480_101,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_1481_102,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_1482_103,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_1483_104,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_1484_105,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_1485_106,axiom,
    ( X1 != X2
    | ~ c_fequal(X1,X3,X4)
    | c_fequal(X2,X3,X4) ) ).

cnf(i_0_1486_107,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X1,X4)
    | c_fequal(X3,X2,X4) ) ).

cnf(i_0_1487_108,axiom,
    ( X1 != X2
    | ~ c_fequal(X3,X4,X1)
    | c_fequal(X3,X4,X2) ) ).

cnf(i_0_1488_109,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_1489_110,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | class_Ring__and__Field_Ozero__neq__one(X2) ) ).

cnf(i_0_1490_111,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X1,X3,X4,X5)
    | c_ListOrder_Ostep1(X2,X3,X4,X5) ) ).

cnf(i_0_1491_112,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X1,X4,X5)
    | c_ListOrder_Ostep1(X3,X2,X4,X5) ) ).

cnf(i_0_1492_113,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X1,X5)
    | c_ListOrder_Ostep1(X3,X4,X2,X5) ) ).

cnf(i_0_1493_114,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X5,X1)
    | c_ListOrder_Ostep1(X3,X4,X5,X2) ) ).

cnf(i_0_1494_115,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X1,X3,X4)
    | c_List_Olistsp(X2,X3,X4) ) ).

cnf(i_0_1495_116,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X1,X4)
    | c_List_Olistsp(X3,X2,X4) ) ).

cnf(i_0_1496_117,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X4,X1)
    | c_List_Olistsp(X3,X4,X2) ) ).

cnf(i_0_1497_118,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_1498_119,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Osemigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X2) ) ).

cnf(i_0_1499_120,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_1500_121,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_1501_122,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_1502_123,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_1503,plain,
    c_List_Omap(X1,X2,X3,X4) = c_List_Omap(X1,X2,X3,X4),
    inference(equality_inference,[],[716]) ).

cnf(i_0_1504,plain,
    c_List_Omap(X1,X2,X3,X4) = c_List_Omap(X1,X2,X3,X4),
    inference(equality_inference,[],[717]) ).

cnf(i_0_1505,plain,
    c_List_Omap(X1,X2,X3,X4) = c_List_Omap(X1,X2,X3,X4),
    inference(equality_inference,[],[718]) ).

cnf(i_0_1506,plain,
    hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X1,X2,X7,X4,X8),X6),
    inference(equality_inference,[],[726]) ).

cnf(i_0_1507,plain,
    hAPP(X1,hAPP(X2,X3)) = hAPP(X1,hAPP(X2,X3)),
    inference(equality_inference,[],[735]) ).

cnf(i_0_1508,plain,
    X1 = X1,
    inference(equality_inference,[],[736]) ).

cnf(i_0_1509,plain,
    X1 = X1,
    inference(equality_inference,[],[737]) ).

cnf(i_0_1510,plain,
    X1 = X1,
    inference(equality_inference,[],[738]) ).

cnf(i_0_1511,plain,
    X1 = X1,
    inference(equality_inference,[],[739]) ).

cnf(i_0_1512,plain,
    X1 = X1,
    inference(equality_inference,[],[742]) ).

cnf(i_0_1513,plain,
    c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),
    inference(equality_inference,[],[817]) ).

cnf(i_0_1514,plain,
    ( ~ c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | X3 = c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X1,X2),X3,X2) ),
    inference(equality_inference,[],[848]) ).

cnf(i_0_1515,plain,
    X1 = X1,
    inference(equality_inference,[],[855]) ).

cnf(i_0_1516,plain,
    X1 = X1,
    inference(equality_inference,[],[856]) ).

cnf(i_0_1517,plain,
    ( c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X1,X2),X3,X2) = X3 ),
    inference(equality_inference,[],[860]) ).

cnf(i_0_1518,plain,
    ( ~ c_List_Odistinct(X1,X2)
    | X3 = X3
    | ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
    inference(equality_inference,[],[880]) ).

cnf(i_0_1519,plain,
    ( ~ c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X1,X2) ),
    inference(equality_inference,[],[888]) ).

cnf(i_0_1520,plain,
    ( c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),X1,X2) = X1 ),
    inference(equality_inference,[],[920]) ).

cnf(i_0_1521,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,[],[923]) ).

cnf(i_0_1522,plain,
    ( X1 = X1
    | ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(equality_inference,[],[953]) ).

cnf(i_0_1523,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[1083]) ).

cnf(i_0_1524,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1084]) ).

cnf(i_0_1525,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(equality_inference,[],[1085]) ).

cnf(i_0_1526,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[1097]) ).

cnf(i_0_1527,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1103]) ).

cnf(i_0_1528,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[1104]) ).

cnf(i_0_1529,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[1105]) ).

cnf(i_0_1530,plain,
    X1 = X1,
    inference(equality_inference,[],[1106]) ).

cnf(i_0_1531,plain,
    X1 = X1,
    inference(equality_inference,[],[1107]) ).

cnf(i_0_1532,plain,
    X1 = X1,
    inference(equality_inference,[],[1108]) ).

cnf(i_0_1533,plain,
    X1 = X1,
    inference(equality_inference,[],[1109]) ).

cnf(i_0_1534,plain,
    X1 = X1,
    inference(equality_inference,[],[1110]) ).

cnf(i_0_1535,plain,
    X1 = X1,
    inference(equality_inference,[],[1176]) ).

cnf(i_0_1536,plain,
    X1 = X1,
    inference(equality_inference,[],[1177]) ).

cnf(i_0_1537,plain,
    X1 = X1,
    inference(equality_inference,[],[1178]) ).

cnf(i_0_1538,plain,
    X1 = X1,
    inference(equality_inference,[],[1179]) ).

cnf(i_0_1539,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | ~ class_Int_Oring__char__0(X1) ),
    inference(equality_inference,[],[1285]) ).

cnf(i_0_1540,plain,
    X1 = X1,
    inference(equality_inference,[],[1302]) ).

cnf(i_0_1541,plain,
    X1 = X1,
    inference(equality_inference,[],[1319]) ).

cnf(i_0_1542,plain,
    X1 = X1,
    inference(equality_inference,[],[1320]) ).

cnf(i_0_1543,plain,
    X1 = X1,
    inference(equality_inference,[],[1322]) ).

cnf(i_0_1544,plain,
    $false,
    inference(scs_inference,[],[i_0_702,i_0_868,i_0_1301,i_0_710]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : LCL814-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32  % Computer : n016.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Mon May  4 23:10:21 EDT 2026
% 0.13/0.32  % CPUTime    : 
% 0.13/0.33  % start to proof: theBenchmark
% 5.47/5.67  % Version  : CSE_E---1.7
% 5.47/5.67  % Problem  : theBenchmark.p
% 5.47/5.67  % SZS status Unsatisfiable for theBenchmark.p
% 5.47/5.67  % SZS output start CNFRefutation
% See solution above
% 5.60/5.75  % Total time : 5.337s
%------------------------------------------------------------------------------