CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : LCL787-1 : 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 : n021.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 04:45:02 PM UTC 2026

% Result   : Unsatisfiable 2.05s 2.62s
% Output   : CNFRefutation 3.35s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named 406)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_var__app__types_0,axiom,
    ( X1 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X2,X1,X3,X4),X2,tc_Type_Otype,tc_Type_Otype)
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X1)
    | ~ c_Type_Otypings(X3,X6,X7)
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_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__types_1,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otypings(X1,X6,X7)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_1) ).

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

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

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

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

cnf(cls_Beta_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,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_that_0,axiom,
    ( v_thesis____
    | ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1)
    | ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,X1),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).

cnf(cls_dB_Orecs_I2_J_0,axiom,
    c_Lambda_OdB_OdB__rec(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(hAPP(hAPP(X2,X4),X5),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X6)),c_Lambda_OdB_OdB__rec(X1,X2,X3,X5,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).

cnf(cls_dB_Osplit__asm_1,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X3,X5),X6)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X6),t_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).

cnf(cls_dB_Osplit_1,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X3,X5),X6)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X6),t_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).

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

cnf(cls_dB_Osplit_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X5)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OVar(X5),t_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).

cnf(cls_dB_Osplit__asm_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X5)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OVar(X5),t_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).

cnf(cls_dB_Osplit__asm_2,axiom,
    ( hBOOL(hAPP(X1,hAPP(X4,X5)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OAbs(X5),t_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).

cnf(cls_dB_Osplit_2,axiom,
    ( hBOOL(hAPP(X1,hAPP(X4,X5)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OAbs(X5),t_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).

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_var__app__typesE_0,axiom,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).

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

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

cnf(cls_list__app__typeI_0,axiom,
    ( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otypings(X1,X3,X5)
    | ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeI_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_var__app__typesE_1,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).

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

cnf(cls_list__app__typeE_1,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))
    | ~ 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_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_foldl__assoc_0,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).

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

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

cnf(cls_foldr_Osimps_I2_J_0,axiom,
    c_List_Ofoldr(X1,c_List_Olist_OCons(X2,X3,X4),X5,X4,X6) = hAPP(hAPP(X1,X2),c_List_Ofoldr(X1,X3,X5,X4,X6)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).

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

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

cnf(cls_dB_Orecs_I3_J_0,axiom,
    c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(hAPP(X3,X4),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).

cnf(cls_CHAINED_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

cnf(cls_headT_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_headT_0) ).

cnf(cls_Var_I2_J_0,axiom,
    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,
    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_Cons__eq__append__conv_2,axiom,
    ( c_List_Olist_OCons(X1,c_List_Osko__List__XCons__eq__append__conv__1__1(X1,X2,X4,X5,X3),X3) = X4
    | c_List_Olist_OCons(X1,X2,X3) = X5
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).

cnf(cls_Cons__eq__append__conv_3,axiom,
    ( X2 = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X1,X2,X4,X5,X3),X5,X3)
    | c_List_Olist_OCons(X1,X2,X3) = X5
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).

cnf(cls_append__eq__Cons__conv_3,axiom,
    ( c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X4,X5,X1,X2,X3),X2,X3) = X5
    | X2 = c_List_Olist_OCons(X4,X5,X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).

cnf(cls_append__eq__Cons__conv_2,axiom,
    ( X1 = c_List_Olist_OCons(X4,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X4,X5,X1,X2,X3),X3)
    | X2 = c_List_Olist_OCons(X4,X5,X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).

cnf(cls_append__eq__Cons__conv_1,axiom,
    ( c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X4,X5,X1,X2,X3),X2,X3) = X5
    | X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).

cnf(cls_Cons__eq__append__conv_0,axiom,
    ( c_List_Olist_OCons(X1,c_List_Osko__List__XCons__eq__append__conv__1__1(X1,X2,X4,X5,X3),X3) = X4
    | X4 = c_List_Olist_ONil(X3)
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).

cnf(cls_Cons__eq__append__conv_1,axiom,
    ( X2 = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X1,X2,X4,X5,X3),X5,X3)
    | X4 = c_List_Olist_ONil(X3)
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).

cnf(cls_append__eq__Cons__conv_0,axiom,
    ( X1 = c_List_Olist_OCons(X4,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X4,X5,X1,X2,X3),X3)
    | X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).

cnf(cls_foldl__Cons_0,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_OCons(X3,X4,X5),X6,X5) = c_List_Ofoldl(X1,hAPP(hAPP(X1,X2),X3),X4,X6,X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).

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

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

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

cnf(cls_type_Osplit_1,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X3,X4),X5)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,hAPP(hAPP(c_Type_Otype_OFun,X4),X5),t_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit_1) ).

cnf(cls_type_Osplit__asm_1,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X3,X4),X5)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,hAPP(hAPP(c_Type_Otype_OFun,X4),X5),t_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit__asm_1) ).

cnf(cls_type_Orecs_I2_J_0,axiom,
    c_Type_Otype_Otype__rec(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),X5) = hAPP(hAPP(hAPP(hAPP(X2,X3),X4),c_Type_Otype_Otype__rec(X1,X2,X3,X5)),c_Type_Otype_Otype__rec(X1,X2,X4,X5)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I2_J_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_Snoc__step1__SnocD_1,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_ListOrder_Ostep1(X1,X4,X5,X6)
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(X6),X6),X6),c_List_Oappend(X5,c_List_Olist_OCons(X3,c_List_Olist_ONil(X6),X6),X6),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).

cnf(cls_Snoc__step1__SnocD_0,axiom,
    ( X1 = X2
    | c_ListOrder_Ostep1(X3,X1,X2,X4)
    | ~ c_ListOrder_Ostep1(X3,c_List_Oappend(X1,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).

cnf(cls_type_Osplit__asm_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X4)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,c_Type_Otype_OAtom(X4),t_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit__asm_0) ).

cnf(cls_type_Osplit_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X4)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,c_Type_Otype_OAtom(X4),t_a))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit_0) ).

cnf(cls_Snoc__step1__SnocD_3,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X2 = X3
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(X5),X5),X5),c_List_Oappend(X6,c_List_Olist_OCons(X3,c_List_Olist_ONil(X5),X5),X5),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).

cnf(cls_Snoc__step1__SnocD_2,axiom,
    ( X1 = X2
    | X3 = X4
    | ~ c_ListOrder_Ostep1(X5,c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X6),X6),X6),c_List_Oappend(X2,c_List_Olist_OCons(X4,c_List_Olist_ONil(X6),X6),X6),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).

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_MI1_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X3,X4,X5)))
    | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
    | ~ c_Type_Otyping(X6,X4,X1)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X6,X5,X1,tc_Type_Otype),X3,X7)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    file('/export/starexec/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)
    | ~ c_Type_Otyping(X6,X4,X2)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X6,X5,X2,tc_Type_Otype),X3,X7)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI2_0) ).

cnf(cls_dB_Osimps_I11_J_0,axiom,
    c_Lambda_OdB_OdB__case(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(X2,X4),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_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_dB_Osimps_I10_J_0,axiom,
    c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).

cnf(cls_dB_Osimps_I12_J_0,axiom,
    c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X3,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).

cnf(cls_dB_Orecs_I1_J_0,axiom,
    c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I1_J_0) ).

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

cnf(cls_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_subst__lemma_0,axiom,
    ( c_Type_Otyping(X1,c_Lambda_Osubst(X5,X2,X4),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).

cnf(cls_rtrancl__beta__App_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
    file('/export/starexec/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_Cons__step1__Cons_1,axiom,
    ( c_ListOrder_Ostep1(X1,X2,X3,X4)
    | hBOOL(hAPP(hAPP(X1,X5),X6))
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X6,X3,X4),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).

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

cnf(cls_Cons__step1__Cons_3,axiom,
    ( c_ListOrder_Ostep1(X1,X2,X3,X4)
    | X3 = X2
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X6,X3,X4),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).

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

cnf(cls_subst__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_conversepD_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversepD_0) ).

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

cnf(cls_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_Cons__step1__Cons_5,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X2,X5,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X3,X5,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).

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_Cons__step1__Cons_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ c_ListOrder_Ostep1(X3,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X1,X6,X5),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_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_typing__elims_I2_J_1,axiom,
    ( c_Type_Otyping(X1,X2,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).

cnf(cls_Cons__step1__Cons_2,axiom,
    ( X1 = X2
    | X3 = X4
    | ~ c_ListOrder_Ostep1(X5,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X1,X3,X6),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).

cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_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_lift__type_0,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),c_Lambda_Olift(X4,X2),X5)
    | ~ c_Type_Otyping(X1,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).

cnf(cls_replicate__app__Cons__same_0,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,X4,X3),X3) = c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X1,X2,X3),X4,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).

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

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

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

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

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

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

cnf(cls_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_Cons__step1__Cons_4,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X3,X4,X5),X5)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).

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_append1__eq__conv_0,axiom,
    ( X1 = X4
    | c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X4,c_List_Olist_OCons(X5,c_List_Olist_ONil(X3),X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

cnf(cls_append1__eq__conv_1,axiom,
    ( X2 = X5
    | c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X4,c_List_Olist_OCons(X5,c_List_Olist_ONil(X3),X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

cnf(cls_append__replicate__commute_0,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X2,X3),X3) = c_List_Oappend(c_List_Oreplicate(X4,X2,X3),c_List_Oreplicate(X1,X2,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).

cnf(cls_argsT_0,axiom,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argsT_0) ).

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

cnf(cls_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_add__less__cancel__right_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

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

cnf(cls_rev__eq__Cons__iff_1,axiom,
    c_List_Orev(c_List_Oappend(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).

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

cnf(cls_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_replicate__append__same_0,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).

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

cnf(cls_accp__downwards__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_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

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

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

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

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

cnf(cls_App_0,axiom,
    ( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
    | ~ c_Type_Otyping(X1,X3,X5)
    | ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X5),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_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_H_0,axiom,
    ( c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otyping(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X4),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).

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

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

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

cnf(cls_butlast__snoc_0,axiom,
    c_List_Obutlast(c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3),X3) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).

cnf(cls_last__snoc_0,axiom,
    c_List_Olast(c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3),X3) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).

cnf(cls_type_Osimps_I6_J_0,axiom,
    c_Type_Otype_Otype__case(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),X5) = hAPP(hAPP(X2,X3),X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).

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

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

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

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

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

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

cnf(cls_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_zero__less__double__add__iff__zero__less__single__add_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

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

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

cnf(cls_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__Cons__conv_5,axiom,
    c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).

cnf(cls_append__Cons_0,axiom,
    c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_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_Cons__eq__append__conv_5,axiom,
    c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).

cnf(cls_Cons__eq__appendI_0,axiom,
    c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

cnf(cls_rev_Osimps_I2_J_0,axiom,
    c_List_Orev(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).

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

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

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

cnf(cls_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_rev__eq__Cons__iff_0,axiom,
    ( X1 = c_List_Oappend(c_List_Orev(X4,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2),X2)
    | c_List_Orev(X1,X2) != c_List_Olist_OCons(X3,X4,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).

cnf(cls_rotate__simps_1,axiom,
    c_List_Orotate1(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oappend(X2,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).

cnf(cls_take__butlast_0,axiom,
    ( c_List_Otake(X1,c_List_Obutlast(X2,X3),X3) = c_List_Otake(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__butlast_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_type_Orecs_I1_J_0,axiom,
    c_Type_Otype_Otype__rec(X1,X2,c_Type_Otype_OAtom(X3),X4) = hAPP(X1,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).

cnf(cls_type_Osimps_I5_J_0,axiom,
    c_Type_Otype_Otype__case(X1,X2,c_Type_Otype_OAtom(X3),X4) = hAPP(X1,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).

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

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

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

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

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

cnf(cls_append__butlast__last__id_0,axiom,
    ( c_List_Oappend(c_List_Obutlast(X1,X2),c_List_Olist_OCons(c_List_Olast(X1,X2),c_List_Olist_ONil(X2),X2),X2) = X1
    | X1 = c_List_Olist_ONil(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__butlast__last__id_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_rev__append_0,axiom,
    c_List_Orev(c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Orev(X1,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).

cnf(cls_append__eq__Cons__conv_4,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_OCons(X2,X3,X1),X1) = c_List_Olist_OCons(X2,X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).

cnf(cls_Cons__eq__append__conv_4,axiom,
    c_List_Olist_OCons(X1,X2,X3) = c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X1,X2,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

cnf(cls_butlast__append_1,axiom,
    ( c_List_Obutlast(c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(X1,c_List_Obutlast(X2,X3),X3)
    | X2 = c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).

cnf(cls_butlast_Osimps_I2_J_1,axiom,
    ( c_List_Obutlast(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_OCons(X1,c_List_Obutlast(X2,X3),X3)
    | X2 = c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).

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_append__eq__conv__conj_0,axiom,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_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_rev__singleton__conv_1,axiom,
    c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).

cnf(cls_singleton__rev__conv_1,axiom,
    c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).

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

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

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

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

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

cnf(cls_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_singleton__rev__conv_0,axiom,
    ( X3 = c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2)
    | c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) != c_List_Orev(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).

cnf(cls_rev__singleton__conv_0,axiom,
    ( X1 = c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2)
    | c_List_Orev(X1,X2) != c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).

cnf(cls_replicate__eq__replicate_1,axiom,
    ( X2 = X5
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).

cnf(cls_rev__replicate_0,axiom,
    c_List_Orev(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(X1,X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).

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

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

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

cnf(cls_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_list_Oinject_0,axiom,
    ( X1 = X4
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

cnf(cls_replicate__eq__replicate_0,axiom,
    ( X1 = X4
    | c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_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_list_Oinject_1,axiom,
    ( X2 = X5
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

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_take__Cons_H_0,axiom,
    c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_ONil(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).

cnf(cls_length__greater__0__conv_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1)),tc_nat),
    file('/export/starexec/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_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_butlast__append_0,axiom,
    c_List_Obutlast(c_List_Oappend(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Obutlast(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).

cnf(cls_last__append_0,axiom,
    c_List_Olast(c_List_Oappend(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olast(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_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_last__append_1,axiom,
    ( c_List_Olast(c_List_Oappend(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | X2 = c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).

cnf(cls_last_Osimps_1,axiom,
    ( c_List_Olast(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | X2 = c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).

cnf(cls_butlast_Osimps_I2_J_0,axiom,
    c_List_Obutlast(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olist_ONil(X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).

cnf(cls_last_Osimps_0,axiom,
    c_List_Olast(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).

cnf(cls_length__replicate_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Oreplicate(X1,X2,X3),tc_List_Olist(X3)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).

cnf(cls_last__replicate_0,axiom,
    ( c_List_Olast(c_List_Oreplicate(X1,X2,X3),X3) = X2
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__replicate_0) ).

cnf(cls_type__induct_0,axiom,
    ( hBOOL(hAPP(X1,X4))
    | hBOOL(hAPP(X1,X2))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_0) ).

cnf(cls_type__induct_1,axiom,
    ( hBOOL(hAPP(X1,X4))
    | hBOOL(hAPP(X1,X3))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_1) ).

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__antisym__conv3_0,axiom,
    ( X2 = X3
    | c_HOL_Oord__class_Oless(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

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

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

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

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

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

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

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

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

cnf(cls_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_replicate__eq__replicate_2,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).

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

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

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

cnf(cls_typing__elims_I1_J_0,axiom,
    ( hAPP(X1,X2) = X3
    | ~ 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_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_class__ringb_Oadd__r0__iff_0,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

cnf(cls_take__eq__Nil_0,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Otake(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).

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

cnf(cls_length__greater__0__conv_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | X1 = c_List_Olist_ONil(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).

cnf(cls_type__induct_2,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Type_Osko__Type__Xtype__induct__1__1(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_2) ).

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_replicate__empty_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).

cnf(cls_empty__replicate_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Olist_ONil(X1) != c_List_Oreplicate(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).

cnf(cls_linorder__neq__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    file('/export/starexec/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_neq__Nil__conv_1,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

cnf(cls_list_Osimps_I3_J_0,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

cnf(cls_list_Osimps_I2_J_0,axiom,
    c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_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_not__Cons__self2_0,axiom,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

cnf(cls_not__Cons__self_0,axiom,
    X1 != c_List_Olist_OCons(X2,X1,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

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

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

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

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

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

cnf(cls_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_class__ringb_Oadd__r0__iff_1,axiom,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

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

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

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

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

cnf(cls_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_monoid__add__class_Oadd__0__right_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

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

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

cnf(cls_length__rev_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).

cnf(cls_length__rotate1_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Orotate1(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate1_0) ).

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

cnf(cls_take__eq__Nil_2,axiom,
    c_List_Otake(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).

cnf(cls_type_Osimps_I4_J_0,axiom,
    hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != c_Type_Otype_OAtom(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).

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

cnf(cls_dB_Osimps_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_type_Osimps_I3_J_0,axiom,
    c_Type_Otype_OAtom(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I3_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_take__0_0,axiom,
    c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__0_0) ).

cnf(cls_replicate__empty_1,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).

cnf(cls_empty__replicate_1,axiom,
    c_List_Olist_ONil(X1) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).

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_Var_I4_J_0,axiom,
    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,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).

cnf(cls_Cons_0,axiom,
    v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_0) ).

cnf(cls_rev__is__rev__conv_0,axiom,
    ( X1 = X3
    | c_List_Orev(X1,X2) != c_List_Orev(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).

cnf(cls_length__0__conv_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).

cnf(cls_rev__rev__ident_0,axiom,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).

cnf(cls_rev__swap_1,axiom,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).

cnf(cls_rev__swap_0,axiom,
    X1 = c_List_Orev(c_List_Orev(X1,X2),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).

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

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

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

cnf(cls_rev__is__Nil__conv_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Orev(X1,X2) != c_List_Olist_ONil(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).

cnf(cls_rotate1__is__Nil__conv_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Orotate1(X1,X2) != c_List_Olist_ONil(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).

cnf(cls_Nil__is__rev__conv_0,axiom,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Orev(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).

cnf(cls_length__0__conv_1,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/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_butlast_Osimps_I1_J_0,axiom,
    c_List_Obutlast(c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).

cnf(cls_rev__is__Nil__conv_1,axiom,
    c_List_Orev(c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).

cnf(cls_rotate__simps_0,axiom,
    c_List_Orotate1(c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_0) ).

cnf(cls_Nil__is__rev__conv_1,axiom,
    c_List_Olist_ONil(X1) = c_List_Orev(c_List_Olist_ONil(X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).

cnf(cls_type_Osimps_I1_J_0,axiom,
    ( X1 = X2
    | c_Type_Otype_OAtom(X1) != c_Type_Otype_OAtom(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).

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

cnf(cls_dB_Osimps_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_nat__Ring__and__Field_Osemiring__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_True_0,axiom,
    v_n____ = v_i____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).

cnf(i_0_378,axiom,
    ( X1 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X2,X1,X3,X4),X2,tc_Type_Otype,tc_Type_Otype)
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X1)
    | ~ c_Type_Otypings(X3,X6,X7)
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X2) ),
    cls_var__app__types_0,
    [final] ).

cnf(i_0_379,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_380,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otypings(X1,X6,X7)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    cls_var__app__types_1,
    [final] ).

cnf(i_0_381,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_382,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_383,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_384,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_385,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_386,axiom,
    ( v_thesis____
    | ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1)
    | ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,X1),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
    cls_that_0,
    [final] ).

cnf(i_0_387,axiom,
    c_Lambda_OdB_OdB__rec(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(hAPP(hAPP(X2,X4),X5),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X6)),c_Lambda_OdB_OdB__rec(X1,X2,X3,X5,X6)),
    cls_dB_Orecs_I2_J_0,
    [final] ).

cnf(i_0_388,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X3,X5),X6)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X6),t_a))) ),
    cls_dB_Osplit__asm_1,
    [final] ).

cnf(i_0_389,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X3,X5),X6)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X6),t_a))) ),
    cls_dB_Osplit_1,
    [final] ).

cnf(i_0_390,axiom,
    ( X1 = X2
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)
    | ~ c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X1) ),
    cls_var__app__type__eq_0,
    [final] ).

cnf(i_0_391,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X5)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OVar(X5),t_a))) ),
    cls_dB_Osplit_0,
    [final] ).

cnf(i_0_392,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X5)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OVar(X5),t_a))) ),
    cls_dB_Osplit__asm_0,
    [final] ).

cnf(i_0_393,axiom,
    ( hBOOL(hAPP(X1,hAPP(X4,X5)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OAbs(X5),t_a))) ),
    cls_dB_Osplit__asm_2,
    [final] ).

cnf(i_0_394,axiom,
    ( hBOOL(hAPP(X1,hAPP(X4,X5)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OAbs(X5),t_a))) ),
    cls_dB_Osplit_2,
    [final] ).

cnf(i_0_395,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_396,axiom,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    cls_var__app__typesE_0,
    [final] ).

cnf(i_0_397,axiom,
    ( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    cls_list__app__typeD_0,
    [final] ).

cnf(i_0_398,axiom,
    ( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    cls_list__app__typeE_0,
    [final] ).

cnf(i_0_399,axiom,
    ( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otypings(X1,X3,X5)
    | ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype)) ),
    cls_list__app__typeI_0,
    [final] ).

cnf(i_0_400,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_401,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_402,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_403,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    cls_var__app__typesE_1,
    [final] ).

cnf(i_0_404,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    cls_list__app__typeD_1,
    [final] ).

cnf(i_0_405,axiom,
    ( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    cls_list__app__typeE_1,
    [final] ).

cnf(i_0_406,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_407,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_408,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_409,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_410,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    cls_foldl__assoc_0,
    [final] ).

cnf(i_0_411,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_412,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_413,axiom,
    c_List_Ofoldr(X1,c_List_Olist_OCons(X2,X3,X4),X5,X4,X6) = hAPP(hAPP(X1,X2),c_List_Ofoldr(X1,X3,X5,X4,X6)),
    cls_foldr_Osimps_I2_J_0,
    [final] ).

cnf(i_0_414,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_foldl__absorb0_0,
    [final] ).

cnf(i_0_415,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1))
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_foldl__foldr1__lemma_0,
    [final] ).

cnf(i_0_416,axiom,
    c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(hAPP(X3,X4),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X5)),
    cls_dB_Orecs_I3_J_0,
    [final] ).

cnf(i_0_417,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    cls_CHAINED_0,
    [final] ).

cnf(i_0_418,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    cls_headT_0,
    [final] ).

cnf(i_0_419,axiom,
    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_420,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
    cls_nT_0,
    [final] ).

cnf(i_0_421,axiom,
    ( c_List_Olist_OCons(X1,c_List_Osko__List__XCons__eq__append__conv__1__1(X1,X2,X4,X5,X3),X3) = X4
    | c_List_Olist_OCons(X1,X2,X3) = X5
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    cls_Cons__eq__append__conv_2,
    [final] ).

cnf(i_0_422,axiom,
    ( X2 = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X1,X2,X4,X5,X3),X5,X3)
    | c_List_Olist_OCons(X1,X2,X3) = X5
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    cls_Cons__eq__append__conv_3,
    [final] ).

cnf(i_0_423,axiom,
    ( c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X4,X5,X1,X2,X3),X2,X3) = X5
    | X2 = c_List_Olist_OCons(X4,X5,X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    cls_append__eq__Cons__conv_3,
    [final] ).

cnf(i_0_424,axiom,
    ( X1 = c_List_Olist_OCons(X4,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X4,X5,X1,X2,X3),X3)
    | X2 = c_List_Olist_OCons(X4,X5,X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    cls_append__eq__Cons__conv_2,
    [final] ).

cnf(i_0_425,axiom,
    ( c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X4,X5,X1,X2,X3),X2,X3) = X5
    | X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    cls_append__eq__Cons__conv_1,
    [final] ).

cnf(i_0_426,axiom,
    ( c_List_Olist_OCons(X1,c_List_Osko__List__XCons__eq__append__conv__1__1(X1,X2,X4,X5,X3),X3) = X4
    | X4 = c_List_Olist_ONil(X3)
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    cls_Cons__eq__append__conv_0,
    [final] ).

cnf(i_0_427,axiom,
    ( X2 = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X1,X2,X4,X5,X3),X5,X3)
    | X4 = c_List_Olist_ONil(X3)
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Oappend(X4,X5,X3) ),
    cls_Cons__eq__append__conv_1,
    [final] ).

cnf(i_0_428,axiom,
    ( X1 = c_List_Olist_OCons(X4,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X4,X5,X1,X2,X3),X3)
    | X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    cls_append__eq__Cons__conv_0,
    [final] ).

cnf(i_0_429,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_OCons(X3,X4,X5),X6,X5) = c_List_Ofoldl(X1,hAPP(hAPP(X1,X2),X3),X4,X6,X5),
    cls_foldl__Cons_0,
    [final] ).

cnf(i_0_430,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_foldl__foldr1_0,
    [final] ).

cnf(i_0_431,axiom,
    ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    cls_foldr__conv__foldl_0,
    [final] ).

cnf(i_0_432,axiom,
    ( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4),X3) ),
    cls_typing__elims_I2_J_0,
    [final] ).

cnf(i_0_433,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X3,X4),X5)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,hAPP(hAPP(c_Type_Otype_OFun,X4),X5),t_a))) ),
    cls_type_Osplit_1,
    [final] ).

cnf(i_0_434,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X3,X4),X5)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,hAPP(hAPP(c_Type_Otype_OFun,X4),X5),t_a))) ),
    cls_type_Osplit__asm_1,
    [final] ).

cnf(i_0_435,axiom,
    c_Type_Otype_Otype__rec(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),X5) = hAPP(hAPP(hAPP(hAPP(X2,X3),X4),c_Type_Otype_Otype__rec(X1,X2,X3,X5)),c_Type_Otype_Otype__rec(X1,X2,X4,X5)),
    cls_type_Orecs_I2_J_0,
    [final] ).

cnf(i_0_436,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_437,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_438,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_439,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_440,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_441,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_442,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_443,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_444,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_445,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_ListOrder_Ostep1(X1,X4,X5,X6)
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(X6),X6),X6),c_List_Oappend(X5,c_List_Olist_OCons(X3,c_List_Olist_ONil(X6),X6),X6),X6) ),
    cls_Snoc__step1__SnocD_1,
    [final] ).

cnf(i_0_446,axiom,
    ( X1 = X2
    | c_ListOrder_Ostep1(X3,X1,X2,X4)
    | ~ c_ListOrder_Ostep1(X3,c_List_Oappend(X1,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    cls_Snoc__step1__SnocD_0,
    [final] ).

cnf(i_0_447,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X4)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,c_Type_Otype_OAtom(X4),t_a))) ),
    cls_type_Osplit__asm_0,
    [final] ).

cnf(i_0_448,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X4)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,c_Type_Otype_OAtom(X4),t_a))) ),
    cls_type_Osplit_0,
    [final] ).

cnf(i_0_449,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X2 = X3
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(X5),X5),X5),c_List_Oappend(X6,c_List_Olist_OCons(X3,c_List_Olist_ONil(X5),X5),X5),X5) ),
    cls_Snoc__step1__SnocD_3,
    [final] ).

cnf(i_0_450,axiom,
    ( X1 = X2
    | X3 = X4
    | ~ c_ListOrder_Ostep1(X5,c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X6),X6),X6),c_List_Oappend(X2,c_List_Olist_OCons(X4,c_List_Olist_ONil(X6),X6),X6),X6) ),
    cls_Snoc__step1__SnocD_2,
    [final] ).

cnf(i_0_451,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_452,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X3,X4,X5)))
    | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
    | ~ c_Type_Otyping(X6,X4,X1)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X6,X5,X1,tc_Type_Otype),X3,X7)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    cls_MI1_0,
    [final] ).

cnf(i_0_453,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X3,X4,X5)))
    | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
    | ~ c_Type_Otyping(X6,X4,X2)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X6,X5,X2,tc_Type_Otype),X3,X7)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
    cls_MI2_0,
    [final] ).

cnf(i_0_454,axiom,
    c_Lambda_OdB_OdB__case(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(X2,X4),X5),
    cls_dB_Osimps_I11_J_0,
    [final] ).

cnf(i_0_455,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_456,axiom,
    c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
    cls_dB_Osimps_I10_J_0,
    [final] ).

cnf(i_0_457,axiom,
    c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X3,X4),
    cls_dB_Osimps_I12_J_0,
    [final] ).

cnf(i_0_458,axiom,
    c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
    cls_dB_Orecs_I1_J_0,
    [final] ).

cnf(i_0_459,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_460,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_461,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_462,axiom,
    c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
    cls_foldr_Osimps_I1_J_0,
    [final] ).

cnf(i_0_463,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
    cls_foldl__Nil_0,
    [final] ).

cnf(i_0_464,axiom,
    ( c_Type_Otyping(X1,c_Lambda_Osubst(X5,X2,X4),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    cls_subst__lemma_0,
    [final] ).

cnf(i_0_465,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_466,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_467,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_468,axiom,
    ( c_ListOrder_Ostep1(X1,X2,X3,X4)
    | hBOOL(hAPP(hAPP(X1,X5),X6))
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X6,X3,X4),X4) ),
    cls_Cons__step1__Cons_1,
    [final] ).

cnf(i_0_469,axiom,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_Type_Otype),X2,X4) ),
    cls_Abs_0,
    [final] ).

cnf(i_0_470,axiom,
    ( c_ListOrder_Ostep1(X1,X2,X3,X4)
    | X3 = X2
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X6,X3,X4),X4) ),
    cls_Cons__step1__Cons_3,
    [final] ).

cnf(i_0_471,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X2,X1,X3),tc_Type_Otype),X3,c_Type_Osko__Type__Xtyping__elims__3__2(X2,X1,X3))
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),X2) ),
    cls_typing__elims_I3_J_1,
    [final] ).

cnf(i_0_472,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_473,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_474,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_475,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_476,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_477,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X2,X5,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X3,X5,X4) ),
    cls_Cons__step1__Cons_5,
    [final] ).

cnf(i_0_478,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_479,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_480,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_481,axiom,
    ( X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ c_ListOrder_Ostep1(X3,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X1,X6,X5),X5) ),
    cls_Cons__step1__Cons_0,
    [final] ).

cnf(i_0_482,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_483,axiom,
    ( c_Type_Otyping(X1,X2,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2),X3) ),
    cls_typing__elims_I2_J_1,
    [final] ).

cnf(i_0_484,axiom,
    ( X1 = X2
    | X3 = X4
    | ~ c_ListOrder_Ostep1(X5,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X1,X3,X6),X6) ),
    cls_Cons__step1__Cons_2,
    [final] ).

cnf(i_0_485,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I20_J_0,
    [final] ).

cnf(i_0_486,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_487,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),c_Lambda_Olift(X4,X2),X5)
    | ~ c_Type_Otyping(X1,X4,X5) ),
    cls_lift__type_0,
    [final] ).

cnf(i_0_488,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,X4,X3),X3) = c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X1,X2,X3),X4,X3),X3),
    cls_replicate__app__Cons__same_0,
    [final] ).

cnf(i_0_489,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_490,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_491,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_492,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_493,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_494,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_495,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_496,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X3,X4,X5),X5)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    cls_Cons__step1__Cons_4,
    [final] ).

cnf(i_0_497,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_498,axiom,
    ( X1 = X4
    | c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X4,c_List_Olist_OCons(X5,c_List_Olist_ONil(X3),X3),X3) ),
    cls_append1__eq__conv_0,
    [final] ).

cnf(i_0_499,axiom,
    ( X2 = X5
    | c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X4,c_List_Olist_OCons(X5,c_List_Olist_ONil(X3),X3),X3) ),
    cls_append1__eq__conv_1,
    [final] ).

cnf(i_0_500,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X2,X3),X3) = c_List_Oappend(c_List_Oreplicate(X4,X2,X3),c_List_Oreplicate(X1,X2,X3),X3),
    cls_append__replicate__commute_0,
    [final] ).

cnf(i_0_501,axiom,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
    cls_argsT_0,
    [final] ).

cnf(i_0_502,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I23_J_0,
    [final] ).

cnf(i_0_503,axiom,
    hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
    cls_shift__eq_0,
    [final] ).

cnf(i_0_504,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_505,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
    cls_add__less__cancel__right_0,
    [final] ).

cnf(i_0_506,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
    cls_add__less__cancel__left_0,
    [final] ).

cnf(i_0_507,axiom,
    c_List_Orev(c_List_Oappend(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    cls_rev__eq__Cons__iff_1,
    [final] ).

cnf(i_0_508,axiom,
    ( X1 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X1,X2,X3)),c_Type_Osko__Type__Xtyping__elims__3__2(X1,X2,X3))
    | ~ c_Type_Otyping(X2,c_Lambda_OdB_OAbs(X3),X1) ),
    cls_typing__elims_I3_J_0,
    [final] ).

cnf(i_0_509,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_510,axiom,
    c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
    cls_replicate__append__same_0,
    [final] ).

cnf(i_0_511,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X5,X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__strict__mono_0,
    [final] ).

cnf(i_0_512,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_513,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_514,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
    [final] ).

cnf(i_0_515,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__assoc_0,
    [final] ).

cnf(i_0_516,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I21_J_0,
    [final] ).

cnf(i_0_517,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I25_J_0,
    [final] ).

cnf(i_0_518,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__a_0,
    [final] ).

cnf(i_0_519,axiom,
    ( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
    | ~ c_Type_Otyping(X1,X3,X5)
    | ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X5),X4)) ),
    cls_App_0,
    [final] ).

cnf(i_0_520,axiom,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
    cls_not__Nil__step1_0,
    [final] ).

cnf(i_0_521,axiom,
    ~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
    cls_not__step1__Nil_0,
    [final] ).

cnf(i_0_522,axiom,
    ( c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otyping(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X4),X2)) ),
    cls_subject__reduction_H_0,
    [final] ).

cnf(i_0_523,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
    cls_add__cancel__21_0,
    [final] ).

cnf(i_0_524,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_add__neg__neg_0,
    [final] ).

cnf(i_0_525,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_add__pos__pos_0,
    [final] ).

cnf(i_0_526,axiom,
    c_List_Obutlast(c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3),X3) = X1,
    cls_butlast__snoc_0,
    [final] ).

cnf(i_0_527,axiom,
    c_List_Olast(c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3),X3) = X2,
    cls_last__snoc_0,
    [final] ).

cnf(i_0_528,axiom,
    c_Type_Otype_Otype__case(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),X5) = hAPP(hAPP(X2,X3),X4),
    cls_type_Osimps_I6_J_0,
    [final] ).

cnf(i_0_529,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_add__less__cancel__left_1,
    [final] ).

cnf(i_0_530,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
    cls_add__strict__left__mono_0,
    [final] ).

cnf(i_0_531,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__less__cancel__right_1,
    [final] ).

cnf(i_0_532,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
    cls_add__strict__right__mono_0,
    [final] ).

cnf(i_0_533,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_534,axiom,
    ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    cls_pos__add__strict_0,
    [final] ).

cnf(i_0_535,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_536,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
    cls_zero__less__double__add__iff__zero__less__single__add_0,
    [final] ).

cnf(i_0_537,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_even__less__0__iff_0,
    [final] ).

cnf(i_0_538,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__less__zero__iff__single__less__zero_0,
    [final] ).

cnf(i_0_539,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_540,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_541,axiom,
    c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3),
    cls_append__eq__Cons__conv_5,
    [final] ).

cnf(i_0_542,axiom,
    c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3),
    cls_append__Cons_0,
    [final] ).

cnf(i_0_543,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_544,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_545,axiom,
    c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
    cls_Cons__eq__append__conv_5,
    [final] ).

cnf(i_0_546,axiom,
    c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
    cls_Cons__eq__appendI_0,
    [final] ).

cnf(i_0_547,axiom,
    c_List_Orev(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),
    cls_rev_Osimps_I2_J_0,
    [final] ).

cnf(i_0_548,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__left__commute_0,
    [final] ).

cnf(i_0_549,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_add__cancel__21_1,
    [final] ).

cnf(i_0_550,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I22_J_0,
    [final] ).

cnf(i_0_551,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_552,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_553,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_554,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_555,axiom,
    ( X1 = c_List_Oappend(c_List_Orev(X4,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2),X2)
    | c_List_Orev(X1,X2) != c_List_Olist_OCons(X3,X4,X2) ),
    cls_rev__eq__Cons__iff_0,
    [final] ).

cnf(i_0_556,axiom,
    c_List_Orotate1(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oappend(X2,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),
    cls_rotate__simps_1,
    [final] ).

cnf(i_0_557,axiom,
    ( c_List_Otake(X1,c_List_Obutlast(X2,X3),X3) = c_List_Otake(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
    cls_take__butlast_0,
    [final] ).

cnf(i_0_558,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_559,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_560,axiom,
    c_Type_Otype_Otype__rec(X1,X2,c_Type_Otype_OAtom(X3),X4) = hAPP(X1,X3),
    cls_type_Orecs_I1_J_0,
    [final] ).

cnf(i_0_561,axiom,
    c_Type_Otype_Otype__case(X1,X2,c_Type_Otype_OAtom(X3),X4) = hAPP(X1,X3),
    cls_type_Osimps_I5_J_0,
    [final] ).

cnf(i_0_562,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_even__less__0__iff_1,
    [final] ).

cnf(i_0_563,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    cls_double__add__less__zero__iff__single__less__zero_1,
    [final] ).

cnf(i_0_564,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    cls_zero__less__double__add__iff__zero__less__single__add_1,
    [final] ).

cnf(i_0_565,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_566,axiom,
    ( c_Type_Otyping(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2))
    | ~ c_Type_Otyping(X1,X4,X3) ),
    cls_subject__reduction_0,
    [final] ).

cnf(i_0_567,axiom,
    ( c_List_Oappend(c_List_Obutlast(X1,X2),c_List_Olist_OCons(c_List_Olast(X1,X2),c_List_Olist_ONil(X2),X2),X2) = X1
    | X1 = c_List_Olist_ONil(X2) ),
    cls_append__butlast__last__id_0,
    [final] ).

cnf(i_0_568,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_569,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_570,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_571,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_572,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_573,axiom,
    c_List_Orev(c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Orev(X1,X3),X3),
    cls_rev__append_0,
    [final] ).

cnf(i_0_574,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_OCons(X2,X3,X1),X1) = c_List_Olist_OCons(X2,X3,X1),
    cls_append__eq__Cons__conv_4,
    [final] ).

cnf(i_0_575,axiom,
    c_List_Olist_OCons(X1,X2,X3) = c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X1,X2,X3),X3),
    cls_Cons__eq__append__conv_4,
    [final] ).

cnf(i_0_576,axiom,
    ( c_List_Obutlast(c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(X1,c_List_Obutlast(X2,X3),X3)
    | X2 = c_List_Olist_ONil(X3) ),
    cls_butlast__append_1,
    [final] ).

cnf(i_0_577,axiom,
    ( c_List_Obutlast(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_OCons(X1,c_List_Obutlast(X2,X3),X3)
    | X2 = c_List_Olist_ONil(X3) ),
    cls_butlast_Osimps_I2_J_1,
    [final] ).

cnf(i_0_578,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_579,axiom,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    cls_append__eq__conv__conj_0,
    [final] ).

cnf(i_0_580,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_581,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_582,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_583,axiom,
    c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),
    cls_rev__singleton__conv_1,
    [final] ).

cnf(i_0_584,axiom,
    c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2),
    cls_singleton__rev__conv_1,
    [final] ).

cnf(i_0_585,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_586,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    cls_rtranclp_Ortrancl__refl_0,
    [final] ).

cnf(i_0_587,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    cls_Nitpick_Ortranclp__def_1,
    [final] ).

cnf(i_0_588,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_589,axiom,
    ( X3 = X4
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    cls_class__ringb_Oadd__cancel_0,
    [final] ).

cnf(i_0_590,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_591,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_592,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_593,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_594,axiom,
    ( X3 = c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2)
    | c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) != c_List_Orev(X3,X2) ),
    cls_singleton__rev__conv_0,
    [final] ).

cnf(i_0_595,axiom,
    ( X1 = c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2)
    | c_List_Orev(X1,X2) != c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2) ),
    cls_rev__singleton__conv_0,
    [final] ).

cnf(i_0_596,axiom,
    ( X2 = X5
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
    cls_replicate__eq__replicate_1,
    [final] ).

cnf(i_0_597,axiom,
    c_List_Orev(c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(X1,X2,X3),
    cls_rev__replicate_0,
    [final] ).

cnf(i_0_598,axiom,
    ( X2 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
    cls_add__right__cancel_0,
    [final] ).

cnf(i_0_599,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    cls_add__left__cancel_0,
    [final] ).

cnf(i_0_600,axiom,
    ( X3 = X4
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    cls_add__imp__eq_0,
    [final] ).

cnf(i_0_601,axiom,
    ( X1 = X4
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X4,X2,X3) ),
    cls_append__same__eq_0,
    [final] ).

cnf(i_0_602,axiom,
    ( X1 = X4
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    cls_list_Oinject_0,
    [final] ).

cnf(i_0_603,axiom,
    ( X1 = X4
    | c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3) ),
    cls_replicate__eq__replicate_0,
    [final] ).

cnf(i_0_604,axiom,
    ( X2 = X4
    | c_List_Oappend(X1,X2,X3) != c_List_Oappend(X1,X4,X3) ),
    cls_same__append__eq_0,
    [final] ).

cnf(i_0_605,axiom,
    ( X2 = X5
    | c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_OCons(X4,X5,X3) ),
    cls_list_Oinject_1,
    [final] ).

cnf(i_0_606,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2)) ),
    cls_ATP__Linkup_Ofequal__imp__equal_0,
    [final] ).

cnf(i_0_607,axiom,
    c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_ONil(X3),
    cls_take__Cons_H_0,
    [final] ).

cnf(i_0_608,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_609,axiom,
    c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
    cls_conversep__conversep_0,
    [final] ).

cnf(i_0_610,axiom,
    ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
    cls_beta__cases_I1_J_0,
    [final] ).

cnf(i_0_611,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_612,axiom,
    c_List_Obutlast(c_List_Oappend(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Obutlast(X1,X2),
    cls_butlast__append_0,
    [final] ).

cnf(i_0_613,axiom,
    c_List_Olast(c_List_Oappend(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olast(X1,X2),
    cls_last__append_0,
    [final] ).

cnf(i_0_614,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_615,axiom,
    ( c_List_Olast(c_List_Oappend(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | X2 = c_List_Olist_ONil(X3) ),
    cls_last__append_1,
    [final] ).

cnf(i_0_616,axiom,
    ( c_List_Olast(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olast(X2,X3)
    | X2 = c_List_Olist_ONil(X3) ),
    cls_last_Osimps_1,
    [final] ).

cnf(i_0_617,axiom,
    c_List_Obutlast(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olist_ONil(X2),
    cls_butlast_Osimps_I2_J_0,
    [final] ).

cnf(i_0_618,axiom,
    c_List_Olast(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = X1,
    cls_last_Osimps_0,
    [final] ).

cnf(i_0_619,axiom,
    c_Nat_Osize__class_Osize(c_List_Oreplicate(X1,X2,X3),tc_List_Olist(X3)) = X1,
    cls_length__replicate_0,
    [final] ).

cnf(i_0_620,axiom,
    ( c_List_Olast(c_List_Oreplicate(X1,X2,X3),X3) = X2
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    cls_last__replicate_0,
    [final] ).

cnf(i_0_621,axiom,
    ( hBOOL(hAPP(X1,X4))
    | hBOOL(hAPP(X1,X2))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3) ),
    cls_type__induct_0,
    [final] ).

cnf(i_0_622,axiom,
    ( hBOOL(hAPP(X1,X4))
    | hBOOL(hAPP(X1,X3))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3) ),
    cls_type__induct_1,
    [final] ).

cnf(i_0_623,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_624,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_625,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_626,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_627,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_628,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_629,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_630,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_631,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_632,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_633,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_634,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_635,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2),
    cls_replicate__eq__replicate_2,
    [final] ).

cnf(i_0_636,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__commute_0,
    [final] ).

cnf(i_0_637,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__c_0,
    [final] ).

cnf(i_0_638,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I24_J_0,
    [final] ).

cnf(i_0_639,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    cls_typing__elims_I1_J_0,
    [final] ).

cnf(i_0_640,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_641,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_642,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_643,axiom,
    hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
    cls_ATP__Linkup_Oequal__imp__fequal_0,
    [final] ).

cnf(i_0_644,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
    cls_class__ringb_Oadd__r0__iff_0,
    [final] ).

cnf(i_0_645,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Otake(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    cls_take__eq__Nil_0,
    [final] ).

cnf(i_0_646,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_double__eq__0__iff_0,
    [final] ).

cnf(i_0_647,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_648,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Type_Osko__Type__Xtype__induct__1__1(X1))) ),
    cls_type__induct_2,
    [final] ).

cnf(i_0_649,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_650,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_651,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_652,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_653,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    cls_replicate__empty_0,
    [final] ).

cnf(i_0_654,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Olist_ONil(X1) != c_List_Oreplicate(X2,X3,X1) ),
    cls_empty__replicate_0,
    [final] ).

cnf(i_0_655,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_linorder__neq__iff_1,
    [final] ).

cnf(i_0_656,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__irrefl_0,
    [final] ).

cnf(i_0_657,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
    cls_order__less__le_1,
    [final] ).

cnf(i_0_658,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_659,axiom,
    ( X1 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != X2 ),
    cls_append__self__conv2_0,
    [final] ).

cnf(i_0_660,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | c_List_Oappend(X1,X2,X3) != X1 ),
    cls_append__self__conv_0,
    [final] ).

cnf(i_0_661,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 != c_List_Oappend(X1,X2,X3) ),
    cls_self__append__conv_0,
    [final] ).

cnf(i_0_662,axiom,
    ( X2 = c_List_Olist_ONil(X3)
    | X1 != c_List_Oappend(X2,X1,X3) ),
    cls_self__append__conv2_0,
    [final] ).

cnf(i_0_663,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    cls_neq__Nil__conv_1,
    [final] ).

cnf(i_0_664,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    cls_list_Osimps_I3_J_0,
    [final] ).

cnf(i_0_665,axiom,
    c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
    cls_list_Osimps_I2_J_0,
    [final] ).

cnf(i_0_666,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_667,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    cls_not__less0_0,
    [final] ).

cnf(i_0_668,axiom,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    cls_not__Cons__self2_0,
    [final] ).

cnf(i_0_669,axiom,
    X1 != c_List_Olist_OCons(X2,X1,X3),
    cls_not__Cons__self_0,
    [final] ).

cnf(i_0_670,axiom,
    c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
    cls_typing_OVar_0,
    [final] ).

cnf(i_0_671,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_less__not__refl_0,
    [final] ).

cnf(i_0_672,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    cls_nat__less__le_1,
    [final] ).

cnf(i_0_673,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    cls_Lambda_0,
    [final] ).

cnf(i_0_674,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    cls_double__eq__0__iff_1,
    [final] ).

cnf(i_0_675,axiom,
    c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
    cls_subst__lift_0,
    [final] ).

cnf(i_0_676,axiom,
    ( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    cls_class__ringb_Oadd__r0__iff_1,
    [final] ).

cnf(i_0_677,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_add__0__left_0,
    [final] ).

cnf(i_0_678,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__1_0,
    [final] ).

cnf(i_0_679,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I5_J_0,
    [final] ).

cnf(i_0_680,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__0_0,
    [final] ).

cnf(i_0_681,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_682,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_683,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    cls_monoid__add__class_Oadd__0__right_0,
    [final] ).

cnf(i_0_684,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_comm__monoid__add_Omult__1__right_0,
    [final] ).

cnf(i_0_685,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I6_J_0,
    [final] ).

cnf(i_0_686,axiom,
    c_Nat_Osize__class_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),
    cls_length__rev_0,
    [final] ).

cnf(i_0_687,axiom,
    c_Nat_Osize__class_Osize(c_List_Orotate1(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),
    cls_length__rotate1_0,
    [final] ).

cnf(i_0_688,axiom,
    c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
    cls_conversep__eq_0,
    [final] ).

cnf(i_0_689,axiom,
    c_List_Otake(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
    cls_take__eq__Nil_2,
    [final] ).

cnf(i_0_690,axiom,
    hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != c_Type_Otype_OAtom(X3),
    cls_type_Osimps_I4_J_0,
    [final] ).

cnf(i_0_691,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
    cls_dB_Osimps_I5_J_0,
    [final] ).

cnf(i_0_692,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
    cls_dB_Osimps_I8_J_0,
    [final] ).

cnf(i_0_693,axiom,
    c_Type_Otype_OAtom(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3),
    cls_type_Osimps_I3_J_0,
    [final] ).

cnf(i_0_694,axiom,
    c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    cls_dB_Osimps_I4_J_0,
    [final] ).

cnf(i_0_695,axiom,
    c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
    cls_dB_Osimps_I9_J_0,
    [final] ).

cnf(i_0_696,axiom,
    c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
    cls_take__0_0,
    [final] ).

cnf(i_0_697,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
    cls_replicate__empty_1,
    [final] ).

cnf(i_0_698,axiom,
    c_List_Olist_ONil(X1) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X2,X1),
    cls_empty__replicate_1,
    [final] ).

cnf(i_0_699,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
    cls_subst__eq_0,
    [final] ).

cnf(i_0_700,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),X2,X1) = X2,
    cls_append__Nil_0,
    [final] ).

cnf(i_0_701,axiom,
    c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
    cls_append__Nil2_0,
    [final] ).

cnf(i_0_702,axiom,
    X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
    cls_self__append__conv2_1,
    [final] ).

cnf(i_0_703,axiom,
    X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
    cls_eq__Nil__appendI_0,
    [final] ).

cnf(i_0_704,axiom,
    X1 = c_List_Oappend(X1,c_List_Olist_ONil(X2),X2),
    cls_self__append__conv_1,
    [final] ).

cnf(i_0_705,axiom,
    c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
    cls_listsp_ONil_0,
    [final] ).

cnf(i_0_706,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_707,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_708,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_709,axiom,
    c_Type_Otyping(v_ea______,v_ua______,v_T____),
    cls_Var_I4_J_0,
    [final] ).

cnf(i_0_710,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    cls_uT_0,
    [final] ).

cnf(i_0_711,axiom,
    v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),
    cls_Cons_0,
    [final] ).

cnf(i_0_712,axiom,
    ( X1 = X3
    | c_List_Orev(X1,X2) != c_List_Orev(X3,X2) ),
    cls_rev__is__rev__conv_0,
    [final] ).

cnf(i_0_713,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_714,axiom,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    cls_rev__rev__ident_0,
    [final] ).

cnf(i_0_715,axiom,
    c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
    cls_rev__swap_1,
    [final] ).

cnf(i_0_716,axiom,
    X1 = c_List_Orev(c_List_Orev(X1,X2),X2),
    cls_rev__swap_0,
    [final] ).

cnf(i_0_717,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
    cls_Var__IT_0,
    [final] ).

cnf(i_0_718,axiom,
    ( class_Orderings_Opreorder(tc_fun(X1,X2))
    | ~ class_Orderings_Opreorder(X2) ),
    clsarity_fun__Orderings_Opreorder,
    [final] ).

cnf(i_0_719,axiom,
    ( class_Orderings_Oorder(tc_fun(X1,X2))
    | ~ class_Orderings_Oorder(X2) ),
    clsarity_fun__Orderings_Oorder,
    [final] ).

cnf(i_0_720,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Orev(X1,X2) != c_List_Olist_ONil(X2) ),
    cls_rev__is__Nil__conv_0,
    [final] ).

cnf(i_0_721,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Orotate1(X1,X2) != c_List_Olist_ONil(X2) ),
    cls_rotate1__is__Nil__conv_0,
    [final] ).

cnf(i_0_722,axiom,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Orev(X2,X1) ),
    cls_Nil__is__rev__conv_0,
    [final] ).

cnf(i_0_723,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_724,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_725,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
    cls_Var_I3_J_0,
    [final] ).

cnf(i_0_726,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    cls_uIT_0,
    [final] ).

cnf(i_0_727,axiom,
    c_List_Obutlast(c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    cls_butlast_Osimps_I1_J_0,
    [final] ).

cnf(i_0_728,axiom,
    c_List_Orev(c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    cls_rev__is__Nil__conv_1,
    [final] ).

cnf(i_0_729,axiom,
    c_List_Orotate1(c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    cls_rotate__simps_0,
    [final] ).

cnf(i_0_730,axiom,
    c_List_Olist_ONil(X1) = c_List_Orev(c_List_Olist_ONil(X1),X1),
    cls_Nil__is__rev__conv_1,
    [final] ).

cnf(i_0_731,axiom,
    ( X1 = X2
    | c_Type_Otype_OAtom(X1) != c_Type_Otype_OAtom(X2) ),
    cls_type_Osimps_I1_J_0,
    [final] ).

cnf(i_0_732,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    cls_dB_Osimps_I1_J_0,
    [final] ).

cnf(i_0_733,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    cls_dB_Osimps_I3_J_0,
    [final] ).

cnf(i_0_734,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    cls_dB_Osimps_I6_J_0,
    [final] ).

cnf(i_0_735,axiom,
    c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
    cls_dB_Osimps_I7_J_0,
    [final] ).

cnf(i_0_736,axiom,
    class_Orderings_Olinorder(tc_nat),
    clsarity_nat__Orderings_Olinorder,
    [final] ).

cnf(i_0_737,axiom,
    class_Orderings_Opreorder(tc_bool),
    clsarity_bool__Orderings_Opreorder,
    [final] ).

cnf(i_0_738,axiom,
    class_Orderings_Opreorder(tc_nat),
    clsarity_nat__Orderings_Opreorder,
    [final] ).

cnf(i_0_739,axiom,
    class_Orderings_Oorder(tc_bool),
    clsarity_bool__Orderings_Oorder,
    [final] ).

cnf(i_0_740,axiom,
    class_Orderings_Oorder(tc_nat),
    clsarity_nat__Orderings_Oorder,
    [final] ).

cnf(i_0_741,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Osemiring__1,
    [final] ).

cnf(i_0_742,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
    [final] ).

cnf(i_0_743,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    clsarity_nat__Ring__and__Field_Oordered__semidom,
    [final] ).

cnf(i_0_744,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    [final] ).

cnf(i_0_745,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
    [final] ).

cnf(i_0_746,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    clsarity_nat__Nat_Osemiring__char__0,
    [final] ).

cnf(i_0_747,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Osemigroup__add,
    [final] ).

cnf(i_0_748,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Omonoid__add,
    [final] ).

cnf(i_0_749,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
    [final] ).

cnf(i_0_750,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
    [final] ).

cnf(i_0_751,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    clsarity_nat__OrderedGroup_Oab__semigroup__add,
    [final] ).

cnf(i_0_752,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    clsarity_nat__OrderedGroup_Ocomm__monoid__add,
    [final] ).

cnf(i_0_753,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
    [final] ).

cnf(i_0_754,negated_conjecture,
    ~ v_thesis____,
    cls_conjecture_0,
    [final] ).

cnf(i_0_755,axiom,
    v_n____ = v_i____,
    cls_True_0,
    [final] ).

cnf(i_0_756,axiom,
    X1 = X1 ).

cnf(i_0_757,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_758,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_759,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X1,X3,X4,X5,X6) = c_List_Ofoldr(X2,X3,X4,X5,X6) ) ).

cnf(i_0_760,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X1,X4,X5,X6) = c_List_Ofoldr(X3,X2,X4,X5,X6) ) ).

cnf(i_0_761,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X1,X5,X6) = c_List_Ofoldr(X3,X4,X2,X5,X6) ) ).

cnf(i_0_762,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X1,X6) = c_List_Ofoldr(X3,X4,X5,X2,X6) ) ).

cnf(i_0_763,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X6,X1) = c_List_Ofoldr(X3,X4,X5,X6,X2) ) ).

cnf(i_0_764,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_765,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__rec(X1,X3,X4,X5,X6) = c_Lambda_OdB_OdB__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_766,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__rec(X3,X1,X4,X5,X6) = c_Lambda_OdB_OdB__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_767,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__rec(X3,X4,X1,X5,X6) = c_Lambda_OdB_OdB__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_768,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__rec(X3,X4,X5,X1,X6) = c_Lambda_OdB_OdB__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_769,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__rec(X3,X4,X5,X6,X1) = c_Lambda_OdB_OdB__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_770,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__case(X1,X3,X4,X5,X6) = c_Lambda_OdB_OdB__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_771,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__case(X3,X1,X4,X5,X6) = c_Lambda_OdB_OdB__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_772,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__case(X3,X4,X1,X5,X6) = c_Lambda_OdB_OdB__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_773,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__case(X3,X4,X5,X1,X6) = c_Lambda_OdB_OdB__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_774,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__case(X3,X4,X5,X6,X1) = c_Lambda_OdB_OdB__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_775,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_776,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_777,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_778,axiom,
    ( X1 != X2
    | c_List_Oappend(X1,X3,X4) = c_List_Oappend(X2,X3,X4) ) ).

cnf(i_0_779,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X1,X4) = c_List_Oappend(X3,X2,X4) ) ).

cnf(i_0_780,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X4,X1) = c_List_Oappend(X3,X4,X2) ) ).

cnf(i_0_781,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X1,X3,X4) = c_List_Olist_OCons(X2,X3,X4) ) ).

cnf(i_0_782,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X3,X1,X4) = c_List_Olist_OCons(X3,X2,X4) ) ).

cnf(i_0_783,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X3,X4,X1) = c_List_Olist_OCons(X3,X4,X2) ) ).

cnf(i_0_784,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_785,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__case(X1,X3,X4,X5) = c_Type_Otype_Otype__case(X2,X3,X4,X5) ) ).

cnf(i_0_786,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__case(X3,X1,X4,X5) = c_Type_Otype_Otype__case(X3,X2,X4,X5) ) ).

cnf(i_0_787,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__case(X3,X4,X1,X5) = c_Type_Otype_Otype__case(X3,X4,X2,X5) ) ).

cnf(i_0_788,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__case(X3,X4,X5,X1) = c_Type_Otype_Otype__case(X3,X4,X5,X2) ) ).

cnf(i_0_789,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__rec(X1,X3,X4,X5) = c_Type_Otype_Otype__rec(X2,X3,X4,X5) ) ).

cnf(i_0_790,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__rec(X3,X1,X4,X5) = c_Type_Otype_Otype__rec(X3,X2,X4,X5) ) ).

cnf(i_0_791,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__rec(X3,X4,X1,X5) = c_Type_Otype_Otype__rec(X3,X4,X2,X5) ) ).

cnf(i_0_792,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__rec(X3,X4,X5,X1) = c_Type_Otype_Otype__rec(X3,X4,X5,X2) ) ).

cnf(i_0_793,axiom,
    ( X1 != X2
    | c_Type_Otype_OAtom(X1) = c_Type_Otype_OAtom(X2) ) ).

cnf(i_0_794,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).

cnf(i_0_795,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).

cnf(i_0_796,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).

cnf(i_0_797,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).

cnf(i_0_798,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).

cnf(i_0_799,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X1,X3) = c_Lambda_Olift(X2,X3) ) ).

cnf(i_0_800,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X3,X1) = c_Lambda_Olift(X3,X2) ) ).

cnf(i_0_801,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_802,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_803,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_804,axiom,
    ( X1 != X2
    | c_List_Orev(X1,X3) = c_List_Orev(X2,X3) ) ).

cnf(i_0_805,axiom,
    ( X1 != X2
    | c_List_Orev(X3,X1) = c_List_Orev(X3,X2) ) ).

cnf(i_0_806,axiom,
    ( X1 != X2
    | c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).

cnf(i_0_807,axiom,
    ( X1 != X2
    | c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).

cnf(i_0_808,axiom,
    ( X1 != X2
    | c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).

cnf(i_0_809,axiom,
    ( X1 != X2
    | c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).

cnf(i_0_810,axiom,
    ( X1 != X2
    | c_List_Orotate1(X1,X3) = c_List_Orotate1(X2,X3) ) ).

cnf(i_0_811,axiom,
    ( X1 != X2
    | c_List_Orotate1(X3,X1) = c_List_Orotate1(X3,X2) ) ).

cnf(i_0_812,axiom,
    ( X1 != X2
    | c_List_Otake(X1,X3,X4) = c_List_Otake(X2,X3,X4) ) ).

cnf(i_0_813,axiom,
    ( X1 != X2
    | c_List_Otake(X3,X1,X4) = c_List_Otake(X3,X2,X4) ) ).

cnf(i_0_814,axiom,
    ( X1 != X2
    | c_List_Otake(X3,X4,X1) = c_List_Otake(X3,X4,X2) ) ).

cnf(i_0_815,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_816,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_817,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_818,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_819,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_820,axiom,
    ( X1 != X2
    | c_fequal(X1) = c_fequal(X2) ) ).

cnf(i_0_821,axiom,
    ( X1 != X2
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) = c_Type_Osko__Type__Xtype__induct__1__1(X2) ) ).

cnf(i_0_822,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_823,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_824,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X1,X3) = c_Transitive__Closure_Ortranclp(X2,X3) ) ).

cnf(i_0_825,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X3,X1) = c_Transitive__Closure_Ortranclp(X3,X2) ) ).

cnf(i_0_826,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_827,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X1,X3,X4) = c_Lambda_Osubst(X2,X3,X4) ) ).

cnf(i_0_828,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X1,X4) = c_Lambda_Osubst(X3,X2,X4) ) ).

cnf(i_0_829,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X4,X1) = c_Lambda_Osubst(X3,X4,X2) ) ).

cnf(i_0_830,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X1,X3,X4)
    | c_Type_Otyping(X2,X3,X4) ) ).

cnf(i_0_831,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X1,X4)
    | c_Type_Otyping(X3,X2,X4) ) ).

cnf(i_0_832,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X4,X1)
    | c_Type_Otyping(X3,X4,X2) ) ).

cnf(i_0_833,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_834,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_835,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_836,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_837,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_838,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_839,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_840,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_841,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_842,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_843,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_844,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_845,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X1,X3,X4)
    | c_Type_Otypings(X2,X3,X4) ) ).

cnf(i_0_846,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X1,X4)
    | c_Type_Otypings(X3,X2,X4) ) ).

cnf(i_0_847,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X4,X1)
    | c_Type_Otypings(X3,X4,X2) ) ).

cnf(i_0_848,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_849,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_850,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_851,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_852,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_853,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

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

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

cnf(i_0_856,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_857,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_858,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_859,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X1,X3,X4,X5)
    | c_ListOrder_Ostep1(X2,X3,X4,X5) ) ).

cnf(i_0_860,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X1,X4,X5)
    | c_ListOrder_Ostep1(X3,X2,X4,X5) ) ).

cnf(i_0_861,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X1,X5)
    | c_ListOrder_Ostep1(X3,X4,X2,X5) ) ).

cnf(i_0_862,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X5,X1)
    | c_ListOrder_Ostep1(X3,X4,X5,X2) ) ).

cnf(i_0_863,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X1,X3,X4)
    | c_Wellfounded_Oaccp(X2,X3,X4) ) ).

cnf(i_0_864,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X1,X4)
    | c_Wellfounded_Oaccp(X3,X2,X4) ) ).

cnf(i_0_865,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X4,X1)
    | c_Wellfounded_Oaccp(X3,X4,X2) ) ).

cnf(i_0_866,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X1,X3,X4)
    | c_List_Olistsp(X2,X3,X4) ) ).

cnf(i_0_867,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X1,X4)
    | c_List_Olistsp(X3,X2,X4) ) ).

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

cnf(i_0_869,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Osemigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X2) ) ).

cnf(i_0_870,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_756_001,axiom,
    X1 = X1 ).

cnf(i_0_757_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_758_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_759_004,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X1,X3,X4,X5,X6) = c_List_Ofoldr(X2,X3,X4,X5,X6) ) ).

cnf(i_0_760_005,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X1,X4,X5,X6) = c_List_Ofoldr(X3,X2,X4,X5,X6) ) ).

cnf(i_0_761_006,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X1,X5,X6) = c_List_Ofoldr(X3,X4,X2,X5,X6) ) ).

cnf(i_0_762_007,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X1,X6) = c_List_Ofoldr(X3,X4,X5,X2,X6) ) ).

cnf(i_0_763_008,axiom,
    ( X1 != X2
    | c_List_Ofoldr(X3,X4,X5,X6,X1) = c_List_Ofoldr(X3,X4,X5,X6,X2) ) ).

cnf(i_0_764_009,axiom,
    ( X1 != X2
    | c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).

cnf(i_0_765_010,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__rec(X1,X3,X4,X5,X6) = c_Lambda_OdB_OdB__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_766_011,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__rec(X3,X1,X4,X5,X6) = c_Lambda_OdB_OdB__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_767_012,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__rec(X3,X4,X1,X5,X6) = c_Lambda_OdB_OdB__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_768_013,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__rec(X3,X4,X5,X1,X6) = c_Lambda_OdB_OdB__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_769_014,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__rec(X3,X4,X5,X6,X1) = c_Lambda_OdB_OdB__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_770_015,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__case(X1,X3,X4,X5,X6) = c_Lambda_OdB_OdB__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_771_016,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__case(X3,X1,X4,X5,X6) = c_Lambda_OdB_OdB__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_772_017,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__case(X3,X4,X1,X5,X6) = c_Lambda_OdB_OdB__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_773_018,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__case(X3,X4,X5,X1,X6) = c_Lambda_OdB_OdB__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_774_019,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OdB__case(X3,X4,X5,X6,X1) = c_Lambda_OdB_OdB__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_775_020,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_776_021,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_777_022,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_778_023,axiom,
    ( X1 != X2
    | c_List_Oappend(X1,X3,X4) = c_List_Oappend(X2,X3,X4) ) ).

cnf(i_0_779_024,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X1,X4) = c_List_Oappend(X3,X2,X4) ) ).

cnf(i_0_780_025,axiom,
    ( X1 != X2
    | c_List_Oappend(X3,X4,X1) = c_List_Oappend(X3,X4,X2) ) ).

cnf(i_0_781_026,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X1,X3,X4) = c_List_Olist_OCons(X2,X3,X4) ) ).

cnf(i_0_782_027,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X3,X1,X4) = c_List_Olist_OCons(X3,X2,X4) ) ).

cnf(i_0_783_028,axiom,
    ( X1 != X2
    | c_List_Olist_OCons(X3,X4,X1) = c_List_Olist_OCons(X3,X4,X2) ) ).

cnf(i_0_784_029,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_785_030,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__case(X1,X3,X4,X5) = c_Type_Otype_Otype__case(X2,X3,X4,X5) ) ).

cnf(i_0_786_031,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__case(X3,X1,X4,X5) = c_Type_Otype_Otype__case(X3,X2,X4,X5) ) ).

cnf(i_0_787_032,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__case(X3,X4,X1,X5) = c_Type_Otype_Otype__case(X3,X4,X2,X5) ) ).

cnf(i_0_788_033,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__case(X3,X4,X5,X1) = c_Type_Otype_Otype__case(X3,X4,X5,X2) ) ).

cnf(i_0_789_034,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__rec(X1,X3,X4,X5) = c_Type_Otype_Otype__rec(X2,X3,X4,X5) ) ).

cnf(i_0_790_035,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__rec(X3,X1,X4,X5) = c_Type_Otype_Otype__rec(X3,X2,X4,X5) ) ).

cnf(i_0_791_036,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__rec(X3,X4,X1,X5) = c_Type_Otype_Otype__rec(X3,X4,X2,X5) ) ).

cnf(i_0_792_037,axiom,
    ( X1 != X2
    | c_Type_Otype_Otype__rec(X3,X4,X5,X1) = c_Type_Otype_Otype__rec(X3,X4,X5,X2) ) ).

cnf(i_0_793_038,axiom,
    ( X1 != X2
    | c_Type_Otype_OAtom(X1) = c_Type_Otype_OAtom(X2) ) ).

cnf(i_0_794_039,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).

cnf(i_0_795_040,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).

cnf(i_0_796_041,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).

cnf(i_0_797_042,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).

cnf(i_0_798_043,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).

cnf(i_0_799_044,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X1,X3) = c_Lambda_Olift(X2,X3) ) ).

cnf(i_0_800_045,axiom,
    ( X1 != X2
    | c_Lambda_Olift(X3,X1) = c_Lambda_Olift(X3,X2) ) ).

cnf(i_0_801_046,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_802_047,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_803_048,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_804_049,axiom,
    ( X1 != X2
    | c_List_Orev(X1,X3) = c_List_Orev(X2,X3) ) ).

cnf(i_0_805_050,axiom,
    ( X1 != X2
    | c_List_Orev(X3,X1) = c_List_Orev(X3,X2) ) ).

cnf(i_0_806_051,axiom,
    ( X1 != X2
    | c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).

cnf(i_0_807_052,axiom,
    ( X1 != X2
    | c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).

cnf(i_0_808_053,axiom,
    ( X1 != X2
    | c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).

cnf(i_0_809_054,axiom,
    ( X1 != X2
    | c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).

cnf(i_0_810_055,axiom,
    ( X1 != X2
    | c_List_Orotate1(X1,X3) = c_List_Orotate1(X2,X3) ) ).

cnf(i_0_811_056,axiom,
    ( X1 != X2
    | c_List_Orotate1(X3,X1) = c_List_Orotate1(X3,X2) ) ).

cnf(i_0_812_057,axiom,
    ( X1 != X2
    | c_List_Otake(X1,X3,X4) = c_List_Otake(X2,X3,X4) ) ).

cnf(i_0_813_058,axiom,
    ( X1 != X2
    | c_List_Otake(X3,X1,X4) = c_List_Otake(X3,X2,X4) ) ).

cnf(i_0_814_059,axiom,
    ( X1 != X2
    | c_List_Otake(X3,X4,X1) = c_List_Otake(X3,X4,X2) ) ).

cnf(i_0_815_060,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).

cnf(i_0_816_061,axiom,
    ( X1 != X2
    | c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).

cnf(i_0_817_062,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).

cnf(i_0_818_063,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).

cnf(i_0_819_064,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).

cnf(i_0_820_065,axiom,
    ( X1 != X2
    | c_fequal(X1) = c_fequal(X2) ) ).

cnf(i_0_821_066,axiom,
    ( X1 != X2
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) = c_Type_Osko__Type__Xtype__induct__1__1(X2) ) ).

cnf(i_0_822_067,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_823_068,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_824_069,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X1,X3) = c_Transitive__Closure_Ortranclp(X2,X3) ) ).

cnf(i_0_825_070,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortranclp(X3,X1) = c_Transitive__Closure_Ortranclp(X3,X2) ) ).

cnf(i_0_826_071,axiom,
    ( X1 != X2
    | c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).

cnf(i_0_827_072,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X1,X3,X4) = c_Lambda_Osubst(X2,X3,X4) ) ).

cnf(i_0_828_073,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X1,X4) = c_Lambda_Osubst(X3,X2,X4) ) ).

cnf(i_0_829_074,axiom,
    ( X1 != X2
    | c_Lambda_Osubst(X3,X4,X1) = c_Lambda_Osubst(X3,X4,X2) ) ).

cnf(i_0_830_075,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X1,X3,X4)
    | c_Type_Otyping(X2,X3,X4) ) ).

cnf(i_0_831_076,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X1,X4)
    | c_Type_Otyping(X3,X2,X4) ) ).

cnf(i_0_832_077,axiom,
    ( X1 != X2
    | ~ c_Type_Otyping(X3,X4,X1)
    | c_Type_Otyping(X3,X4,X2) ) ).

cnf(i_0_833_078,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X2) ) ).

cnf(i_0_834_079,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).

cnf(i_0_835_080,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X2,X3,X4) ) ).

cnf(i_0_836_081,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X1,X4)
    | c_HOL_Oord__class_Oless(X3,X2,X4) ) ).

cnf(i_0_837_082,axiom,
    ( X1 != X2
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X2) ) ).

cnf(i_0_838_083,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_839_084,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_840_085,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X2) ) ).

cnf(i_0_841_086,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X2) ) ).

cnf(i_0_842_087,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).

cnf(i_0_843_088,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semidom(X2) ) ).

cnf(i_0_844_089,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | class_OrderedGroup_Olordered__ab__group__add(X2) ) ).

cnf(i_0_845_090,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X1,X3,X4)
    | c_Type_Otypings(X2,X3,X4) ) ).

cnf(i_0_846_091,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X1,X4)
    | c_Type_Otypings(X3,X2,X4) ) ).

cnf(i_0_847_092,axiom,
    ( X1 != X2
    | ~ c_Type_Otypings(X3,X4,X1)
    | c_Type_Otypings(X3,X4,X2) ) ).

cnf(i_0_848_093,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__idom(X2) ) ).

cnf(i_0_849_094,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_850_095,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_851_096,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oidom(X2) ) ).

cnf(i_0_852_097,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_853_098,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_854_099,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_855_100,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_856_101,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_857_102,axiom,
    ( X1 != X2
    | ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X2) ) ).

cnf(i_0_858_103,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_859_104,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X1,X3,X4,X5)
    | c_ListOrder_Ostep1(X2,X3,X4,X5) ) ).

cnf(i_0_860_105,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X1,X4,X5)
    | c_ListOrder_Ostep1(X3,X2,X4,X5) ) ).

cnf(i_0_861_106,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X1,X5)
    | c_ListOrder_Ostep1(X3,X4,X2,X5) ) ).

cnf(i_0_862_107,axiom,
    ( X1 != X2
    | ~ c_ListOrder_Ostep1(X3,X4,X5,X1)
    | c_ListOrder_Ostep1(X3,X4,X5,X2) ) ).

cnf(i_0_863_108,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X1,X3,X4)
    | c_Wellfounded_Oaccp(X2,X3,X4) ) ).

cnf(i_0_864_109,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X1,X4)
    | c_Wellfounded_Oaccp(X3,X2,X4) ) ).

cnf(i_0_865_110,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oaccp(X3,X4,X1)
    | c_Wellfounded_Oaccp(X3,X4,X2) ) ).

cnf(i_0_866_111,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X1,X3,X4)
    | c_List_Olistsp(X2,X3,X4) ) ).

cnf(i_0_867_112,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X1,X4)
    | c_List_Olistsp(X3,X2,X4) ) ).

cnf(i_0_868_113,axiom,
    ( X1 != X2
    | ~ c_List_Olistsp(X3,X4,X1)
    | c_List_Olistsp(X3,X4,X2) ) ).

cnf(i_0_869_114,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Osemigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X2) ) ).

cnf(i_0_870_115,axiom,
    ( X1 != X2
    | ~ class_OrderedGroup_Omonoid__add(X1)
    | class_OrderedGroup_Omonoid__add(X2) ) ).

cnf(i_0_871,plain,
    X1 = X1,
    inference(equality_inference,[],[406]) ).

cnf(i_0_872,plain,
    X1 = X1,
    inference(equality_inference,[],[407]) ).

cnf(i_0_873,plain,
    X1 = X1,
    inference(equality_inference,[],[408]) ).

cnf(i_0_874,plain,
    X1 = X1,
    inference(equality_inference,[],[409]) ).

cnf(i_0_875,plain,
    X1 = X1,
    inference(equality_inference,[],[412]) ).

cnf(i_0_876,plain,
    X1 = X1,
    inference(equality_inference,[],[498]) ).

cnf(i_0_877,plain,
    X1 = X1,
    inference(equality_inference,[],[499]) ).

cnf(i_0_878,plain,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
    inference(equality_inference,[],[523]) ).

cnf(i_0_879,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | X2 = X2
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(equality_inference,[],[589]) ).

cnf(i_0_880,plain,
    ( X1 = X1
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(equality_inference,[],[596]) ).

cnf(i_0_881,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[598]) ).

cnf(i_0_882,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[599]) ).

cnf(i_0_883,plain,
    ( X1 = X1
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[600]) ).

cnf(i_0_884,plain,
    X1 = X1,
    inference(equality_inference,[],[601]) ).

cnf(i_0_885,plain,
    X1 = X1,
    inference(equality_inference,[],[602]) ).

cnf(i_0_886,plain,
    X1 = X1,
    inference(equality_inference,[],[603]) ).

cnf(i_0_887,plain,
    X1 = X1,
    inference(equality_inference,[],[604]) ).

cnf(i_0_888,plain,
    X1 = X1,
    inference(equality_inference,[],[605]) ).

cnf(i_0_889,plain,
    X1 = X1,
    inference(equality_inference,[],[630]) ).

cnf(i_0_890,plain,
    X1 = X1,
    inference(equality_inference,[],[631]) ).

cnf(i_0_891,plain,
    X1 = X1,
    inference(equality_inference,[],[632]) ).

cnf(i_0_892,plain,
    X1 = X1,
    inference(equality_inference,[],[633]) ).

cnf(i_0_893,plain,
    ( X1 = X1
    | ~ class_Nat_Osemiring__char__0(X2) ),
    inference(equality_inference,[],[708]) ).

cnf(i_0_894,plain,
    X1 = X1,
    inference(equality_inference,[],[712]) ).

cnf(i_0_895,plain,
    X1 = X1,
    inference(equality_inference,[],[731]) ).

cnf(i_0_896,plain,
    X1 = X1,
    inference(equality_inference,[],[732]) ).

cnf(i_0_897,plain,
    X1 = X1,
    inference(equality_inference,[],[733]) ).

cnf(i_0_898,plain,
    ( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1)
    | ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,X1),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
    inference(scs_inference,[],[i_0_754,i_0_386]) ).

cnf(i_0_899,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_a____)),
    inference(scs_inference,[],[i_0_418,i_0_483]) ).

cnf(i_0_900,plain,
    ( ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
    | c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)) ),
    inference(rename_variables,[],[i_0_483]) ).

cnf(i_0_901,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),c_Lambda_OdB_OdB__case(X3,X4,X5,hAPP(hAPP(c_Lambda_OdB_OApp,X6),X7),t_a)),hAPP(hAPP(X4,X6),X7))),
    inference(scs_inference,[],[i_0_418,i_0_587,i_0_483,i_0_389]) ).

cnf(i_0_902,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    inference(rename_variables,[],[i_0_587]) ).

cnf(i_0_903,plain,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X6),t_a)))
    | hBOOL(hAPP(X1,hAPP(hAPP(X3,X5),X6))) ),
    inference(rename_variables,[],[i_0_389]) ).

cnf(i_0_904,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),c_Lambda_OdB_OdB__case(X3,X4,X5,c_Lambda_OdB_OVar(X6),t_a)),hAPP(X3,X6))),
    inference(scs_inference,[],[i_0_418,i_0_587,i_0_902,i_0_483,i_0_389,i_0_392]) ).

cnf(i_0_905,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    inference(rename_variables,[],[i_0_587]) ).

cnf(i_0_906,plain,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OVar(X5),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X5))) ),
    inference(rename_variables,[],[i_0_392]) ).

cnf(i_0_907,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),c_Lambda_OdB_OdB__case(X3,X4,X5,c_Lambda_OdB_OAbs(X6),t_a)),hAPP(X5,X6))),
    inference(scs_inference,[],[i_0_418,i_0_587,i_0_902,i_0_905,i_0_483,i_0_389,i_0_392,i_0_394]) ).

cnf(i_0_908,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    inference(rename_variables,[],[i_0_587]) ).

cnf(i_0_909,plain,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OAbs(X5),t_a)))
    | hBOOL(hAPP(X1,hAPP(X4,X5))) ),
    inference(rename_variables,[],[i_0_394]) ).

cnf(i_0_910,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_n____,v_rs____),v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396]) ).

cnf(i_0_911,plain,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | 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(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)) ),
    inference(rename_variables,[],[i_0_396]) ).

cnf(i_0_912,plain,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xvar__app__typesE__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_n____,v_rs____)),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403]) ).

cnf(i_0_913,plain,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3)) ),
    inference(rename_variables,[],[i_0_403]) ).

cnf(i_0_914,plain,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404]) ).

cnf(i_0_915,plain,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3)) ),
    inference(rename_variables,[],[i_0_404]) ).

cnf(i_0_916,plain,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xlist__app__typeE__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____)),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405]) ).

cnf(i_0_917,plain,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3)) ),
    inference(rename_variables,[],[i_0_405]) ).

cnf(i_0_918,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),c_Type_Otype_Otype__case(X3,X4,hAPP(hAPP(c_Type_Otype_OFun,X5),X6),t_a)),hAPP(hAPP(X4,X5),X6))),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434]) ).

cnf(i_0_919,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    inference(rename_variables,[],[i_0_587]) ).

cnf(i_0_920,plain,
    ( ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,hAPP(hAPP(c_Type_Otype_OFun,X4),X5),t_a)))
    | hBOOL(hAPP(X1,hAPP(hAPP(X3,X4),X5))) ),
    inference(rename_variables,[],[i_0_434]) ).

cnf(i_0_921,plain,
    c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Olist_OCons(X2,X3,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X4),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_664,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441]) ).

cnf(i_0_922,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    inference(rename_variables,[],[i_0_664]) ).

cnf(i_0_923,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    inference(rename_variables,[],[i_0_441]) ).

cnf(i_0_924,plain,
    c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,c_List_Olist_OCons(X3,X4,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_664,i_0_922,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442]) ).

cnf(i_0_925,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    inference(rename_variables,[],[i_0_664]) ).

cnf(i_0_926,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(rename_variables,[],[i_0_442]) ).

cnf(i_0_927,plain,
    c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,c_List_Olist_OCons(X3,X4,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_664,i_0_922,i_0_925,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443]) ).

cnf(i_0_928,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    inference(rename_variables,[],[i_0_664]) ).

cnf(i_0_929,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(rename_variables,[],[i_0_443]) ).

cnf(i_0_930,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),hAPP(hAPP(X3,X4),X5)),c_Lambda_OdB_OdB__case(X6,X3,X7,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),t_a))),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_664,i_0_922,i_0_925,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444]) ).

cnf(i_0_931,plain,
    ( ~ 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)) ),
    inference(rename_variables,[],[i_0_444]) ).

cnf(i_0_932,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),c_Type_Otype_Otype__case(X3,X4,c_Type_Otype_OAtom(X5),t_a)),hAPP(X3,X5))),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_664,i_0_922,i_0_925,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448]) ).

cnf(i_0_933,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    inference(rename_variables,[],[i_0_587]) ).

cnf(i_0_934,plain,
    ( ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X3,c_Type_Otype_OAtom(X4),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X4))) ),
    inference(rename_variables,[],[i_0_448]) ).

cnf(i_0_935,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,c_Lambda_OdB_OdB__case(X2,X3,X4,c_Lambda_OdB_OVar(X5),t_a),X6)),c_Lambda_Osubst(X1,hAPP(X2,X5),X6))),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_664,i_0_922,i_0_925,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466]) ).

cnf(i_0_936,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4))) ),
    inference(rename_variables,[],[i_0_466]) ).

cnf(i_0_937,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),t_a),X5,X6)),c_Lambda_Osubst(hAPP(X1,X4),X5,X6))),
    inference(scs_inference,[],[i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_664,i_0_922,i_0_925,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467]) ).

cnf(i_0_938,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4))) ),
    inference(rename_variables,[],[i_0_467]) ).

cnf(i_0_939,plain,
    c_Type_Otyping(X1,c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X2)),hAPP(hAPP(c_Type_Otype_OFun,X3),hAPP(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_Type_Otype),X2))),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_664,i_0_922,i_0_925,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469]) ).

cnf(i_0_940,plain,
    c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
    inference(rename_variables,[],[i_0_670]) ).

cnf(i_0_941,plain,
    ( ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4)
    | c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4)) ),
    inference(rename_variables,[],[i_0_469]) ).

cnf(i_0_942,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2)),X3),X4)),c_Lambda_Osubst(X1,c_Lambda_Osubst(X2,X3,c_HOL_Ozero__class_Ozero(tc_nat)),X4))),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472]) ).

cnf(i_0_943,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4))) ),
    inference(rename_variables,[],[i_0_472]) ).

cnf(i_0_944,plain,
    hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,X4)),c_Lambda_Osubst(c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,X4))),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480]) ).

cnf(i_0_945,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4))) ),
    inference(rename_variables,[],[i_0_480]) ).

cnf(i_0_946,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),t_a),X5)),c_Lambda_Olift(hAPP(X1,X4),X5))),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497]) ).

cnf(i_0_947,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3))) ),
    inference(rename_variables,[],[i_0_497]) ).

cnf(i_0_948,plain,
    ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),c_Type_Otype_OAtom(X3)),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508]) ).

cnf(i_0_949,plain,
    c_Type_Otype_OAtom(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X3),
    inference(rename_variables,[],[i_0_693]) ).

cnf(i_0_950,plain,
    ( X1 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X1,X2,X3)),c_Type_Osko__Type__Xtyping__elims__3__2(X1,X2,X3))
    | ~ c_Type_Otyping(X2,c_Lambda_OdB_OAbs(X3),X1) ),
    inference(rename_variables,[],[i_0_508]) ).

cnf(i_0_951,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),t_a))),c_Lambda_OdB_OAbs(hAPP(X1,X4)))),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509]) ).

cnf(i_0_952,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2))) ),
    inference(rename_variables,[],[i_0_509]) ).

cnf(i_0_953,plain,
    hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3)),c_Lambda_Olift(c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3))),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533]) ).

cnf(i_0_954,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3))) ),
    inference(rename_variables,[],[i_0_533]) ).

cnf(i_0_955,plain,
    c_List_Orev(c_List_Olist_OCons(X1,c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil(X3),X3),X3),X5),X3) != c_List_Olist_OCons(X4,X2,X3),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555]) ).

cnf(i_0_956,plain,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(rename_variables,[],[i_0_668]) ).

cnf(i_0_957,plain,
    ( X1 = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil(X3),X3),X3)
    | c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3) ),
    inference(rename_variables,[],[i_0_555]) ).

cnf(i_0_958,plain,
    hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2))),c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))))),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571]) ).

cnf(i_0_959,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2))) ),
    inference(rename_variables,[],[i_0_571]) ).

cnf(i_0_960,plain,
    c_List_Oappend(c_List_Orev(c_List_Olist_ONil(X1),X1),c_List_Olist_OCons(X2,c_List_Olist_ONil(X1),X1),X1) = c_List_Olist_OCons(X2,c_List_Olist_ONil(X1),X1),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595]) ).

cnf(i_0_961,plain,
    c_List_Orev(c_List_Oappend(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    inference(rename_variables,[],[i_0_507]) ).

cnf(i_0_962,plain,
    ( c_List_Orev(X1,X2) != c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2)
    | X1 = c_List_Olist_OCons(X3,c_List_Olist_ONil(X2),X2) ),
    inference(rename_variables,[],[i_0_595]) ).

cnf(i_0_963,plain,
    ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Olist_OCons(X3,hAPP(X1,X2),X4)),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_669,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639]) ).

cnf(i_0_964,plain,
    X1 != c_List_Olist_OCons(X2,X1,X3),
    inference(rename_variables,[],[i_0_669]) ).

cnf(i_0_965,plain,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    inference(rename_variables,[],[i_0_639]) ).

cnf(i_0_966,plain,
    c_List_Oreplicate(c_List_Olist_OCons(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2),X3,X4) != c_List_Olist_ONil(X4),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_956,i_0_669,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653]) ).

cnf(i_0_967,plain,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(rename_variables,[],[i_0_668]) ).

cnf(i_0_968,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    inference(rename_variables,[],[i_0_653]) ).

cnf(i_0_969,plain,
    c_List_Olist_ONil(X1) != c_List_Oreplicate(c_List_Olist_OCons(X2,c_HOL_Ozero__class_Ozero(tc_nat),X3),X4,X1),
    inference(scs_inference,[],[i_0_670,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_956,i_0_967,i_0_669,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654]) ).

cnf(i_0_970,plain,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(rename_variables,[],[i_0_668]) ).

cnf(i_0_971,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Olist_ONil(X2) != c_List_Oreplicate(X1,X3,X2) ),
    inference(rename_variables,[],[i_0_654]) ).

cnf(i_0_972,plain,
    v_i____ = v_n____,
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_956,i_0_967,i_0_669,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757]) ).

cnf(i_0_973,plain,
    c_ListOrder_Ostep1(c_Transitive__Closure_Ortranclp(X1,X2),c_List_Olist_OCons(X3,X4,X5),c_List_Olist_OCons(X3,X4,X5),X5),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_956,i_0_967,i_0_669,i_0_693,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496]) ).

cnf(i_0_974,plain,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X3,X4,X5),X5) ),
    inference(rename_variables,[],[i_0_496]) ).

cnf(i_0_975,plain,
    c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_ua______,tc_Lambda_OdB),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_956,i_0_967,i_0_669,i_0_693,i_0_725,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582]) ).

cnf(i_0_976,plain,
    ( ~ 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) ),
    inference(rename_variables,[],[i_0_582]) ).

cnf(i_0_977,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OdB__case(X1,c_Lambda_OdB_OApp,X2,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),t_a),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_956,i_0_967,i_0_669,i_0_693,i_0_725,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522]) ).

cnf(i_0_978,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | c_Type_Otyping(X3,X2,X4)
    | ~ c_Type_Otyping(X3,X1,X4) ),
    inference(rename_variables,[],[i_0_522]) ).

cnf(i_0_979,plain,
    ~ c_Type_Otyping(v_n____,c_Lambda_OdB_OVar(X1),c_List_Olist_OCons(X2,hAPP(v_i____,X1),X3)),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_956,i_0_967,i_0_669,i_0_693,i_0_725,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830]) ).

cnf(i_0_980,plain,
    ~ c_Type_Otyping(X1,c_Predicate_Oconversep(c_Predicate_Oconversep(c_Lambda_OdB_OAbs(X2),X3,X4),X4,X3),c_Type_Otype_OAtom(X5)),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_609,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_956,i_0_967,i_0_669,i_0_693,i_0_725,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831]) ).

cnf(i_0_981,plain,
    c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
    inference(rename_variables,[],[i_0_609]) ).

cnf(i_0_982,plain,
    ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),c_Predicate_Oconversep(c_Predicate_Oconversep(c_Type_Otype_OAtom(X3),X4,X5),X5,X4)),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_956,i_0_967,i_0_669,i_0_693,i_0_725,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832]) ).

cnf(i_0_983,plain,
    c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
    inference(rename_variables,[],[i_0_609]) ).

cnf(i_0_984,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_664,i_0_922,i_0_925,i_0_668,i_0_956,i_0_967,i_0_669,i_0_501,i_0_693,i_0_725,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399]) ).

cnf(i_0_985,plain,
    ( ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
    | c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otypings(X1,X5,X3) ),
    inference(rename_variables,[],[i_0_399]) ).

cnf(i_0_986,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Oappend(c_List_Olist_ONil(X3),X2,X3),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_664,i_0_922,i_0_925,i_0_928,i_0_668,i_0_956,i_0_967,i_0_970,i_0_669,i_0_501,i_0_693,i_0_725,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421]) ).

cnf(i_0_987,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
    inference(rename_variables,[],[i_0_664]) ).

cnf(i_0_988,plain,
    ( c_List_Olist_OCons(X1,c_List_Osko__List__XCons__eq__append__conv__1__1(X1,X2,X3,X4,X5),X5) = X3
    | c_List_Olist_OCons(X1,X2,X5) = X4
    | c_List_Olist_OCons(X1,X2,X5) != c_List_Oappend(X3,X4,X5) ),
    inference(rename_variables,[],[i_0_421]) ).

cnf(i_0_989,plain,
    c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_OCons(X2,c_List_Olist_OCons(X3,X4,X1),X5),X1) != c_List_Olist_OCons(X3,X4,X1),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_669,i_0_501,i_0_693,i_0_725,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424]) ).

cnf(i_0_990,plain,
    c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
    inference(rename_variables,[],[i_0_665]) ).

cnf(i_0_991,plain,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(rename_variables,[],[i_0_668]) ).

cnf(i_0_992,plain,
    ( X1 = c_List_Olist_OCons(X2,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X2,X3,X1,X4,X5),X5)
    | X4 = c_List_Olist_OCons(X2,X3,X5)
    | c_List_Oappend(X1,X4,X5) != c_List_Olist_OCons(X2,X3,X5) ),
    inference(rename_variables,[],[i_0_424]) ).

cnf(i_0_993,plain,
    ~ c_ListOrder_Ostep1(c_Lambda_Obeta,c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_OCons(c_Lambda_OdB_OVar(X2),c_List_Olist_ONil(X1),X1),X1),c_List_Oappend(X3,c_List_Olist_OCons(X4,c_List_Olist_ONil(X1),X1),X1),X1),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_520,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_669,i_0_501,i_0_693,i_0_725,i_0_610,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445]) ).

cnf(i_0_994,plain,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
    inference(rename_variables,[],[i_0_520]) ).

cnf(i_0_995,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(X5),X5),X5),c_List_Oappend(X6,c_List_Olist_OCons(X3,c_List_Olist_ONil(X5),X5),X5),X5)
    | c_ListOrder_Ostep1(X1,X4,X6,X5) ),
    inference(rename_variables,[],[i_0_445]) ).

cnf(i_0_996,plain,
    ~ c_ListOrder_Ostep1(c_Lambda_Obeta,c_List_Oappend(X1,c_List_Olist_OCons(c_Lambda_OdB_OVar(X2),c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X4,c_List_Olist_OCons(c_List_Olist_OCons(X5,c_Lambda_OdB_OVar(X2),X6),c_List_Olist_ONil(X3),X3),X3),X3),
    inference(scs_inference,[],[i_0_670,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_520,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_669,i_0_964,i_0_501,i_0_693,i_0_725,i_0_610,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449]) ).

cnf(i_0_997,plain,
    ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
    inference(rename_variables,[],[i_0_610]) ).

cnf(i_0_998,plain,
    X1 != c_List_Olist_OCons(X2,X1,X3),
    inference(rename_variables,[],[i_0_669]) ).

cnf(i_0_999,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X4,c_List_Olist_OCons(X2,c_List_Olist_ONil(X5),X5),X5),c_List_Oappend(X6,c_List_Olist_OCons(X3,c_List_Olist_ONil(X5),X5),X5),X5)
    | X2 = X3 ),
    inference(rename_variables,[],[i_0_449]) ).

cnf(i_0_1000,plain,
    c_Type_Otyping(v_ea______,c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),v_ua______,X2),hAPP(c_Type_Oshift(v_ea______,X2,v_T____,tc_Type_Otype),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_709,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_520,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_669,i_0_964,i_0_501,i_0_693,i_0_725,i_0_610,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464]) ).

cnf(i_0_1001,plain,
    c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
    inference(rename_variables,[],[i_0_670]) ).

cnf(i_0_1002,plain,
    ( ~ c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),X4,X5)
    | c_Type_Otyping(X1,c_Lambda_Osubst(X4,X6,X2),X5)
    | ~ c_Type_Otyping(X1,X6,X3) ),
    inference(rename_variables,[],[i_0_464]) ).

cnf(i_0_1003,plain,
    ~ c_ListOrder_Ostep1(c_Lambda_Obeta,c_List_Olist_OCons(c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(X2),X2),c_List_Olist_OCons(X3,X4,X2),X2),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_709,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_669,i_0_964,i_0_501,i_0_693,i_0_725,i_0_610,i_0_997,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468]) ).

cnf(i_0_1004,plain,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
    inference(rename_variables,[],[i_0_520]) ).

cnf(i_0_1005,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X3,X6,X5),X5)
    | c_ListOrder_Ostep1(X1,X4,X6,X5) ),
    inference(rename_variables,[],[i_0_468]) ).

cnf(i_0_1006,plain,
    ~ c_ListOrder_Ostep1(c_Lambda_Obeta,c_List_Olist_OCons(c_Lambda_OdB_OVar(X1),X2,X3),c_List_Olist_OCons(c_List_Olist_OCons(X4,c_Lambda_OdB_OVar(X1),X5),X6,X3),X3),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_709,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_669,i_0_964,i_0_501,i_0_693,i_0_725,i_0_610,i_0_997,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481]) ).

cnf(i_0_1007,plain,
    ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
    inference(rename_variables,[],[i_0_610]) ).

cnf(i_0_1008,plain,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(rename_variables,[],[i_0_668]) ).

cnf(i_0_1009,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X4,X5),c_List_Olist_OCons(X3,X6,X5),X5)
    | X3 = X2 ),
    inference(rename_variables,[],[i_0_481]) ).

cnf(i_0_1010,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,X1),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2)),X3)),c_Lambda_Osubst(X2,X3,c_HOL_Ozero__class_Ozero(tc_nat)))),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_709,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_669,i_0_964,i_0_501,i_0_693,i_0_725,i_0_610,i_0_997,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494]) ).

cnf(i_0_1011,plain,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
    inference(rename_variables,[],[i_0_587]) ).

cnf(i_0_1012,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
    inference(rename_variables,[],[i_0_494]) ).

cnf(i_0_1013,plain,
    c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X2))),c_Lambda_OdB_OVar(X3)),hAPP(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(X1,X3),tc_Type_Otype),X2)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_669,i_0_964,i_0_501,i_0_693,i_0_725,i_0_610,i_0_997,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519]) ).

cnf(i_0_1014,plain,
    ( ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
    | c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
    | ~ c_Type_Otyping(X1,X5,X3) ),
    inference(rename_variables,[],[i_0_519]) ).

cnf(i_0_1015,plain,
    c_List_Oreplicate(c_List_Olist_OCons(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2),c_List_Olist_OCons(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2),X3) != c_List_Oreplicate(X4,c_HOL_Ozero__class_Ozero(tc_nat),X3),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_669,i_0_964,i_0_501,i_0_693,i_0_725,i_0_610,i_0_997,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596]) ).

cnf(i_0_1016,plain,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(rename_variables,[],[i_0_668]) ).

cnf(i_0_1017,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Oreplicate(X4,X5,X3)
    | X2 = X5 ),
    inference(rename_variables,[],[i_0_596]) ).

cnf(i_0_1018,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_669,i_0_964,i_0_667,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641]) ).

cnf(i_0_1019,plain,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_667]) ).

cnf(i_0_1020,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X1 = X2 ),
    inference(rename_variables,[],[i_0_641]) ).

cnf(i_0_1021,plain,
    c_List_Olist_OCons(X1,v_i____,X2) != v_n____,
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758]) ).

cnf(i_0_1022,plain,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(rename_variables,[],[i_0_668]) ).

cnf(i_0_1023,plain,
    hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3) != hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X4)),X5),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858]) ).

cnf(i_0_1024,plain,
    class_OrderedGroup_Omonoid__add(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_748,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870]) ).

cnf(i_0_1025,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1026,plain,
    class_OrderedGroup_Oab__semigroup__add(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_748,i_0_751,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833]) ).

cnf(i_0_1027,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1028,plain,
    class_Ring__and__Field_Ocomm__semiring__1(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_748,i_0_751,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834]) ).

cnf(i_0_1029,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1030,plain,
    ~ c_HOL_Oord__class_Oless(v_n____,v_i____,tc_nat),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_748,i_0_751,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835]) ).

cnf(i_0_1031,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_672]) ).

cnf(i_0_1032,plain,
    ~ c_HOL_Oord__class_Oless(v_i____,v_n____,tc_nat),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_609,i_0_981,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_748,i_0_751,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836]) ).

cnf(i_0_1033,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_672]) ).

cnf(i_0_1034,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,c_Predicate_Oconversep(c_Predicate_Oconversep(tc_nat,X2,X3),X3,X2)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_748,i_0_751,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837]) ).

cnf(i_0_1035,plain,
    c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
    inference(rename_variables,[],[i_0_609]) ).

cnf(i_0_1036,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_744,i_0_748,i_0_751,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838]) ).

cnf(i_0_1037,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1038,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_744,i_0_745,i_0_748,i_0_751,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839]) ).

cnf(i_0_1039,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1040,plain,
    class_OrderedGroup_Ocomm__monoid__add(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_744,i_0_745,i_0_748,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840]) ).

cnf(i_0_1041,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1042,plain,
    class_OrderedGroup_Opordered__comm__monoid__add(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_742,i_0_744,i_0_745,i_0_748,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842]) ).

cnf(i_0_1043,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1044,plain,
    class_Ring__and__Field_Oordered__semidom(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_742,i_0_743,i_0_744,i_0_745,i_0_748,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843]) ).

cnf(i_0_1045,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1046,plain,
    class_Orderings_Opreorder(c_List_Otake(c_Nat_Osize__class_Osize(tc_bool,tc_List_Olist(X1)),c_List_Oappend(tc_bool,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_737,i_0_742,i_0_743,i_0_744,i_0_745,i_0_748,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849]) ).

cnf(i_0_1047,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1048,plain,
    class_Orderings_Oorder(c_List_Otake(c_Nat_Osize__class_Osize(tc_bool,tc_List_Olist(X1)),c_List_Oappend(tc_bool,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_737,i_0_739,i_0_742,i_0_743,i_0_744,i_0_745,i_0_748,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850]) ).

cnf(i_0_1049,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1050,plain,
    class_Orderings_Olinorder(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_742,i_0_743,i_0_744,i_0_745,i_0_748,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853]) ).

cnf(i_0_1051,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1052,plain,
    class_OrderedGroup_Ocancel__semigroup__add(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_742,i_0_743,i_0_744,i_0_745,i_0_748,i_0_749,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854]) ).

cnf(i_0_1053,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1054,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_742,i_0_743,i_0_744,i_0_745,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855]) ).

cnf(i_0_1055,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1056,plain,
    class_Nat_Osemiring__char__0(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856]) ).

cnf(i_0_1057,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1058,plain,
    class_Ring__and__Field_Osemiring__1(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_609,i_0_981,i_0_983,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857]) ).

cnf(i_0_1059,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1060,plain,
    ~ c_ListOrder_Ostep1(c_Predicate_Oconversep(c_Predicate_Oconversep(c_Lambda_Obeta,X1,X2),X2,X1),c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(c_Lambda_OdB_OVar(X4),c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X5,c_List_Olist_OCons(c_List_Olist_OCons(X6,c_Lambda_OdB_OVar(X4),X7),c_List_Olist_ONil(X3),X3),X3),X3),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_609,i_0_981,i_0_983,i_0_1035,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857,i_0_859]) ).

cnf(i_0_1061,plain,
    c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
    inference(rename_variables,[],[i_0_609]) ).

cnf(i_0_1062,plain,
    ~ c_ListOrder_Ostep1(X1,c_List_Obutlast(c_List_Olist_ONil(X2),X2),X3,X2),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_727,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_609,i_0_981,i_0_983,i_0_1035,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_1004,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857,i_0_859,i_0_860]) ).

cnf(i_0_1063,plain,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
    inference(rename_variables,[],[i_0_520]) ).

cnf(i_0_1064,plain,
    ~ c_ListOrder_Ostep1(X1,X2,c_List_Obutlast(c_List_Olist_ONil(X3),X3),X3),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_727,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_609,i_0_981,i_0_983,i_0_1035,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_1004,i_0_521,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857,i_0_859,i_0_860,i_0_861]) ).

cnf(i_0_1065,plain,
    ~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
    inference(rename_variables,[],[i_0_521]) ).

cnf(i_0_1066,plain,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(v_i____),X2,v_n____),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_727,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_609,i_0_981,i_0_983,i_0_1035,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_1004,i_0_1063,i_0_521,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857,i_0_859,i_0_860,i_0_861,i_0_862]) ).

cnf(i_0_1067,plain,
    ~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
    inference(rename_variables,[],[i_0_520]) ).

cnf(i_0_1068,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_727,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_609,i_0_981,i_0_983,i_0_1035,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_1004,i_0_1063,i_0_521,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857,i_0_859,i_0_860,i_0_861,i_0_862,i_0_580]) ).

cnf(i_0_1069,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_672]) ).

cnf(i_0_1070,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(rename_variables,[],[i_0_580]) ).

cnf(i_0_1071,plain,
    class_OrderedGroup_Osemigroup__add(c_List_Otake(c_Nat_Osize__class_Osize(tc_nat,tc_List_Olist(X1)),c_List_Oappend(tc_nat,X2,X1),X1)),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_727,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_1059,i_0_609,i_0_981,i_0_983,i_0_1035,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_1004,i_0_1063,i_0_521,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_669,i_0_964,i_0_667,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_747,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857,i_0_859,i_0_860,i_0_861,i_0_862,i_0_580,i_0_869]) ).

cnf(i_0_1072,plain,
    X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
    inference(rename_variables,[],[i_0_579]) ).

cnf(i_0_1073,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2),tc_nat),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_727,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_1059,i_0_609,i_0_981,i_0_983,i_0_1035,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_1004,i_0_1063,i_0_521,i_0_672,i_0_1031,i_0_1033,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_1022,i_0_669,i_0_964,i_0_667,i_0_1019,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_747,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857,i_0_859,i_0_860,i_0_861,i_0_862,i_0_580,i_0_869,i_0_628]) ).

cnf(i_0_1074,plain,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(rename_variables,[],[i_0_667]) ).

cnf(i_0_1075,plain,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(rename_variables,[],[i_0_668]) ).

cnf(i_0_1076,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_628]) ).

cnf(i_0_1077,plain,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Olist_OCons(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2)),X3),X3,tc_nat),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_727,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_1059,i_0_609,i_0_981,i_0_983,i_0_1035,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_1004,i_0_1063,i_0_521,i_0_672,i_0_1031,i_0_1033,i_0_1069,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_1022,i_0_669,i_0_964,i_0_667,i_0_1019,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_747,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857,i_0_859,i_0_860,i_0_861,i_0_862,i_0_580,i_0_869,i_0_628,i_0_534]) ).

cnf(i_0_1078,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(rename_variables,[],[i_0_672]) ).

cnf(i_0_1079,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X4,X2) ),
    inference(rename_variables,[],[i_0_534]) ).

cnf(i_0_1080,plain,
    ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_727,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_1059,i_0_609,i_0_981,i_0_983,i_0_1035,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_1004,i_0_1063,i_0_521,i_0_672,i_0_1031,i_0_1033,i_0_1069,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_1022,i_0_669,i_0_964,i_0_667,i_0_1019,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_747,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857,i_0_859,i_0_860,i_0_861,i_0_862,i_0_580,i_0_869,i_0_628,i_0_534,i_0_898]) ).

cnf(i_0_1081,plain,
    ( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1)
    | ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,X1),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
    inference(rename_variables,[],[i_0_898]) ).

cnf(i_0_1082,plain,
    $false,
    inference(scs_inference,[],[i_0_670,i_0_940,i_0_1001,i_0_709,i_0_755,i_0_727,i_0_579,i_0_1025,i_0_1027,i_0_1029,i_0_1037,i_0_1039,i_0_1041,i_0_1043,i_0_1045,i_0_1047,i_0_1049,i_0_1051,i_0_1053,i_0_1055,i_0_1057,i_0_1059,i_0_609,i_0_981,i_0_983,i_0_1035,i_0_420,i_0_418,i_0_507,i_0_587,i_0_902,i_0_905,i_0_908,i_0_919,i_0_933,i_0_1011,i_0_486,i_0_520,i_0_994,i_0_1004,i_0_1063,i_0_521,i_0_672,i_0_1031,i_0_1033,i_0_1069,i_0_664,i_0_922,i_0_925,i_0_928,i_0_665,i_0_668,i_0_956,i_0_967,i_0_970,i_0_991,i_0_1008,i_0_1016,i_0_1022,i_0_669,i_0_964,i_0_667,i_0_1019,i_0_736,i_0_737,i_0_739,i_0_741,i_0_742,i_0_743,i_0_744,i_0_745,i_0_746,i_0_747,i_0_748,i_0_749,i_0_750,i_0_751,i_0_752,i_0_753,i_0_501,i_0_693,i_0_608,i_0_725,i_0_610,i_0_997,i_0_1007,i_0_483,i_0_389,i_0_392,i_0_394,i_0_396,i_0_403,i_0_404,i_0_405,i_0_434,i_0_441,i_0_442,i_0_443,i_0_444,i_0_448,i_0_466,i_0_467,i_0_469,i_0_472,i_0_480,i_0_497,i_0_508,i_0_509,i_0_533,i_0_555,i_0_571,i_0_595,i_0_639,i_0_653,i_0_654,i_0_757,i_0_496,i_0_582,i_0_522,i_0_830,i_0_831,i_0_832,i_0_399,i_0_421,i_0_424,i_0_445,i_0_449,i_0_464,i_0_468,i_0_481,i_0_494,i_0_519,i_0_596,i_0_641,i_0_758,i_0_858,i_0_870,i_0_833,i_0_834,i_0_835,i_0_836,i_0_837,i_0_838,i_0_839,i_0_840,i_0_842,i_0_843,i_0_849,i_0_850,i_0_853,i_0_854,i_0_855,i_0_856,i_0_857,i_0_859,i_0_860,i_0_861,i_0_862,i_0_580,i_0_869,i_0_628,i_0_534,i_0_898,i_0_432]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LCL787-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12  % 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
% 0.15/0.33  % Computer : n021.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Mon May  4 23:08:25 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 2.05/2.62  % Version  : CSE_E---1.7
% 2.05/2.62  % Problem  : theBenchmark.p
% 2.05/2.62  % SZS status Unsatisfiable for theBenchmark.p
% 2.05/2.62  % SZS output start CNFRefutation
% See solution above
% 3.35/4.02  % Total time : 2.274s
%------------------------------------------------------------------------------