CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : LCL822-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  5 04:45:10 PM UTC 2026

% Result   : Unsatisfiable 0.35s 1.61s
% Output   : CNFRefutation 0.35s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named 259)

% 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)
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X1))
    | ~ c_Type_Otypings(X3,X6,X7)
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_Var_I2_J_0,axiom,
    hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,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_Ha______)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).

cnf(cls_nT_0,axiom,
    hBOOL(hAPP(hAPP(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/sandbox2/benchmark/theBenchmark.p',cls_nT_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,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).

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

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

cnf(cls_conjecture_0,negated_conjecture,
    ~ c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_rs____,tc_Lambda_OdB),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

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

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

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

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

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_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/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).

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

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

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

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

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

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

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

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

cnf(cls_image__image_0,axiom,
    c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).

cnf(cls_lists__typings_0,axiom,
    ( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(X1),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),X2,tc_Lambda_OdB)
    | ~ c_Type_Otypings(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists__typings_0) ).

cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
    hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).

cnf(cls_COMBB__def_0,axiom,
    hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_0) ).

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_shift__gt_0) ).

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

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

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

cnf(cls_CHAINED_0,axiom,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,v_Ts____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

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

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

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

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

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

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

cnf(cls_in__listsp__conv__set_2,axiom,
    ( c_List_Olistsp(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__listsp__conv__set_2) ).

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

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

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

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

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

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

cnf(cls_listsp__infI_0,axiom,
    ( c_List_Olistsp(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,X3)
    | ~ c_List_Olistsp(X2,X4,X3)
    | ~ c_List_Olistsp(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp__infI_0) ).

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

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).

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

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

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

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

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

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

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_append__same__eq_0,axiom,
    ( X1 = X4
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X2,X3) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

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

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_lift_Osimps_I1_J_0,axiom,
    ( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

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

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_append__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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

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

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

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

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

cnf(cls_append__self__conv2_0,axiom,
    ( X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != X2 ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

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

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

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

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

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

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

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

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

cnf(cls_Int__absorb_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

cnf(cls_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

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

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

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

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

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

cnf(cls_inf__idem_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).

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

cnf(cls_append__Nil_0,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),X2,X1) = X2,
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).

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

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

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

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

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).

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

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

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

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

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

cnf(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/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).

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

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

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

cnf(cls_dB_Osimps_I1_J_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

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

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

cnf(cls_dB_Osimps_I7_J_0,axiom,
    c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(i_0_230,axiom,
    ( X1 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X2,X1,X3,X4),X2,tc_Type_Otype,tc_Type_Otype)
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X1))
    | ~ c_Type_Otypings(X3,X6,X7)
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X2)) ),
    cls_var__app__types_0,
    [final] ).

cnf(i_0_231,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
    | ~ c_Type_Otypings(X1,X6,X7)
    | ~ hBOOL(hAPP(hAPP(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_232,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X2))
    | ~ hBOOL(hAPP(hAPP(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_233,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_Lambda_OdB_OVar(X2)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_var__app__typesE_0,
    [final] ).

cnf(i_0_234,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_list__app__typeE_0,
    [final] ).

cnf(i_0_235,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_list__app__typeD_0,
    [final] ).

cnf(i_0_236,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
    | ~ c_Type_Otypings(X1,X3,X5)
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype))) ),
    cls_list__app__typeI_0,
    [final] ).

cnf(i_0_237,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_238,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_var__app__typesE_1,
    [final] ).

cnf(i_0_239,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_list__app__typeE_1,
    [final] ).

cnf(i_0_240,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    cls_list__app__typeD_1,
    [final] ).

cnf(i_0_241,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_242,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_243,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_244,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_245,axiom,
    hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,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_Ha______)),
    cls_Var_I2_J_0,
    [final] ).

cnf(i_0_246,axiom,
    hBOOL(hAPP(hAPP(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_247,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,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_248,axiom,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB) ),
    cls_double__induction__lemma_0,
    [final] ).

cnf(i_0_249,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_Lambda_Osubst(X5,X2,X4)),X6))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype)),X5),X6)) ),
    cls_subst__lemma_0,
    [final] ).

cnf(i_0_250,negated_conjecture,
    ~ c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_rs____,tc_Lambda_OdB),
    cls_conjecture_0,
    [final] ).

cnf(i_0_251,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X3,X4,X5)))
    | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X6),X4),X1))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ hBOOL(hAPP(hAPP(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_252,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X3,X4,X5)))
    | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X6),X4),X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ hBOOL(hAPP(hAPP(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_253,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_Lambda_OdB_OAbs(X2)),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(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_254,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_255,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,
    [final] ).

cnf(i_0_256,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_257,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)),X3)) ),
    cls_typing__elims_I2_J_0,
    [final] ).

cnf(i_0_258,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype)),c_Lambda_Olift(X4,X2)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X4),X5)) ),
    cls_lift__type_0,
    [final] ).

cnf(i_0_259,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_260,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_261,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_262,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_263,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_264,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_265,axiom,
    c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6),
    cls_image__image_0,
    [final] ).

cnf(i_0_266,axiom,
    ( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(X1),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),X2,tc_Lambda_OdB)
    | ~ c_Type_Otypings(X1,X2,X3) ),
    cls_lists__typings_0,
    [final] ).

cnf(i_0_267,axiom,
    hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    cls_ATP__Linkup_OCOMBB__def_0,
    [final] ).

cnf(i_0_268,axiom,
    hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
    cls_COMBB__def_0,
    [final] ).

cnf(i_0_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3)) ),
    cls_rtranclp__converseD_0,
    [final] ).

cnf(i_0_278,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2)),X3)) ),
    cls_typing__elims_I2_J_1,
    [final] ).

cnf(i_0_279,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3)) ),
    cls_rtranclp__converseI_0,
    [final] ).

cnf(i_0_280,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_281,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_282,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_283,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_284,axiom,
    c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
    cls_foldr_Osimps_I1_J_0,
    [final] ).

cnf(i_0_285,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
    cls_foldl__Nil_0,
    [final] ).

cnf(i_0_286,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_287,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X2,X3)),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_288,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X2,X3)),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_289,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X5),X4))) ),
    cls_App_0,
    [final] ).

cnf(i_0_290,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X2,X3)),c_Lambda_Osubst(X1,X4,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
    cls_subst__preserves__beta2_0,
    [final] ).

cnf(i_0_291,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
    cls_conversep_Ocases_0,
    [final] ).

cnf(i_0_292,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
    cls_conversepD_0,
    [final] ).

cnf(i_0_293,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_294,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_295,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_296,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_297,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X2,X3)),c_Lambda_Osubst(X4,X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X4)) ),
    cls_subst__preserves__beta_0,
    [final] ).

cnf(i_0_298,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_299,axiom,
    hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)))),
    cls_beta_0,
    [final] ).

cnf(i_0_300,axiom,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
    cls_conversep_Ointros_0,
    [final] ).

cnf(i_0_301,axiom,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
    cls_conversep__iff_1,
    [final] ).

cnf(i_0_302,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_303,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_304,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_305,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_306,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_307,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X2)),c_Lambda_Olift(X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    cls_lift__preserves__beta_H_0,
    [final] ).

cnf(i_0_308,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
    cls_inf1E_0,
    [final] ).

cnf(i_0_309,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
    cls_inf1E_1,
    [final] ).

cnf(i_0_310,axiom,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,v_Ts____),
    cls_CHAINED_0,
    [final] ).

cnf(i_0_311,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X4),X2)) ),
    cls_subject__reduction_H_0,
    [final] ).

cnf(i_0_312,axiom,
    hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
    cls_shift__eq_0,
    [final] ).

cnf(i_0_313,axiom,
    c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)),
    cls_subst__App_0,
    [final] ).

cnf(i_0_314,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
    cls_Int__assoc_0,
    [final] ).

cnf(i_0_315,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
    cls_Int__left__commute_0,
    [final] ).

cnf(i_0_316,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_317,axiom,
    ( c_List_Olistsp(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,c_List_Osko__List__Xin__listsp__conv__set__1__1(X1,X2,X3))) ),
    cls_in__listsp__conv__set_2,
    [final] ).

cnf(i_0_318,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X4)) ),
    cls_accp__downwards__aux_0,
    [final] ).

cnf(i_0_319,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X3) ),
    cls_accp__downwards_0,
    [final] ).

cnf(i_0_320,axiom,
    ( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
    | ~ hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(X1,X4)) ),
    cls_inf1I_0,
    [final] ).

cnf(i_0_321,axiom,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
    cls_not__Nil__step1_0,
    [final] ).

cnf(i_0_322,axiom,
    ~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
    cls_not__step1__Nil_0,
    [final] ).

cnf(i_0_323,axiom,
    ( hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),X4),X3)) ),
    cls_subject__reduction_0,
    [final] ).

cnf(i_0_324,axiom,
    ( c_List_Olistsp(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,X3)
    | ~ c_List_Olistsp(X2,X4,X3)
    | ~ c_List_Olistsp(X1,X4,X3) ),
    cls_listsp__infI_0,
    [final] ).

cnf(i_0_325,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X2)),c_Lambda_Olift(X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
    cls_lift__preserves__beta_0,
    [final] ).

cnf(i_0_326,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_327,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__assoc_0,
    [final] ).

cnf(i_0_328,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I2_J_0,
    [final] ).

cnf(i_0_329,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__left__commute_0,
    [final] ).

cnf(i_0_330,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I3_J_0,
    [final] ).

cnf(i_0_331,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_332,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_333,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_334,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_335,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_336,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_337,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_338,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,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_339,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
    cls_Int__left__absorb_0,
    [final] ).

cnf(i_0_340,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X3) ),
    cls_accp__downward_0,
    [final] ).

cnf(i_0_341,axiom,
    ( c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X3) ),
    cls_accp_Ocases_0,
    [final] ).

cnf(i_0_342,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
    cls_termi__implies__IT_0,
    [final] ).

cnf(i_0_343,axiom,
    ( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_less__infI1_0,
    [final] ).

cnf(i_0_344,axiom,
    ( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
    | ~ class_Lattices_Olower__semilattice(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_less__infI2_0,
    [final] ).

cnf(i_0_345,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_346,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_347,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_348,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_349,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
    cls_of__nat__less__iff_0,
    [final] ).

cnf(i_0_350,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__left__idem_0,
    [final] ).

cnf(i_0_351,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I4_J_0,
    [final] ).

cnf(i_0_352,axiom,
    ( hAPP(X1,X2) = X3
    | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_Lambda_OdB_OVar(X2)),X3)) ),
    cls_typing__elims_I1_J_0,
    [final] ).

cnf(i_0_353,axiom,
    c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)),
    cls_lift_Osimps_I2_J_0,
    [final] ).

cnf(i_0_354,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
    cls_of__nat__0__less__iff_0,
    [final] ).

cnf(i_0_355,axiom,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    cls_of__nat__less__iff_1,
    [final] ).

cnf(i_0_356,axiom,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_IT__implies__termi_0,
    [final] ).

cnf(i_0_357,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_358,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    cls_Nitpick_Ortranclp__def_1,
    [final] ).

cnf(i_0_359,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    cls_rtranclp_Ortrancl__refl_0,
    [final] ).

cnf(i_0_360,axiom,
    hBOOL(hAPP(hAPP(c_Type_Otyping(X1),c_Lambda_OdB_OVar(X2)),hAPP(X1,X2))),
    cls_typing_OVar_0,
    [final] ).

cnf(i_0_361,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    cls_of__nat__0__less__iff_1,
    [final] ).

cnf(i_0_362,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_363,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_364,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_365,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_366,axiom,
    ( X1 = X4
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X2,X3) ),
    cls_append__same__eq_0,
    [final] ).

cnf(i_0_367,axiom,
    ( X2 = X4
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X1,X4,X3) ),
    cls_same__append__eq_0,
    [final] ).

cnf(i_0_368,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2)) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0,
    [final] ).

cnf(i_0_369,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_370,axiom,
    c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
    cls_conversep__conversep_0,
    [final] ).

cnf(i_0_371,axiom,
    ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
    cls_beta__cases_I1_J_0,
    [final] ).

cnf(i_0_372,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
    cls_Int__commute_0,
    [final] ).

cnf(i_0_373,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    cls_subst__lt_0,
    [final] ).

cnf(i_0_374,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_of__nat__less__0__iff_0,
    [final] ).

cnf(i_0_375,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_lift__IT_0,
    [final] ).

cnf(i_0_376,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
    | X1 = X3
    | c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    cls_subst__Var_2,
    [final] ).

cnf(i_0_377,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_378,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_379,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_380,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_381,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_382,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_383,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_384,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_385,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_386,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__commute_0,
    [final] ).

cnf(i_0_387,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
    | ~ class_Lattices_Olattice(X1) ),
    cls_inf__sup__aci_I1_J_0,
    [final] ).

cnf(i_0_388,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2 ),
    cls_subst__Var_1,
    [final] ).

cnf(i_0_389,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_390,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_391,axiom,
    ( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    cls_lift_Osimps_I1_J_0,
    [final] ).

cnf(i_0_392,axiom,
    hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
    cls_ATP__Linkup_Oequal__imp__fequal_0,
    [final] ).

cnf(i_0_393,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_394,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_395,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_396,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_397,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_398,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__neq__iff_1,
    [final] ).

cnf(i_0_399,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__irrefl_0,
    [final] ).

cnf(i_0_400,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__le_1,
    [final] ).

cnf(i_0_401,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_402,axiom,
    ( X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != X2 ),
    cls_append__self__conv2_0,
    [final] ).

cnf(i_0_403,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != X1 ),
    cls_append__self__conv_0,
    [final] ).

cnf(i_0_404,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 != c_List_Oappend(X1,X2,X3) ),
    cls_self__append__conv_0,
    [final] ).

cnf(i_0_405,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 != c_List_Oappend(X2,X1,X3) ),
    cls_self__append__conv2_0,
    [final] ).

cnf(i_0_406,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_407,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_not__less0_0,
    [final] ).

cnf(i_0_408,axiom,
    hBOOL(hAPP(hAPP(c_Type_Otyping(v_ea______),v_ua______),v_T____)),
    cls_Var_I4_J_0,
    [final] ).

cnf(i_0_409,axiom,
    hBOOL(hAPP(hAPP(c_Type_Otyping(v_e____),v_u____),v_T____)),
    cls_uT_0,
    [final] ).

cnf(i_0_410,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_less__not__refl_0,
    [final] ).

cnf(i_0_411,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_nat__less__le_1,
    [final] ).

cnf(i_0_412,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_Lambda_0,
    [final] ).

cnf(i_0_413,axiom,
    c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
    cls_subst__lift_0,
    [final] ).

cnf(i_0_414,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
    cls_Int__absorb_0,
    [final] ).

cnf(i_0_415,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_416,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_417,axiom,
    c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
    cls_conversep__eq_0,
    [final] ).

cnf(i_0_418,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
    cls_dB_Osimps_I5_J_0,
    [final] ).

cnf(i_0_419,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
    cls_dB_Osimps_I8_J_0,
    [final] ).

cnf(i_0_420,axiom,
    c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    cls_dB_Osimps_I4_J_0,
    [final] ).

cnf(i_0_421,axiom,
    c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    cls_dB_Osimps_I9_J_0,
    [final] ).

cnf(i_0_422,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
    | ~ class_Lattices_Olower__semilattice(X1) ),
    cls_inf__idem_0,
    [final] ).

cnf(i_0_423,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
    cls_subst__eq_0,
    [final] ).

cnf(i_0_424,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),X2,X1) = X2,
    cls_append__Nil_0,
    [final] ).

cnf(i_0_425,axiom,
    c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
    cls_append__Nil2_0,
    [final] ).

cnf(i_0_426,axiom,
    X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
    cls_self__append__conv2_1,
    [final] ).

cnf(i_0_427,axiom,
    X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
    cls_eq__Nil__appendI_0,
    [final] ).

cnf(i_0_428,axiom,
    X1 = c_List_Oappend(X1,c_List_Olist_ONil(X2),X2),
    cls_self__append__conv_1,
    [final] ).

cnf(i_0_429,axiom,
    c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
    cls_listsp_ONil_0,
    [final] ).

cnf(i_0_430,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_431,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_432,axiom,
    ( X2 = X3
    | ~ class_Nat_Osemiring__char__0(X1)
    | c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
    cls_of__nat__eq__iff_0,
    [final] ).

cnf(i_0_433,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_434,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
    cls_Var__IT_0,
    [final] ).

cnf(i_0_435,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_436,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_437,axiom,
    ( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_438,axiom,
    ( class_Lattices_Olattice(tc_fun(X1,X2))
    | ~ class_Lattices_Olattice(X2) ),
    clsarity_fun__Lattices_Olattice,
    [final] ).

cnf(i_0_439,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_440,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    cls_of__nat__0_0,
    [final] ).

cnf(i_0_441,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
    cls_Var_I3_J_0,
    [final] ).

cnf(i_0_442,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    cls_uIT_0,
    [final] ).

cnf(i_0_443,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    cls_dB_Osimps_I1_J_0,
    [final] ).

cnf(i_0_444,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    cls_dB_Osimps_I3_J_0,
    [final] ).

cnf(i_0_445,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    cls_dB_Osimps_I6_J_0,
    [final] ).

cnf(i_0_446,axiom,
    c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
    cls_dB_Osimps_I7_J_0,
    [final] ).

cnf(i_0_447,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_448,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_449,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_450,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_451,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_452,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    clsarity_bool__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_453,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    clsarity_nat__Lattices_Olower__semilattice,
    [final] ).

cnf(i_0_454,axiom,
    class_Lattices_Olattice(tc_bool),
    clsarity_bool__Lattices_Olattice,
    [final] ).

cnf(i_0_455,axiom,
    class_Lattices_Olattice(tc_nat),
    clsarity_nat__Lattices_Olattice,
    [final] ).

cnf(i_0_456,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Osemiring__1,
    [final] ).

cnf(i_0_457,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semidom,
    [final] ).

cnf(i_0_458,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    clsarity_nat__Nat_Osemiring__char__0,
    [final] ).

cnf(i_0_459,axiom,
    v_n____ != v_i____,
    cls_False_0,
    [final] ).

cnf(i_0_460,axiom,
    X1 = X1 ).

cnf(i_0_461,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_462,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_463,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X1,X3,X4,X5,X6) = c_List_Ofoldr(X2,X3,X4,X5,X6) ) ).

cnf(i_0_464,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X1,X4,X5,X6) = c_List_Ofoldr(X3,X2,X4,X5,X6) ) ).

cnf(i_0_465,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X1,X5,X6) = c_List_Ofoldr(X3,X4,X2,X5,X6) ) ).

cnf(i_0_466,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X1,X6) = c_List_Ofoldr(X3,X4,X5,X2,X6) ) ).

cnf(i_0_467,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X6,X1) = c_List_Ofoldr(X3,X4,X5,X6,X2) ) ).

cnf(i_0_468,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X1,X3) = c_Transitive__Closure_Ortranclp(X2,X3) ) ).

cnf(i_0_469,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X3,X1) = c_Transitive__Closure_Ortranclp(X3,X2) ) ).

cnf(i_0_470,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_471,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X1,X3,X4) = c_Lambda_Osubst(X2,X3,X4) ) ).

cnf(i_0_472,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X1,X4) = c_Lambda_Osubst(X3,X2,X4) ) ).

cnf(i_0_473,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X4,X1) = c_Lambda_Osubst(X3,X4,X2) ) ).

cnf(i_0_474,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_475,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_476,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_477,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_478,axiom,
    ( X1 != X2
    | c_List_Oappend(X1,X3,X4) = c_List_Oappend(X2,X3,X4) ) ).

cnf(i_0_479,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X1,X4) = c_List_Oappend(X3,X2,X4) ) ).

cnf(i_0_480,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X4,X1) = c_List_Oappend(X3,X4,X2) ) ).

cnf(i_0_481,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X1,X3) = c_Lambda_Olift(X2,X3) ) ).

cnf(i_0_482,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X3,X1) = c_Lambda_Olift(X3,X2) ) ).

cnf(i_0_483,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_484,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_485,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_486,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_487,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_488,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).

cnf(i_0_489,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).

cnf(i_0_490,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).

cnf(i_0_491,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_492,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_493,axiom,
    ( X1 != X2
    | c_fequal(X1) = c_fequal(X2) ) ).

cnf(i_0_494,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_495,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_496,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_497,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_498,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).

cnf(i_0_499,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).

cnf(i_0_500,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).

cnf(i_0_501,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).

cnf(i_0_502,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).

cnf(i_0_503,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_504,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_505,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_506,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_507,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_508,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_509,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_510,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_511,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X1,X3,X4)
    | c_Type_Otypings(X2,X3,X4) ) ).

cnf(i_0_512,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X1,X4)
    | c_Type_Otypings(X3,X2,X4) ) ).

cnf(i_0_513,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X4,X1)
    | c_Type_Otypings(X3,X4,X2) ) ).

cnf(i_0_514,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X1,X3,X4,X5)
    | c_ListOrder_Ostep1(X2,X3,X4,X5) ) ).

cnf(i_0_515,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X1,X4,X5)
    | c_ListOrder_Ostep1(X3,X2,X4,X5) ) ).

cnf(i_0_516,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X1,X5)
    | c_ListOrder_Ostep1(X3,X4,X2,X5) ) ).

cnf(i_0_517,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X5,X1)
    | c_ListOrder_Ostep1(X3,X4,X5,X2) ) ).

cnf(i_0_518,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X1,X3,X4)
    | c_Wellfounded_Oaccp(X2,X3,X4) ) ).

cnf(i_0_519,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X1,X4)
    | c_Wellfounded_Oaccp(X3,X2,X4) ) ).

cnf(i_0_520,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X4,X1)
    | c_Wellfounded_Oaccp(X3,X4,X2) ) ).

cnf(i_0_521,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X1,X3,X4)
    | c_List_Olistsp(X2,X3,X4) ) ).

cnf(i_0_522,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X1,X4)
    | c_List_Olistsp(X3,X2,X4) ) ).

cnf(i_0_523,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X4,X1)
    | c_List_Olistsp(X3,X4,X2) ) ).

cnf(i_0_524,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_525,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_526,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_527,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_528,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_529,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_460_001,axiom,
    X1 = X1 ).

cnf(i_0_461_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_462_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_463_004,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X1,X3,X4,X5,X6) = c_List_Ofoldr(X2,X3,X4,X5,X6) ) ).

cnf(i_0_464_005,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X1,X4,X5,X6) = c_List_Ofoldr(X3,X2,X4,X5,X6) ) ).

cnf(i_0_465_006,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X1,X5,X6) = c_List_Ofoldr(X3,X4,X2,X5,X6) ) ).

cnf(i_0_466_007,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X1,X6) = c_List_Ofoldr(X3,X4,X5,X2,X6) ) ).

cnf(i_0_467_008,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X6,X1) = c_List_Ofoldr(X3,X4,X5,X6,X2) ) ).

cnf(i_0_468_009,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X1,X3) = c_Transitive__Closure_Ortranclp(X2,X3) ) ).

cnf(i_0_469_010,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X3,X1) = c_Transitive__Closure_Ortranclp(X3,X2) ) ).

cnf(i_0_470_011,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_471_012,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X1,X3,X4) = c_Lambda_Osubst(X2,X3,X4) ) ).

cnf(i_0_472_013,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X1,X4) = c_Lambda_Osubst(X3,X2,X4) ) ).

cnf(i_0_473_014,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X4,X1) = c_Lambda_Osubst(X3,X4,X2) ) ).

cnf(i_0_474_015,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_475_016,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_476_017,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_477_018,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_478_019,axiom,
    ( X1 != X2
    | c_List_Oappend(X1,X3,X4) = c_List_Oappend(X2,X3,X4) ) ).

cnf(i_0_479_020,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X1,X4) = c_List_Oappend(X3,X2,X4) ) ).

cnf(i_0_480_021,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X4,X1) = c_List_Oappend(X3,X4,X2) ) ).

cnf(i_0_481_022,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X1,X3) = c_Lambda_Olift(X2,X3) ) ).

cnf(i_0_482_023,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X3,X1) = c_Lambda_Olift(X3,X2) ) ).

cnf(i_0_483_024,axiom,
    ( X1 != X2
    | c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).

cnf(i_0_484_025,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).

cnf(i_0_485_026,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).

cnf(i_0_486_027,axiom,
    ( X1 != X2
    | c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).

cnf(i_0_487_028,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_488_029,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).

cnf(i_0_489_030,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).

cnf(i_0_490_031,axiom,
    ( X1 != X2
    | c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).

cnf(i_0_491_032,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_492_033,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_493_034,axiom,
    ( X1 != X2
    | c_fequal(X1) = c_fequal(X2) ) ).

cnf(i_0_494_035,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_495_036,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_496_037,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_497_038,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_498_039,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).

cnf(i_0_499_040,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).

cnf(i_0_500_041,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).

cnf(i_0_501_042,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).

cnf(i_0_502_043,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).

cnf(i_0_503_044,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_504_045,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_505_046,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_506_047,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_507_048,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_508_049,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_509_050,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_510_051,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_511_052,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X1,X3,X4)
    | c_Type_Otypings(X2,X3,X4) ) ).

cnf(i_0_512_053,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X1,X4)
    | c_Type_Otypings(X3,X2,X4) ) ).

cnf(i_0_513_054,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X4,X1)
    | c_Type_Otypings(X3,X4,X2) ) ).

cnf(i_0_514_055,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X1,X3,X4,X5)
    | c_ListOrder_Ostep1(X2,X3,X4,X5) ) ).

cnf(i_0_515_056,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X1,X4,X5)
    | c_ListOrder_Ostep1(X3,X2,X4,X5) ) ).

cnf(i_0_516_057,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X1,X5)
    | c_ListOrder_Ostep1(X3,X4,X2,X5) ) ).

cnf(i_0_517_058,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X5,X1)
    | c_ListOrder_Ostep1(X3,X4,X5,X2) ) ).

cnf(i_0_518_059,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X1,X3,X4)
    | c_Wellfounded_Oaccp(X2,X3,X4) ) ).

cnf(i_0_519_060,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X1,X4)
    | c_Wellfounded_Oaccp(X3,X2,X4) ) ).

cnf(i_0_520_061,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X4,X1)
    | c_Wellfounded_Oaccp(X3,X4,X2) ) ).

cnf(i_0_521_062,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X1,X3,X4)
    | c_List_Olistsp(X2,X3,X4) ) ).

cnf(i_0_522_063,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X1,X4)
    | c_List_Olistsp(X3,X2,X4) ) ).

cnf(i_0_523_064,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X4,X1)
    | c_List_Olistsp(X3,X4,X2) ) ).

cnf(i_0_524_065,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_525_066,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_526_067,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_527_068,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olower__semilattice(X1)
    | class_Lattices_Olower__semilattice(X2) ) ).

cnf(i_0_528_069,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_529_070,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_530,plain,
    X1 = X1,
    inference(equality_inference,[],[259]) ).

cnf(i_0_531,plain,
    X1 = X1,
    inference(equality_inference,[],[260]) ).

cnf(i_0_532,plain,
    X1 = X1,
    inference(equality_inference,[],[261]) ).

cnf(i_0_533,plain,
    X1 = X1,
    inference(equality_inference,[],[262]) ).

cnf(i_0_534,plain,
    X1 = X1,
    inference(equality_inference,[],[264]) ).

cnf(i_0_535,plain,
    X1 = X1,
    inference(equality_inference,[],[366]) ).

cnf(i_0_536,plain,
    X1 = X1,
    inference(equality_inference,[],[367]) ).

cnf(i_0_537,plain,
    X1 = X1,
    inference(equality_inference,[],[382]) ).

cnf(i_0_538,plain,
    X1 = X1,
    inference(equality_inference,[],[383]) ).

cnf(i_0_539,plain,
    X1 = X1,
    inference(equality_inference,[],[384]) ).

cnf(i_0_540,plain,
    X1 = X1,
    inference(equality_inference,[],[385]) ).

cnf(i_0_541,plain,
    ( X1 = X1
    | ~ class_Nat_Osemiring__char__0(X2) ),
    inference(equality_inference,[],[432]) ).

cnf(i_0_542,plain,
    X1 = X1,
    inference(equality_inference,[],[443]) ).

cnf(i_0_543,plain,
    X1 = X1,
    inference(equality_inference,[],[444]) ).

cnf(i_0_544,plain,
    $false,
    inference(scs_inference,[],[i_0_250,i_0_310,i_0_266]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : LCL822-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32  % Computer : n011.cluster.edu
% 0.16/0.32  % Model    : x86_64 x86_64
% 0.16/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32  % Memory   : 8042.1875MB
% 0.16/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32  % CPULimit   : 300
% 0.16/0.32  % WCLimit    : 300
% 0.16/0.32  % DateTime   : Mon May  4 23:17:47 EDT 2026
% 0.16/0.32  % CPUTime    : 
% 0.16/0.33  % start to proof: theBenchmark
% 0.35/1.61  % Version  : CSE_E---1.7
% 0.35/1.61  % Problem  : theBenchmark.p
% 0.35/1.61  % SZS status Unsatisfiable for theBenchmark.p
% 0.35/1.61  % SZS output start CNFRefutation
% See solution above
% 0.35/1.65  % Total time : 1.272s
%------------------------------------------------------------------------------