TSTP Solution File: LCL839-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : LCL839-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n004.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 : 600s
% DateTime : Sun Jul 17 11:40:35 EDT 2022
% Result : Unsatisfiable 158.22s 158.47s
% Output : CNFRefutation 158.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 393
% Syntax : Number of formulae : 2727 ( 752 unt; 0 def)
% Number of atoms : 5752 (1861 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 5970 (2945 ~;3025 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 34 ( 32 usr; 2 prp; 0-4 aty)
% Number of functors : 53 ( 53 usr; 21 con; 0-5 aty)
% Number of variables : 7091 ( 533 sgn2919 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X29,X27,X14,X18,X30,X31,X19] :
( X30 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X19,X30,X18,X29),X19,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X30)
| ~ c_Type_Otypings(X18,X27,X31)
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X29,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
file('<stdin>',cls_var__app__types_0) ).
fof(c_0_1,axiom,
! [X35,X36,X2] :
( X35 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X36,X35),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X36,tc_Lambda_OdB,tc_Lambda_OdB)),X35)) ),
file('<stdin>',cls_head__Var__reduction_1) ).
fof(c_0_2,axiom,
! [X29,X27,X14,X18,X30,X31,X19] :
( c_Type_Otypings(X18,X29,c_Type_Osko__Type__Xvar__app__types__1__1(X19,X30,X18,X29))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X30)
| ~ c_Type_Otypings(X18,X27,X31)
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X29,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
file('<stdin>',cls_var__app__types_1) ).
fof(c_0_3,axiom,
! [X37,X14,X18,X52] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X37,X14)))
| ~ c_Type_Otyping(X18,X37,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X37))
| ~ c_Type_Otyping(c_Type_Oshift(X18,X14,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X52) ),
file('<stdin>',cls_SI1_0) ).
fof(c_0_4,axiom,
! [X35,X36,X2] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X36,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X36,X35),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X36,tc_Lambda_OdB,tc_Lambda_OdB)),X35)) ),
file('<stdin>',cls_head__Var__reduction_0) ).
fof(c_0_5,axiom,
! [X47,X36,X20] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X36,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X47,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X36,X47,tc_Lambda_OdB) ),
file('<stdin>',cls_apps__preserves__betas_0) ).
fof(c_0_6,axiom,
! [X47,X26,X20] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X47,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X26)) ),
file('<stdin>',cls_apps__preserves__beta2_0) ).
fof(c_0_7,axiom,
! [X47,X26,X20] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X47,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X26)) ),
file('<stdin>',cls_apps__preserves__beta_0) ).
fof(c_0_8,axiom,
! [X47,X26,X20] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20)),X26),X47,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X20,X26,c_HOL_Ozero__class_Ozero(tc_nat)),X47,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('<stdin>',cls_IT_OBeta_0) ).
fof(c_0_9,axiom,
! [X27,X14,X18,X30,X19] :
( X19 = X30
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X30)
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
file('<stdin>',cls_var__app__type__eq_0) ).
fof(c_0_10,axiom,
! [X47,X26,X20] :
( ~ 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(X20,X26,c_HOL_Ozero__class_Ozero(tc_nat)),X47,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X26,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20)),X26),X47,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('<stdin>',cls_double__induction__lemma_0) ).
fof(c_0_11,axiom,
! [X27,X14,X18,X19] :
( c_Type_Otyping(X18,c_Lambda_OdB_OVar(X14),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X19,X18,X14,X27),X19,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
file('<stdin>',cls_var__app__typesE_0) ).
fof(c_0_12,axiom,
! [X27,X28,X18,X19] :
( c_Type_Otyping(X18,X28,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X19,X18,X28,X27),X19,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
file('<stdin>',cls_list__app__typeE_0) ).
fof(c_0_13,axiom,
! [X27,X28,X18,X19] :
( c_Type_Otyping(X18,X28,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X19,X18,X28,X27),X19,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
file('<stdin>',cls_list__app__typeD_0) ).
fof(c_0_14,axiom,
! [X27,X28,X18,X31,X19] :
( c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X19)
| ~ c_Type_Otypings(X18,X27,X31)
| ~ c_Type_Otyping(X18,X28,c_List_Ofoldr(c_Type_Otype_OFun,X31,X19,tc_Type_Otype,tc_Type_Otype)) ),
file('<stdin>',cls_list__app__typeI_0) ).
fof(c_0_15,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
file('<stdin>',cls_Beta_I1_J_0) ).
fof(c_0_16,axiom,
! [X36,X2] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X36,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X36,tc_Lambda_OdB) ),
file('<stdin>',cls_IT_OVar_0) ).
fof(c_0_17,axiom,
! [X27,X14,X18,X19] :
( c_Type_Otypings(X18,X27,c_Type_Osko__Type__Xvar__app__typesE__1__1(X19,X18,X14,X27))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
file('<stdin>',cls_var__app__typesE_1) ).
fof(c_0_18,axiom,
! [X27,X28,X18,X19] :
( c_Type_Otypings(X18,X27,c_Type_Osko__Type__Xlist__app__typeD__1__1(X19,X18,X28,X27))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
file('<stdin>',cls_list__app__typeD_1) ).
fof(c_0_19,axiom,
! [X27,X28,X18,X19] :
( c_Type_Otypings(X18,X27,c_Type_Osko__Type__Xlist__app__typeE__1__1(X19,X18,X28,X27))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
file('<stdin>',cls_list__app__typeE_1) ).
fof(c_0_20,axiom,
! [X47,X36,X2,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X3 = X2 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_0) ).
fof(c_0_21,axiom,
! [X47,X36,X2,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X36 = X47 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_1) ).
fof(c_0_22,axiom,
! [X47,X26,X36,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26),X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X20 = X26 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_0) ).
fof(c_0_23,axiom,
! [X47,X26,X36,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26),X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X36 = X47 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_1) ).
fof(c_0_24,axiom,
! [X32,X9,X11,X7] :
( ~ class_OrderedGroup_Osemigroup__add(X7)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X9),X32,X7,X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),X9,X32,X7,X7)) ),
file('<stdin>',cls_foldl__assoc_0) ).
fof(c_0_25,axiom,
! [X27,X47,X20,X2] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X27,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X47,tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Var__apps__neq__Abs__apps_0) ).
fof(c_0_26,axiom,
! [X27,X26,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X27,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X27,tc_Lambda_OdB,tc_Lambda_OdB)
| X20 = X26 ),
file('<stdin>',cls_apps__eq__tail__conv_0) ).
fof(c_0_27,axiom,
! [X21,X5,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),X5,X21,X7,X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X7),X21,c_HOL_Ozero__class_Ozero(X7),X7,X7)) ),
file('<stdin>',cls_foldl__foldr1__lemma_0) ).
fof(c_0_28,axiom,
! [X32,X11,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7),X32,X7,X7)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),X11,X32,X7,X7) ),
file('<stdin>',cls_foldl__absorb0_0) ).
fof(c_0_29,axiom,
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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('<stdin>',cls_T_0) ).
fof(c_0_30,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
file('<stdin>',cls_Beta_I5_J_0) ).
fof(c_0_31,axiom,
! [X21,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7),X21,X7,X7) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X7),X21,c_HOL_Ozero__class_Ozero(X7),X7,X7) ),
file('<stdin>',cls_foldl__foldr1_0) ).
fof(c_0_32,axiom,
! [X21,X5,X7] :
( ~ class_OrderedGroup_Oab__semigroup__add(X7)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X7),X21,X5,X7,X7) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),X5,X21,X7,X7) ),
file('<stdin>',cls_foldr__conv__foldl_0) ).
fof(c_0_33,axiom,
! [X37,X28,X18,X19] :
( c_Type_Otyping(X18,X28,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X19,X18,X28,X37)),X19))
| ~ c_Type_Otyping(X18,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X37),X19) ),
file('<stdin>',cls_typing__elims_I2_J_0) ).
fof(c_0_34,axiom,
! [X28,X26,X20] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X20),X26) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X20),X26) = X28 ),
file('<stdin>',cls_App__eq__foldl__conv_0) ).
fof(c_0_35,axiom,
! [X28,X47,X26,X2] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X28) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X47,tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Abs__App__neq__Var__apps_0) ).
fof(c_0_36,axiom,
! [X47,X26,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X20)
| X26 = c_Lambda_OdB_OAbs(X20) ),
file('<stdin>',cls_apps__eq__Abs__conv_0) ).
fof(c_0_37,axiom,
! [X47,X26,X3] :
( c_Lambda_OdB_OVar(X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X3) = X26 ),
file('<stdin>',cls_Var__eq__apps__conv_0) ).
fof(c_0_38,axiom,
! [X47,X26,X20] :
( c_Lambda_OdB_OAbs(X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X20) = X26 ),
file('<stdin>',cls_Abs__eq__apps__conv_0) ).
fof(c_0_39,axiom,
! [X47,X26,X3] :
( c_Lambda_OdB_OVar(X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X47 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Var__eq__apps__conv_1) ).
fof(c_0_40,axiom,
! [X47,X26,X20] :
( c_Lambda_OdB_OAbs(X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X47 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Abs__eq__apps__conv_1) ).
fof(c_0_41,axiom,
! [X47,X26,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X20)
| X47 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_apps__eq__Abs__conv_1) ).
fof(c_0_42,axiom,
! [X9,X11,X20,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X20,X7,X7),X7),X11),X9)) ),
file('<stdin>',cls_rtranclp__converseD_0) ).
fof(c_0_43,axiom,
! [X14,X18,X30,X19,X7] : c_Type_Oshift(c_Type_Oshift(X18,X14,X30,X7),c_HOL_Ozero__class_Ozero(tc_nat),X19,X7) = c_Type_Oshift(c_Type_Oshift(X18,c_HOL_Ozero__class_Ozero(tc_nat),X19,X7),c_Suc(X14),X30,X7),
file('<stdin>',cls_shift__commute_0) ).
fof(c_0_44,axiom,
! [X9,X11,X20,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X20,X7,X7),X7),X11),X9))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X9),X11)) ),
file('<stdin>',cls_rtranclp__converseI_0) ).
fof(c_0_45,axiom,
! [X37,X28,X14,X18,X55,X56,X57] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X57),X56)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X28,X37,X14)))
| ~ c_Type_Otyping(X18,X37,X57)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X37))
| ~ c_Type_Otyping(c_Type_Oshift(X18,X14,X57,tc_Type_Otype),X28,X55)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
file('<stdin>',cls_MI1_0) ).
fof(c_0_46,axiom,
! [X37,X28,X14,X18,X55,X56,X57] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X57),X56)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X28,X37,X14)))
| ~ c_Type_Otyping(X18,X37,X56)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X37))
| ~ c_Type_Otyping(c_Type_Oshift(X18,X14,X56,tc_Type_Otype),X28,X55)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
file('<stdin>',cls_MI2_0) ).
fof(c_0_47,axiom,
! [X26,X20] : hAPP(hAPP(c_Lambda_OdB_OApp,X20),X26) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X20),X26),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_App__eq__foldl__conv_4) ).
fof(c_0_48,axiom,
! [X3] : c_Lambda_OdB_OVar(X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Var__eq__apps__conv_2) ).
fof(c_0_49,axiom,
! [X20] : c_Lambda_OdB_OAbs(X20) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Abs__eq__apps__conv_2) ).
fof(c_0_50,axiom,
! [X20] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X20),
file('<stdin>',cls_apps__eq__Abs__conv_2) ).
fof(c_0_51,axiom,
! [X37,X14,X18,X52] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X37,X14)))
| ~ c_Type_Otyping(X18,X37,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X37))
| ~ c_Type_Otyping(c_Type_Oshift(X18,X14,v_T____,tc_Type_Otype),v_a____,X52) ),
file('<stdin>',cls_SI2_0) ).
fof(c_0_52,axiom,
! [X22,X5,X23,X7] : c_List_Ofoldr(X22,c_List_Olist_ONil(X23),X5,X23,X7) = X5,
file('<stdin>',cls_foldr_Osimps_I1_J_0) ).
fof(c_0_53,axiom,
! [X22,X5,X23,X7] : c_List_Ofoldl(X22,X5,c_List_Olist_ONil(X23),X7,X23) = X5,
file('<stdin>',cls_foldl__Nil_0) ).
fof(c_0_54,axiom,
! [X37,X28,X14,X59,X30,X19] :
( ~ c_Type_Otyping(X59,X37,X30)
| ~ c_Type_Otyping(c_Type_Oshift(X59,X14,X30,tc_Type_Otype),X28,X19)
| c_Type_Otyping(X59,c_Lambda_Osubst(X28,X37,X14),X19) ),
file('<stdin>',cls_subst__lemma_0) ).
fof(c_0_55,axiom,
! [X33,X28,X34,X26] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X33)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X33))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X34)) ),
file('<stdin>',cls_rtrancl__beta__App_0) ).
fof(c_0_56,axiom,
! [X28,X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X28,X20,X14)),c_Lambda_Osubst(X28,X26,X14)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X26)) ),
file('<stdin>',cls_subst__preserves__beta2_H_0) ).
fof(c_0_57,axiom,
! [X28,X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X20,X28,X14)),c_Lambda_Osubst(X26,X28,X14)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X26)) ),
file('<stdin>',cls_subst__preserves__beta_H_0) ).
fof(c_0_58,axiom,
! [X28,X51,X30,X19] :
( c_Type_Otyping(X51,c_Lambda_OdB_OAbs(X28),hAPP(hAPP(c_Type_Otype_OFun,X19),X30))
| ~ c_Type_Otyping(c_Type_Oshift(X51,c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_Type_Otype),X28,X30) ),
file('<stdin>',cls_Abs_0) ).
fof(c_0_59,axiom,
! [X16,X4,X6] :
( ~ hBOOL(hAPP(X6,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X16),X4,tc_nat)))
| hBOOL(hAPP(X6,X16)) ),
file('<stdin>',cls_nat__diff__split_1) ).
fof(c_0_60,axiom,
! [X11,X4,X6] :
( ~ hBOOL(hAPP(X6,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X11),X4,tc_nat)))
| hBOOL(hAPP(X6,X11)) ),
file('<stdin>',cls_nat__diff__split__asm_1) ).
fof(c_0_61,axiom,
! [X28,X18,X19] :
( c_Type_Otyping(c_Type_Oshift(X18,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X19,X18,X28),tc_Type_Otype),X28,c_Type_Osko__Type__Xtyping__elims__3__2(X19,X18,X28))
| ~ c_Type_Otyping(X18,c_Lambda_OdB_OAbs(X28),X19) ),
file('<stdin>',cls_typing__elims_I3_J_1) ).
fof(c_0_62,axiom,
! [X28,X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X28,X20,X14)),c_Lambda_Osubst(X28,X26,X14)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X26)) ),
file('<stdin>',cls_subst__preserves__beta2_0) ).
fof(c_0_63,axiom,
! [X20,X4,X5,X23,X7] :
( hBOOL(hAPP(hAPP(X20,X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X20,X7,X23),X5),X4)) ),
file('<stdin>',cls_conversepD_0) ).
fof(c_0_64,axiom,
! [X20,X45,X46,X23,X7] :
( hBOOL(hAPP(hAPP(X20,X45),X46))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X20,X7,X23),X46),X45)) ),
file('<stdin>',cls_conversep_Ocases_0) ).
fof(c_0_65,axiom,
! [X33,X28,X26] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X33)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X33)) ),
file('<stdin>',cls_rtrancl__beta__AppR_0) ).
fof(c_0_66,axiom,
! [X28,X34,X26] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X28)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X34)) ),
file('<stdin>',cls_rtrancl__beta__AppL_0) ).
fof(c_0_67,axiom,
! [X58] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X58) ),
file('<stdin>',cls_that_0) ).
fof(c_0_68,axiom,
! [X28,X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X20,X28,X14)),c_Lambda_Osubst(X26,X28,X14)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X26)) ),
file('<stdin>',cls_subst__preserves__beta_0) ).
fof(c_0_69,axiom,
! [X43,X9,X11,X20,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X11),X43))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X9),X43))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X11),X9)) ),
file('<stdin>',cls_rtranclp__trans_0) ).
fof(c_0_70,axiom,
! [X37,X28,X18,X19] :
( c_Type_Otyping(X18,X37,c_Type_Osko__Type__Xtyping__elims__2__1(X19,X18,X28,X37))
| ~ c_Type_Otyping(X18,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X37),X19) ),
file('<stdin>',cls_typing__elims_I2_J_1) ).
fof(c_0_71,axiom,
! [X35,X37,X28,X13,X14] :
( c_Lambda_Osubst(c_Lambda_Osubst(X28,c_Lambda_Olift(X35,X14),c_Suc(X13)),c_Lambda_Osubst(X37,X35,X13),X14) = c_Lambda_Osubst(c_Lambda_Osubst(X28,X37,X14),X35,X13)
| ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_subst__subst_0) ).
fof(c_0_72,axiom,
! [X16,X24,X4,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X16)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_73,axiom,
! [X28,X18,X19] :
( c_Type_Otyping(c_Type_Oshift(X18,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X18,X28),tc_Type_Otype),X28,c_Type_Osko__Type__Xabs__typeE__1__2(X18,X28))
| ~ c_Type_Otyping(X18,c_Lambda_OdB_OAbs(X28),X19) ),
file('<stdin>',cls_abs__typeE_0) ).
fof(c_0_74,axiom,
! [X13,X14,X18,X19,X7] :
( hAPP(c_Type_Oshift(X18,X14,X19,X7),X13) = hAPP(X18,c_HOL_Ominus__class_Ominus(X13,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
file('<stdin>',cls_shift__lt_0) ).
fof(c_0_75,axiom,
! [X28,X26] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X28)),c_Lambda_Osubst(X26,X28,c_HOL_Ozero__class_Ozero(tc_nat)))),
file('<stdin>',cls_beta_0) ).
fof(c_0_76,axiom,
! [X28,X14,X18,X30,X19] :
( c_Type_Otyping(c_Type_Oshift(X18,X14,X30,tc_Type_Otype),c_Lambda_Olift(X28,X14),X19)
| ~ c_Type_Otyping(X18,X28,X19) ),
file('<stdin>',cls_lift__type_0) ).
fof(c_0_77,axiom,
! [X28,X26,X13,X14] :
( c_Lambda_Olift(c_Lambda_Osubst(X28,X26,X13),X14) = c_Lambda_Osubst(c_Lambda_Olift(X28,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Olift(X26,X14),X13)
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_lift__subst_0) ).
fof(c_0_78,axiom,
! [X20,X4,X5,X23,X7] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X20,X7,X23),X5),X4))
| ~ hBOOL(hAPP(hAPP(X20,X4),X5)) ),
file('<stdin>',cls_conversep__iff_1) ).
fof(c_0_79,axiom,
! [X20,X4,X5,X23,X7] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X20,X7,X23),X4),X5))
| ~ hBOOL(hAPP(hAPP(X20,X5),X4)) ),
file('<stdin>',cls_conversep_Ointros_0) ).
fof(c_0_80,axiom,
! [X37,X28,X26] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X37),X26)),hAPP(hAPP(c_Lambda_OdB_OApp,X37),X28)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28)) ),
file('<stdin>',cls_appR_0) ).
fof(c_0_81,axiom,
! [X37,X28,X26] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X37)),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X37)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28)) ),
file('<stdin>',cls_appL_0) ).
fof(c_0_82,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_OAbs(v_r____)),v_a____),v_Ua____),
file('<stdin>',cls_CHAINED_0) ).
fof(c_0_83,axiom,
! [X20,X24,X4,X5,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X5),X24))
| ~ hBOOL(hAPP(hAPP(X20,X4),X24))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X5),X4)) ),
file('<stdin>',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
fof(c_0_84,axiom,
! [X20,X24,X4,X5,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X5),X24))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X4),X24))
| ~ hBOOL(hAPP(hAPP(X20,X5),X4)) ),
file('<stdin>',cls_converse__rtranclp__into__rtranclp_0) ).
fof(c_0_85,axiom,
! [X13,X14,X18,X19,X7] :
( hAPP(c_Type_Oshift(X18,X14,X19,X7),X13) = hAPP(X18,X13)
| ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat) ),
file('<stdin>',cls_shift__gt_0) ).
fof(c_0_86,axiom,
! [X41,X42] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X42,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X41,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_dB_Osize_I5_J_0) ).
fof(c_0_87,axiom,
! [X38,X39] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X39),X38),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X39,tc_Type_Otype)),c_Nat_Osize__class_Osize(X38,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_type_Osize_I4_J_0) ).
fof(c_0_88,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__if_1) ).
fof(c_0_89,axiom,
! [X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X20,X14)),c_Lambda_Olift(X26,X14)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X26)) ),
file('<stdin>',cls_lift__preserves__beta_H_0) ).
fof(c_0_90,axiom,
! [X28,X26,X13,X14] :
( c_Lambda_Olift(c_Lambda_Osubst(X28,X26,X13),X14) = c_Lambda_Osubst(c_Lambda_Olift(X28,X14),c_Lambda_Olift(X26,X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_lift__subst__lt_0) ).
fof(c_0_91,axiom,
! [X24,X4,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)),X4) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_92,axiom,
! [X11,X18,X19,X7] : hAPP(c_Type_Oshift(X18,X11,X19,X7),X11) = X19,
file('<stdin>',cls_shift__eq_0) ).
fof(c_0_93,axiom,
! [X4,X5,X6] :
( hBOOL(hAPP(X6,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ hBOOL(hAPP(X6,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat))) ),
file('<stdin>',cls_nat__diff__split_0) ).
fof(c_0_94,axiom,
! [X37,X28,X26,X12] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X28),X37),X26,X12) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X28,X26,X12)),c_Lambda_Osubst(X37,X26,X12)),
file('<stdin>',cls_subst__App_0) ).
fof(c_0_95,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X7)
| c_HOL_Oord__class_Oless(X5,X4,X7)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X4),X7) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_96,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X7)
| c_HOL_Oord__class_Oless(X5,X4,X7)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24),X7) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_97,axiom,
! [X28,X18,X19] :
( X19 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X19,X18,X28)),c_Type_Osko__Type__Xtyping__elims__3__2(X19,X18,X28))
| ~ c_Type_Otyping(X18,c_Lambda_OdB_OAbs(X28),X19) ),
file('<stdin>',cls_typing__elims_I3_J_0) ).
fof(c_0_98,axiom,
! [X34,X26] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X26)),c_Lambda_OdB_OAbs(X34)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X34)) ),
file('<stdin>',cls_rtrancl__beta__Abs_0) ).
fof(c_0_99,axiom,
! [X16,X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X16),X7)
| ~ c_HOL_Oord__class_Oless(X24,X16,X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_100,axiom,
! [X20,X4,X5,X7] :
( c_Wellfounded_Oaccp(X20,X4,X7)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X4),X5))
| ~ c_Wellfounded_Oaccp(X20,X5,X7) ),
file('<stdin>',cls_accp__downwards_0) ).
fof(c_0_101,axiom,
! [X20,X4,X5,X7] :
( c_Wellfounded_Oaccp(X20,X4,X7)
| ~ c_Wellfounded_Oaccp(X20,X5,X7)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X4),X5)) ),
file('<stdin>',cls_accp__downwards__aux_0) ).
fof(c_0_102,axiom,
! [X2,X3,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X2,tc_nat),c_HOL_Ominus__class_Ominus(X15,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_diff__less__mono2_0) ).
fof(c_0_103,axiom,
! [X28,X26,X12] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X28),X26,X12) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X28,c_Lambda_Olift(X26,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)))),
file('<stdin>',cls_subst__Abs_0) ).
fof(c_0_104,axiom,
! [X2,X3,X12] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X2),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_0) ).
fof(c_0_105,axiom,
! [X24,X4,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_106,axiom,
! [X16,X24,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)),X16) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_107,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Oab__semigroup__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24)) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_108,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24)) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_109,axiom,
! [X43,X9,X11,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),X43)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X9)),X43) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_110,axiom,
! [X28,X26,X51,X30,X19] :
( c_Type_Otyping(X51,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28),X30)
| ~ c_Type_Otyping(X51,X28,X19)
| ~ c_Type_Otyping(X51,X26,hAPP(hAPP(c_Type_Otype_OFun,X19),X30)) ),
file('<stdin>',cls_App_0) ).
fof(c_0_111,axiom,
! [X15,X12,X13,X14] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
file('<stdin>',cls_add__less__mono_0) ).
fof(c_0_112,axiom,
! [X21,X20,X7] : ~ c_ListOrder_Ostep1(X20,X21,c_List_Olist_ONil(X7),X7),
file('<stdin>',cls_not__step1__Nil_0) ).
fof(c_0_113,axiom,
! [X21,X20,X7] : ~ c_ListOrder_Ostep1(X20,c_List_Olist_ONil(X7),X21,X7),
file('<stdin>',cls_not__Nil__step1_0) ).
fof(c_0_114,axiom,
! [X33,X28,X18,X19] :
( c_Type_Otyping(X18,X33,X19)
| ~ c_Type_Otyping(X18,X28,X19)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X33)) ),
file('<stdin>',cls_subject__reduction_H_0) ).
fof(c_0_115,axiom,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X12),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat) ),
file('<stdin>',cls_less__diff__conv_0) ).
fof(c_0_116,axiom,
! [X41,X42] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X42)),c_Lambda_OdB_OdB__size(X41))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_dB_Osize_I2_J_0) ).
fof(c_0_117,axiom,
! [X38,X39] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X39),X38)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X39)),c_Type_Otype_Otype__size(X38))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_type_Osize_I2_J_0) ).
fof(c_0_118,axiom,
! [X43,X9,X11,X37,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),X43)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),X37)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X43) = X37 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_119,axiom,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(X14,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X12),X13,tc_nat) ),
file('<stdin>',cls_less__diff__conv_1) ).
fof(c_0_120,axiom,
! [X2,X3,X12] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X12)),
file('<stdin>',cls_nat__add__assoc_0) ).
fof(c_0_121,axiom,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X4,X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X5,X7) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_122,axiom,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4),c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X7),X7) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_123,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X4),X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_124,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X4),X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_125,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24),X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_126,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24),X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_127,axiom,
! [X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X20,X14)),c_Lambda_Olift(X26,X14)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X26)) ),
file('<stdin>',cls_lift__preserves__beta_0) ).
fof(c_0_128,axiom,
! [X24,X4,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24),X7)
| ~ c_HOL_Oord__class_Oless(X4,X24,X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X5,X7) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_129,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
file('<stdin>',cls_add__gr__0_0) ).
fof(c_0_130,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_diff__less_0) ).
fof(c_0_131,axiom,
! [X2,X3,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X2,tc_nat),c_Suc(X12),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X12,tc_nat),
file('<stdin>',cls_Suc__diff__diff_0) ).
fof(c_0_132,axiom,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(X5,X4,X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,X7),c_HOL_Ozero__class_Ozero(X7),X7) ),
file('<stdin>',cls_less__iff__diff__less__0_1) ).
fof(c_0_133,axiom,
! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),c_HOL_Ozero__class_Ozero(X7),X7) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_134,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),c_HOL_Ozero__class_Ozero(X7),X7) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_135,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X5,X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),X7) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_136,axiom,
! [X28,X12,X14] :
( c_Lambda_Olift(c_Lambda_Olift(X28,X14),c_Suc(X12)) = c_Lambda_Olift(c_Lambda_Olift(X28,X12),X14)
| ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('<stdin>',cls_lift__lift_0) ).
fof(c_0_137,axiom,
! [X8,X9,X10,X11,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X11,X9,X7) != c_HOL_Ominus__class_Ominus(X10,X8,X7)
| c_HOL_Oord__class_Oless(X10,X8,X7)
| ~ c_HOL_Oord__class_Oless(X11,X9,X7) ),
file('<stdin>',cls_less__eqI_0) ).
fof(c_0_138,axiom,
! [X8,X9,X10,X11,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X11,X9,X7) != c_HOL_Ominus__class_Ominus(X10,X8,X7)
| c_HOL_Oord__class_Oless(X11,X9,X7)
| ~ c_HOL_Oord__class_Oless(X10,X8,X7) ),
file('<stdin>',cls_less__eqI_1) ).
fof(c_0_139,axiom,
! [X2,X3,X12] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_1) ).
fof(c_0_140,axiom,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
file('<stdin>',cls_add__less__mono1_0) ).
fof(c_0_141,axiom,
! [X16,X24,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X16)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_142,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_143,axiom,
! [X43,X9,X11,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),X43)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X43)) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_144,axiom,
! [X9,X11,X20,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X11),X9))
| ~ hBOOL(hAPP(hAPP(X20,X11),X9)) ),
file('<stdin>',cls_r__into__rtranclp_0) ).
fof(c_0_145,axiom,
! [X12,X13,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X14,X12,tc_nat),X13,tc_nat),
file('<stdin>',cls_diff__commute_0) ).
fof(c_0_146,axiom,
! [X20,X13,X14] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X20,c_Lambda_OdB_OVar(X14),X13)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X20)) ),
file('<stdin>',cls_subst__Var__IT_0) ).
fof(c_0_147,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
file('<stdin>',cls_zero__less__diff_0) ).
fof(c_0_148,axiom,
! [X12,X13,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12),tc_nat),
file('<stdin>',cls_diff__diff__left_0) ).
fof(c_0_149,axiom,
! [X2,X3,X12] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),
file('<stdin>',cls_diff__cancel_0) ).
fof(c_0_150,axiom,
! [X2,X3,X12] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X12),tc_nat) = c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),
file('<stdin>',cls_diff__cancel2_0) ).
fof(c_0_151,axiom,
! [X2,X3,X15,X12] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X2)
| ~ c_HOL_Oord__class_Oless(X12,X15,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_less__add__eq__less_0) ).
fof(c_0_152,axiom,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(X14,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X13),X12,tc_nat) ),
file('<stdin>',cls_add__lessD1_0) ).
fof(c_0_153,axiom,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ominus__class_Ominus(X5,X4,X7)),X4) = X5 ),
file('<stdin>',cls_diff__add__cancel_0) ).
fof(c_0_154,axiom,
! [X43,X9,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X43)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X43)),
file('<stdin>',cls_nat__add__left__commute_0) ).
fof(c_0_155,axiom,
! [X20,X4,X5,X7] :
( c_Wellfounded_Oaccp(X20,X5,X7)
| ~ hBOOL(hAPP(hAPP(X20,X5),X4))
| ~ c_Wellfounded_Oaccp(X20,X4,X7) ),
file('<stdin>',cls_accp__downward_0) ).
fof(c_0_156,axiom,
! [X9,X20,X5,X7] :
( c_Wellfounded_Oaccp(X20,X9,X7)
| ~ hBOOL(hAPP(hAPP(X20,X9),X5))
| ~ c_Wellfounded_Oaccp(X20,X5,X7) ),
file('<stdin>',cls_accp_Ocases_0) ).
fof(c_0_157,axiom,
! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X7),X7) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_158,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X7),X7) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_159,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X5,X7) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_160,axiom,
! [X20] :
( hBOOL(hAPP(c_InductTermi_OIT,X20))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X20,tc_Lambda_OdB) ),
file('<stdin>',cls_termi__implies__IT_0) ).
fof(c_0_161,axiom,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,X7),c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
file('<stdin>',cls_less__iff__diff__less__0_0) ).
fof(c_0_162,axiom,
! [X33,X28,X18,X19] :
( c_Type_Otyping(X18,X33,X19)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X33))
| ~ c_Type_Otyping(X18,X28,X19) ),
file('<stdin>',cls_subject__reduction_0) ).
fof(c_0_163,axiom,
! [X26,X12,X14] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X26,X12) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
file('<stdin>',cls_subst__Var_0) ).
fof(c_0_164,axiom,
! [X37,X13,X14] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X37,X14) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X13,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
file('<stdin>',cls_subst__gt_0) ).
fof(c_0_165,axiom,
! [X2,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,c_Suc(X14),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_diff__Suc__less_0) ).
fof(c_0_166,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_zero__less__diff_1) ).
fof(c_0_167,axiom,
! [X26,X12] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X26),X12) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X26,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)))),
file('<stdin>',cls_lift_Osimps_I3_J_0) ).
fof(c_0_168,axiom,
! [X2,X3,X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_Nat_Osemiring__1__class_Oof__nat(X3,X7)),c_Nat_Osemiring__1__class_Oof__nat(X2,X7)) ),
file('<stdin>',cls_of__nat__add_0) ).
fof(c_0_169,axiom,
! [X2,X12,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X2,tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
file('<stdin>',cls_less__imp__diff__less_0) ).
fof(c_0_170,axiom,
! [X3,X14] : c_HOL_Oord__class_Oless(X14,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X3)),tc_nat),
file('<stdin>',cls_less__add__Suc1_0) ).
fof(c_0_171,axiom,
! [X3,X14] : c_HOL_Oord__class_Oless(X14,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X14)),tc_nat),
file('<stdin>',cls_less__add__Suc2_0) ).
fof(c_0_172,axiom,
! [X11,X3] : c_HOL_Oord__class_Oless(X3,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X11)),tc_nat),
file('<stdin>',cls_less__iff__Suc__add_1) ).
fof(c_0_173,axiom,
! [X28,X14] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X28),c_Lambda_OdB_OVar(X14))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
file('<stdin>',cls_app__Var__IT_0) ).
fof(c_0_174,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_add__gr__0_2) ).
fof(c_0_175,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
file('<stdin>',cls_add__gr__0_1) ).
fof(c_0_176,axiom,
! [X43,X9,X11,X7] :
( ~ class_Orderings_Opreorder(X7)
| c_HOL_Oord__class_Oless(X11,X43,X7)
| ~ c_HOL_Oord__class_Oless(X9,X43,X7)
| ~ c_HOL_Oord__class_Oless(X11,X9,X7) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_177,axiom,
! [X43,X9,X11,X7] :
( ~ class_Orderings_Oorder(X7)
| c_HOL_Oord__class_Oless(X43,X11,X7)
| ~ c_HOL_Oord__class_Oless(X43,X9,X7)
| ~ c_HOL_Oord__class_Oless(X9,X11,X7) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_178,axiom,
! [X28,X26] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X26)),c_Lambda_OdB_OAbs(X28)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28)) ),
file('<stdin>',cls_abs_0) ).
fof(c_0_179,axiom,
! [X2,X3,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X7),c_Nat_Osemiring__1__class_Oof__nat(X2,X7),X7) ),
file('<stdin>',cls_of__nat__less__iff_0) ).
fof(c_0_180,axiom,
! [X43,X9,X11] :
( c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X43),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X9,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I1_J_0) ).
fof(c_0_181,axiom,
! [X43,X9,X11] :
( c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X43),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X43,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I2_J_0) ).
fof(c_0_182,axiom,
! [X3,X13,X14] :
( c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
file('<stdin>',cls_trans__less__add1_0) ).
fof(c_0_183,axiom,
! [X3,X13,X14] :
( c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
file('<stdin>',cls_trans__less__add2_0) ).
fof(c_0_184,axiom,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(c_Suc(X14),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
file('<stdin>',cls_less__trans__Suc_0) ).
fof(c_0_185,axiom,
! [X13,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X14),X14,tc_nat),
file('<stdin>',cls_not__add__less2_0) ).
fof(c_0_186,axiom,
! [X13,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X13),X14,tc_nat),
file('<stdin>',cls_not__add__less1_0) ).
fof(c_0_187,axiom,
! [X2] :
( c_Suc(c_HOL_Ominus__class_Ominus(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_Suc__pred_0) ).
fof(c_0_188,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(X3,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
file('<stdin>',cls_diff__Suc__eq__diff__pred_0) ).
fof(c_0_189,axiom,
! [X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Oone__class_Oone(X7)),c_HOL_Oone__class_Oone(X7)),X7) ),
file('<stdin>',cls_zero__less__two_0) ).
fof(c_0_190,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)) = X3
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_add__diff__inverse_0) ).
fof(c_0_191,axiom,
! [X2] :
( X2 = c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_Suc__pred_H_0) ).
fof(c_0_192,axiom,
! [X2] :
( c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_Suc__diff__1_0) ).
fof(c_0_193,axiom,
! [X28,X26,X12] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28),X12) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X26,X12)),c_Lambda_Olift(X28,X12)),
file('<stdin>',cls_lift_Osimps_I2_J_0) ).
fof(c_0_194,axiom,
! [X2,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),c_Nat_Osemiring__1__class_Oof__nat(X2,X7),X7) ),
file('<stdin>',cls_of__nat__0__less__iff_0) ).
fof(c_0_195,axiom,
! [X2,X3,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X7),c_Nat_Osemiring__1__class_Oof__nat(X2,X7),X7)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_of__nat__less__iff_1) ).
fof(c_0_196,axiom,
! [X28] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X28,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
file('<stdin>',cls_IT__implies__termi_0) ).
fof(c_0_197,axiom,
! [X2,X3,X6] :
( hBOOL(hAPP(hAPP(X6,X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_nat__less__cases_0) ).
fof(c_0_198,axiom,
! [X20,X5,X7] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X5),X5)),
file('<stdin>',cls_rtranclp_Ortrancl__refl_0) ).
fof(c_0_199,axiom,
! [X11,X20,X7] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X11),X11)),
file('<stdin>',cls_Nitpick_Ortranclp__def_1) ).
fof(c_0_200,axiom,
! [X2,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),c_Nat_Osemiring__1__class_Oof__nat(X2,X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('<stdin>',cls_of__nat__0__less__iff_1) ).
fof(c_0_201,axiom,
! [X43,X9,X11,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X43)
| X9 = X43 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_202,axiom,
! [X8,X10,X11,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X11,X11,X7) != c_HOL_Ominus__class_Ominus(X10,X8,X7)
| X10 = X8 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_203,axiom,
! [X9,X17,X11,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X17,X9,X7) != c_HOL_Ominus__class_Ominus(X11,X11,X7)
| X17 = X9 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_204,axiom,
! [X4,X5,X7] :
( ~ class_Orderings_Opreorder(X7)
| ~ c_HOL_Oord__class_Oless(X4,X5,X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_205,axiom,
! [X9,X11,X7] :
( ~ class_Orderings_Opreorder(X7)
| ~ c_HOL_Oord__class_Oless(X9,X11,X7)
| ~ c_HOL_Oord__class_Oless(X11,X9,X7) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_206,axiom,
! [X9,X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| ~ c_HOL_Oord__class_Oless(X11,X9,X7)
| ~ c_HOL_Oord__class_Oless(X9,X11,X7) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_207,axiom,
! [X4,X5,X7] :
( ~ class_Orderings_Oorder(X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7)
| ~ c_HOL_Oord__class_Oless(X4,X5,X7) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_208,axiom,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat) ),
file('<stdin>',cls_not__less__eq_1) ).
fof(c_0_209,axiom,
! [X2,X3] :
( c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = X2 ),
file('<stdin>',cls_diffs0__imp__equal_0) ).
fof(c_0_210,axiom,
! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),c_HOL_Oone__class_Oone(X7)),X7) ),
file('<stdin>',cls_less__add__one_0) ).
fof(c_0_211,axiom,
! [X12,X14] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X14),X12) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X14,X12,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_1) ).
fof(c_0_212,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X5)
| X4 = X24 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_213,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)
| X4 = X24 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_214,axiom,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)
| X4 = X24 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_215,axiom,
! [X62,X63,X7] :
( X63 = X62
| ~ hBOOL(hAPP(hAPP(c_fequal(X7),X63),X62)) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_216,axiom,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4),X4,X7) = X5 ),
file('<stdin>',cls_add__diff__cancel_0) ).
fof(c_0_217,axiom,
! [X2,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_Suc(X3),tc_nat),
file('<stdin>',cls_diff__less__Suc_0) ).
fof(c_0_218,axiom,
! [X20,X23,X7] : c_Predicate_Oconversep(c_Predicate_Oconversep(X20,X7,X23),X23,X7) = X20,
file('<stdin>',cls_conversep__conversep_0) ).
fof(c_0_219,axiom,
! [X28,X14] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X14)),X28)),
file('<stdin>',cls_beta__cases_I1_J_0) ).
fof(c_0_220,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X2),tc_nat) ),
file('<stdin>',cls_Suc__less__eq_0) ).
fof(c_0_221,axiom,
! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X3)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)),
file('<stdin>',cls_add__Suc_0) ).
fof(c_0_222,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_Suc__mono_0) ).
fof(c_0_223,axiom,
! [X11,X2] :
( c_HOL_Oord__class_Oless(c_Suc(X11),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X2,tc_nat) ),
file('<stdin>',cls_less__Suc__eq__0__disj_3) ).
fof(c_0_224,axiom,
! [X2,X3] :
( X2 = X3
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_0) ).
fof(c_0_225,axiom,
! [X2,X3] :
( X3 = X2
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('<stdin>',cls_less__antisym_0) ).
fof(c_0_226,axiom,
! [X2,X3] :
( X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X2),tc_nat) ),
file('<stdin>',cls_less__SucE_0) ).
fof(c_0_227,axiom,
! [X37,X13,X14] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X37,X14) = c_Lambda_OdB_OVar(X13)
| ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat) ),
file('<stdin>',cls_subst__lt_0) ).
fof(c_0_228,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_Suc(X3),X2,tc_nat)
| c_Suc(X3) = X2
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_Suc__lessI_0) ).
fof(c_0_229,axiom,
! [X2,X3,X12] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X2)
| X3 = X2 ),
file('<stdin>',cls_nat__add__left__cancel_0) ).
fof(c_0_230,axiom,
! [X2,X3,X12] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X12)
| X3 = X2 ),
file('<stdin>',cls_nat__add__right__cancel_0) ).
fof(c_0_231,axiom,
! [X43,X9,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X43)
| X9 = X43 ),
file('<stdin>',cls_natgb_Oadd__cancel_0) ).
fof(c_0_232,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),X2,tc_nat) ),
file('<stdin>',cls_Suc__lessD_0) ).
fof(c_0_233,axiom,
! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)),
file('<stdin>',cls_add__Suc__right_0) ).
fof(c_0_234,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__add__0_0) ).
fof(c_0_235,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat) = X3,
file('<stdin>',cls_diff__add__inverse_0) ).
fof(c_0_236,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X2,tc_nat) = X3,
file('<stdin>',cls_diff__add__inverse2_0) ).
fof(c_0_237,axiom,
! [X3,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X7),c_HOL_Ozero__class_Ozero(X7),X7) ),
file('<stdin>',cls_of__nat__less__0__iff_0) ).
fof(c_0_238,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_less__SucI_0) ).
fof(c_0_239,axiom,
! [X40] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X40),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X40,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_dB_Osize_I6_J_0) ).
fof(c_0_240,axiom,
! [X28,X14] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X28,X14)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
file('<stdin>',cls_lift__IT_0) ).
fof(c_0_241,axiom,
! [X26,X12,X14] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X26,X12) = c_Lambda_OdB_OVar(X14)
| X14 = X12
| c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
file('<stdin>',cls_subst__Var_2) ).
fof(c_0_242,axiom,
! [X9,X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| X11 = X9
| c_HOL_Oord__class_Oless(X11,X9,X7)
| c_HOL_Oord__class_Oless(X9,X11,X7) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_243,axiom,
! [X9,X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| c_HOL_Oord__class_Oless(X9,X11,X7)
| X11 = X9
| c_HOL_Oord__class_Oless(X11,X9,X7) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_244,axiom,
! [X9,X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| c_HOL_Oord__class_Oless(X9,X11,X7)
| c_HOL_Oord__class_Oless(X11,X9,X7)
| X11 = X9 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_245,axiom,
! [X9,X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| X11 = X9
| c_HOL_Oord__class_Oless(X9,X11,X7)
| c_HOL_Oord__class_Oless(X11,X9,X7) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_246,axiom,
! [X9,X11,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| c_HOL_Oord__class_Oless(X9,X11,X7)
| c_HOL_Oord__class_Oless(X11,X9,X7)
| X11 = X9 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_247,axiom,
! [X53,X38,X54,X39] :
( hAPP(hAPP(c_Type_Otype_OFun,X39),X38) != hAPP(hAPP(c_Type_Otype_OFun,X54),X53)
| X39 = X54 ),
file('<stdin>',cls_type_Osimps_I2_J_0) ).
fof(c_0_248,axiom,
! [X53,X38,X54,X39] :
( hAPP(hAPP(c_Type_Otype_OFun,X39),X38) != hAPP(hAPP(c_Type_Otype_OFun,X54),X53)
| X38 = X53 ),
file('<stdin>',cls_type_Osimps_I2_J_1) ).
fof(c_0_249,axiom,
! [X48,X41,X49,X42] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41) != hAPP(hAPP(c_Lambda_OdB_OApp,X49),X48)
| X42 = X49 ),
file('<stdin>',cls_dB_Osimps_I2_J_0) ).
fof(c_0_250,axiom,
! [X48,X41,X49,X42] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41) != hAPP(hAPP(c_Lambda_OdB_OApp,X49),X48)
| X41 = X48 ),
file('<stdin>',cls_dB_Osimps_I2_J_1) ).
fof(c_0_251,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),
file('<stdin>',cls_diff__Suc__Suc_0) ).
fof(c_0_252,axiom,
! [X3,X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X3),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Oone__class_Oone(X7)),c_Nat_Osemiring__1__class_Oof__nat(X3,X7)) ),
file('<stdin>',cls_of__nat__Suc_0) ).
fof(c_0_253,axiom,
! [X11,X26] :
( c_HOL_Oord__class_Oless(X11,X11,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X26,X11) = X26 ),
file('<stdin>',cls_subst__Var_1) ).
fof(c_0_254,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('<stdin>',cls_not__less__eq_0) ).
fof(c_0_255,axiom,
! [X11] :
( c_HOL_Oord__class_Oless(X11,X11,tc_nat)
| c_HOL_Oord__class_Oless(X11,c_Suc(X11),tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_1) ).
fof(c_0_256,axiom,
! [X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),c_HOL_Ozero__class_Ozero(X7),X7) ),
file('<stdin>',cls_not__one__less__zero_0) ).
fof(c_0_257,axiom,
! [X24,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X5) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_258,axiom,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X5) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_259,axiom,
! [X9,X11,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),X11) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_260,axiom,
! [X14,X18,X19] :
( hAPP(X18,X14) = X19
| ~ c_Type_Otyping(X18,c_Lambda_OdB_OVar(X14),X19) ),
file('<stdin>',cls_typing__elims_I1_J_0) ).
fof(c_0_261,axiom,
! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X3)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_Suc(X2)),
file('<stdin>',cls_add__Suc__shift_0) ).
fof(c_0_262,axiom,
! [X9,X11] :
( c_HOL_Oord__class_Oless(X9,X11,tc_nat)
| c_HOL_Oord__class_Oless(X11,X9,tc_nat)
| X11 = X9 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_263,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| X3 = X2 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_264,axiom,
! [X9,X11,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| c_HOL_Ominus__class_Ominus(X11,X9,X7) != c_HOL_Ozero__class_Ozero(X7)
| X11 = X9 ),
file('<stdin>',cls_class__ringb_Osubr0__iff_0) ).
fof(c_0_265,axiom,
! [X12,X14] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X14),X12) = c_Lambda_OdB_OVar(X14)
| ~ c_HOL_Oord__class_Oless(X14,X12,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_0) ).
fof(c_0_266,axiom,
! [X2] :
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('<stdin>',cls_less__Suc0_0) ).
fof(c_0_267,axiom,
! [X11,X7] : hBOOL(hAPP(hAPP(c_fequal(X7),X11),X11)),
file('<stdin>',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(c_0_268,axiom,
! [X11,X5,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| X11 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X5)
| X5 = c_HOL_Ozero__class_Ozero(X7) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_269,axiom,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X5,X4,X7) != c_HOL_Ozero__class_Ozero(X7)
| X5 = X4 ),
file('<stdin>',cls_eq__iff__diff__eq__0_1) ).
fof(c_0_270,axiom,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(X5,X4,X7) != c_HOL_Ozero__class_Ozero(X7)
| X5 = X4 ),
file('<stdin>',cls_right__minus__eq_0) ).
fof(c_0_271,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5) != c_HOL_Ozero__class_Ozero(X7)
| X5 = c_HOL_Ozero__class_Ozero(X7) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_272,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_1) ).
fof(c_0_273,axiom,
! [X2,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_1) ).
fof(c_0_274,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_0) ).
fof(c_0_275,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_3) ).
fof(c_0_276,axiom,
! [X2,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_0) ).
fof(c_0_277,axiom,
! [X2,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_3) ).
fof(c_0_278,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_neq0__conv_1) ).
fof(c_0_279,axiom,
! [X11,X7] :
( ~ class_Orderings_Opreorder(X7)
| ~ c_HOL_Oord__class_Oless(X11,X11,X7) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_280,axiom,
! [X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| ~ c_HOL_Oord__class_Oless(X11,X11,X7) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_281,axiom,
! [X11,X7] :
( ~ class_Orderings_Oorder(X7)
| ~ c_HOL_Oord__class_Oless(X11,X11,X7) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_282,axiom,
! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),
file('<stdin>',cls_nat__add__commute_0) ).
fof(c_0_283,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_2) ).
fof(c_0_284,axiom,
! [X2,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_2) ).
fof(c_0_285,axiom,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_gr__implies__not0_0) ).
fof(c_0_286,axiom,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_not__less0_0) ).
fof(c_0_287,axiom,
! [X11,X51] : c_Type_Otyping(X51,c_Lambda_OdB_OVar(X11),hAPP(X51,X11)),
file('<stdin>',cls_typing_OVar_0) ).
fof(c_0_288,axiom,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat),
file('<stdin>',cls_less__not__refl_0) ).
fof(c_0_289,axiom,
! [X11] : ~ c_HOL_Oord__class_Oless(X11,X11,tc_nat),
file('<stdin>',cls_nat__less__le_1) ).
fof(c_0_290,axiom,
! [X20] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X20)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X20)) ),
file('<stdin>',cls_Lambda_0) ).
fof(c_0_291,axiom,
! [X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7)),c_HOL_Ozero__class_Ozero(X7)) = c_HOL_Ozero__class_Ozero(X7) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_292,axiom,
! [X28,X26,X12] : c_Lambda_Osubst(c_Lambda_Olift(X28,X12),X26,X12) = X28,
file('<stdin>',cls_subst__lift_0) ).
fof(c_0_293,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_add__is__1_4) ).
fof(c_0_294,axiom,
! [X40] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X40)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X40)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_dB_Osize_I3_J_0) ).
fof(c_0_295,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_one__is__add_4) ).
fof(c_0_296,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_0) ).
fof(c_0_297,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_1) ).
fof(c_0_298,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != X3
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__self__zero_0) ).
fof(c_0_299,axiom,
! [X11,X5] :
( X11 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X5)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).
fof(c_0_300,axiom,
! [X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),c_HOL_Oone__class_Oone(X7),X7) ),
file('<stdin>',cls_zero__less__one_0) ).
fof(c_0_301,axiom,
! [X11,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| X11 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),c_HOL_Ozero__class_Ozero(X7)) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_302,axiom,
! [X11,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| c_HOL_Ominus__class_Ominus(X11,X11,X7) = c_HOL_Ozero__class_Ozero(X7) ),
file('<stdin>',cls_class__ringb_Osubr0__iff_1) ).
fof(c_0_303,axiom,
! [X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7)),X5) = X5 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_304,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7)),X5) = X5 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_305,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7)),X5) = X5 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_306,axiom,
! [X11,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7)),X11) = X11 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_307,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('<stdin>',cls_one__is__add_5) ).
fof(c_0_308,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_add__is__1_5) ).
fof(c_0_309,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X7),X7) = X5 ),
file('<stdin>',cls_diff__0__right_0) ).
fof(c_0_310,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('<stdin>',cls_less__Suc0_1) ).
fof(c_0_311,axiom,
! [X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),c_HOL_Ozero__class_Ozero(X7)) = X5 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_312,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),c_HOL_Ozero__class_Ozero(X7)) = X5 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_313,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),c_HOL_Ozero__class_Ozero(X7)) = X5 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_314,axiom,
! [X11,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X11,X11,X7) = c_HOL_Ozero__class_Ozero(X7) ),
file('<stdin>',cls_eq__iff__diff__eq__0_0) ).
fof(c_0_315,axiom,
! [X11,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(X11,X11,X7) = c_HOL_Ozero__class_Ozero(X7) ),
file('<stdin>',cls_right__minus__eq_1) ).
fof(c_0_316,axiom,
! [X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(X5,X5,X7) = c_HOL_Ozero__class_Ozero(X7) ),
file('<stdin>',cls_diff__self_0) ).
fof(c_0_317,axiom,
! [X7] : c_Predicate_Oconversep(c_fequal(X7),X7,X7) = c_fequal(X7),
file('<stdin>',cls_conversep__eq_0) ).
fof(c_0_318,axiom,
! [X50,X41,X42] : hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41) != c_Lambda_OdB_OAbs(X50),
file('<stdin>',cls_dB_Osimps_I8_J_0) ).
fof(c_0_319,axiom,
! [X50,X41,X42] : c_Lambda_OdB_OAbs(X50) != hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41),
file('<stdin>',cls_dB_Osimps_I9_J_0) ).
fof(c_0_320,axiom,
! [X1,X48,X49] : c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X49),X48),
file('<stdin>',cls_dB_Osimps_I4_J_0) ).
fof(c_0_321,axiom,
! [X1,X48,X49] : hAPP(hAPP(c_Lambda_OdB_OApp,X49),X48) != c_Lambda_OdB_OVar(X1),
file('<stdin>',cls_dB_Osimps_I5_J_0) ).
fof(c_0_322,axiom,
! [X2] : c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2,
file('<stdin>',cls_diff__Suc__1_0) ).
fof(c_0_323,axiom,
! [X2] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X2),tc_nat),
file('<stdin>',cls_zero__less__Suc_0) ).
fof(c_0_324,axiom,
! [X11] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X11),tc_nat),
file('<stdin>',cls_gr0__conv__Suc_1) ).
fof(c_0_325,axiom,
! [X37,X12] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X37,X12) = X37,
file('<stdin>',cls_subst__eq_0) ).
fof(c_0_326,axiom,
! [X44,X7] : c_List_Olistsp(X44,c_List_Olist_ONil(X7),X7),
file('<stdin>',cls_listsp_ONil_0) ).
fof(c_0_327,axiom,
! [X2] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_gr0I_0) ).
fof(c_0_328,axiom,
! [X11] : c_HOL_Oord__class_Oless(X11,c_Suc(X11),tc_nat),
file('<stdin>',cls_less__Suc__eq_2) ).
fof(c_0_329,axiom,
! [X2] : c_HOL_Oord__class_Oless(X2,c_Suc(X2),tc_nat),
file('<stdin>',cls_lessI_0) ).
fof(c_0_330,axiom,
! [X2] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__0__eq__0_0) ).
fof(c_0_331,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_add__is__0_2) ).
fof(c_0_332,axiom,
! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
file('<stdin>',cls_minus__nat_Odiff__0_0) ).
fof(c_0_333,axiom,
! [X2] : c_Suc(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X2),
file('<stdin>',cls_Suc__eq__plus1__left_0) ).
fof(c_0_334,axiom,
! [X3] : c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_diff__self__eq__0_0) ).
fof(c_0_335,axiom,
! [X20,X7] : c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X20,X7),X7) = c_Transitive__Closure_Ortranclp(X20,X7),
file('<stdin>',cls_rtranclp__idemp_0) ).
fof(c_0_336,axiom,
! [X2,X3,X7] :
( ~ class_Nat_Osemiring__char__0(X7)
| c_Nat_Osemiring__1__class_Oof__nat(X3,X7) != c_Nat_Osemiring__1__class_Oof__nat(X2,X7)
| X3 = X2 ),
file('<stdin>',cls_of__nat__eq__iff_0) ).
fof(c_0_337,axiom,
! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2,
file('<stdin>',cls_plus__nat_Oadd__0_0) ).
fof(c_0_338,axiom,
! [X2] : c_Suc(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),
file('<stdin>',cls_Suc__eq__plus1_0) ).
fof(c_0_339,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
file('<stdin>',cls_Beta_I7_J_0) ).
fof(c_0_340,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('<stdin>',cls_uT_0) ).
fof(c_0_341,axiom,
! [X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ozero__class_Ozero(tc_nat)) = X3,
file('<stdin>',cls_Nat_Oadd__0__right_0) ).
fof(c_0_342,axiom,
! [X11] : X11 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_natgb_Oadd__r0__iff_1) ).
fof(c_0_343,axiom,
! [X2] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X2))),
file('<stdin>',cls_Var__IT_0) ).
fof(c_0_344,axiom,
! [X60,X61] :
( class_Orderings_Oorder(tc_fun(X60,X61))
| ~ class_Orderings_Oorder(X61) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_345,axiom,
! [X60,X61] :
( class_Orderings_Opreorder(tc_fun(X60,X61))
| ~ class_Orderings_Opreorder(X61) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_346,axiom,
! [X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X7) = c_HOL_Oone__class_Oone(X7) ),
file('<stdin>',cls_of__nat__1_0) ).
fof(c_0_347,axiom,
! [X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X7) = c_HOL_Ozero__class_Ozero(X7) ),
file('<stdin>',cls_of__nat__0_0) ).
fof(c_0_348,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
file('<stdin>',cls_Beta_I3_J_0) ).
fof(c_0_349,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
file('<stdin>',cls_Beta_I6_J_0) ).
fof(c_0_350,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('<stdin>',cls_uIT_0) ).
fof(c_0_351,axiom,
! [X1] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_dB_Osize_I4_J_0) ).
fof(c_0_352,axiom,
! [X7] :
( ~ class_Ring__and__Field_Ozero__neq__one(X7)
| c_HOL_Ozero__class_Ozero(X7) != c_HOL_Oone__class_Oone(X7) ),
file('<stdin>',cls_zero__neq__one_0) ).
fof(c_0_353,axiom,
! [X7] :
( ~ class_Ring__and__Field_Ozero__neq__one(X7)
| c_HOL_Oone__class_Oone(X7) != c_HOL_Ozero__class_Ozero(X7) ),
file('<stdin>',cls_one__neq__zero_0) ).
fof(c_0_354,axiom,
! [X25,X1] :
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X25)
| X1 = X25 ),
file('<stdin>',cls_dB_Osimps_I1_J_0) ).
fof(c_0_355,axiom,
! [X50,X40] :
( c_Lambda_OdB_OAbs(X40) != c_Lambda_OdB_OAbs(X50)
| X40 = X50 ),
file('<stdin>',cls_dB_Osimps_I3_J_0) ).
fof(c_0_356,axiom,
! [X9,X11] :
( c_Suc(X11) != c_Suc(X9)
| X11 = X9 ),
file('<stdin>',cls_Suc__inject_0) ).
fof(c_0_357,axiom,
! [X25,X1] :
( c_Suc(X1) != c_Suc(X25)
| X1 = X25 ),
file('<stdin>',cls_nat_Oinject_0) ).
fof(c_0_358,axiom,
! [X1,X50] : c_Lambda_OdB_OAbs(X50) != c_Lambda_OdB_OVar(X1),
file('<stdin>',cls_dB_Osimps_I7_J_0) ).
fof(c_0_359,axiom,
! [X1,X50] : c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X50),
file('<stdin>',cls_dB_Osimps_I6_J_0) ).
fof(c_0_360,axiom,
! [X1] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_dB_Osize_I1_J_0) ).
fof(c_0_361,axiom,
! [X25] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X25),
file('<stdin>',cls_nat_Osimps_I2_J_0) ).
fof(c_0_362,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X3),
file('<stdin>',cls_Zero__neq__Suc_0) ).
fof(c_0_363,axiom,
! [X3] : c_Suc(X3) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_Suc__neq__Zero_0) ).
fof(c_0_364,axiom,
! [X25] : c_Suc(X25) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_nat_Osimps_I3_J_0) ).
fof(c_0_365,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_One__nat__def_0) ).
fof(c_0_366,axiom,
! [X2] : X2 != c_Suc(X2),
file('<stdin>',cls_n__not__Suc__n_0) ).
fof(c_0_367,axiom,
! [X2] : c_Suc(X2) != X2,
file('<stdin>',cls_Suc__n__not__n_0) ).
fof(c_0_368,axiom,
class_Orderings_Oorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Oorder) ).
fof(c_0_369,axiom,
class_Orderings_Opreorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Opreorder) ).
fof(c_0_370,axiom,
class_Orderings_Oorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Oorder) ).
fof(c_0_371,axiom,
class_Orderings_Olinorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Olinorder) ).
fof(c_0_372,axiom,
class_Orderings_Opreorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Opreorder) ).
fof(c_0_373,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('<stdin>',clsarity_nat__Nat_Osemiring__char__0) ).
fof(c_0_374,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(c_0_375,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(c_0_376,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(c_0_377,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_378,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_379,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_380,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_381,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(c_0_382,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_383,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_384,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_385,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(c_0_386,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_387,plain,
! [X29,X27,X14,X18,X30,X31,X19] :
( X30 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X19,X30,X18,X29),X19,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X30)
| ~ c_Type_Otypings(X18,X27,X31)
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X29,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_388,plain,
! [X35,X36,X2] :
( X35 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X36,X35),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X36,tc_Lambda_OdB,tc_Lambda_OdB)),X35)) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_389,plain,
! [X29,X27,X14,X18,X30,X31,X19] :
( c_Type_Otypings(X18,X29,c_Type_Osko__Type__Xvar__app__types__1__1(X19,X30,X18,X29))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X30)
| ~ c_Type_Otypings(X18,X27,X31)
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X29,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_390,plain,
! [X37,X14,X18,X52] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X37,X14)))
| ~ c_Type_Otyping(X18,X37,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X37))
| ~ c_Type_Otyping(c_Type_Oshift(X18,X14,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X52) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_391,plain,
! [X35,X36,X2] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X36,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X36,X35),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X36,tc_Lambda_OdB,tc_Lambda_OdB)),X35)) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_392,plain,
! [X47,X36,X20] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X36,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X47,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X36,X47,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_393,plain,
! [X47,X26,X20] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X47,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_394,plain,
! [X47,X26,X20] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X47,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_395,plain,
! [X47,X26,X20] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20)),X26),X47,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X20,X26,c_HOL_Ozero__class_Ozero(tc_nat)),X47,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_396,plain,
! [X27,X14,X18,X30,X19] :
( X19 = X30
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X30)
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_397,plain,
! [X47,X26,X20] :
( ~ 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(X20,X26,c_HOL_Ozero__class_Ozero(tc_nat)),X47,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X26,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20)),X26),X47,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_398,plain,
! [X27,X14,X18,X19] :
( c_Type_Otyping(X18,c_Lambda_OdB_OVar(X14),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X19,X18,X14,X27),X19,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_399,plain,
! [X27,X28,X18,X19] :
( c_Type_Otyping(X18,X28,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X19,X18,X28,X27),X19,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_400,plain,
! [X27,X28,X18,X19] :
( c_Type_Otyping(X18,X28,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X19,X18,X28,X27),X19,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_401,plain,
! [X27,X28,X18,X31,X19] :
( c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X19)
| ~ c_Type_Otypings(X18,X27,X31)
| ~ c_Type_Otyping(X18,X28,c_List_Ofoldr(c_Type_Otype_OFun,X31,X19,tc_Type_Otype,tc_Type_Otype)) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_402,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_15 ).
fof(c_0_403,plain,
! [X36,X2] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X36,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X36,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_404,plain,
! [X27,X14,X18,X19] :
( c_Type_Otypings(X18,X27,c_Type_Osko__Type__Xvar__app__typesE__1__1(X19,X18,X14,X27))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_405,plain,
! [X27,X28,X18,X19] :
( c_Type_Otypings(X18,X27,c_Type_Osko__Type__Xlist__app__typeD__1__1(X19,X18,X28,X27))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_406,plain,
! [X27,X28,X18,X19] :
( c_Type_Otypings(X18,X27,c_Type_Osko__Type__Xlist__app__typeE__1__1(X19,X18,X28,X27))
| ~ c_Type_Otyping(X18,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X19) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_407,axiom,
! [X47,X36,X2,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X3 = X2 ),
c_0_20 ).
fof(c_0_408,axiom,
! [X47,X36,X2,X3] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X36 = X47 ),
c_0_21 ).
fof(c_0_409,axiom,
! [X47,X26,X36,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26),X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X20 = X26 ),
c_0_22 ).
fof(c_0_410,axiom,
! [X47,X26,X36,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26),X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X36 = X47 ),
c_0_23 ).
fof(c_0_411,plain,
! [X32,X9,X11,X7] :
( ~ class_OrderedGroup_Osemigroup__add(X7)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X9),X32,X7,X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),X9,X32,X7,X7)) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_412,axiom,
! [X27,X47,X20,X2] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X27,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X47,tc_Lambda_OdB,tc_Lambda_OdB),
c_0_25 ).
fof(c_0_413,axiom,
! [X27,X26,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X27,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X27,tc_Lambda_OdB,tc_Lambda_OdB)
| X20 = X26 ),
c_0_26 ).
fof(c_0_414,plain,
! [X21,X5,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),X5,X21,X7,X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X7),X21,c_HOL_Ozero__class_Ozero(X7),X7,X7)) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_415,plain,
! [X32,X11,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7),X32,X7,X7)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),X11,X32,X7,X7) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_416,axiom,
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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
c_0_29 ).
fof(c_0_417,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
c_0_30 ).
fof(c_0_418,plain,
! [X21,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7),X21,X7,X7) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X7),X21,c_HOL_Ozero__class_Ozero(X7),X7,X7) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_419,plain,
! [X21,X5,X7] :
( ~ class_OrderedGroup_Oab__semigroup__add(X7)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X7),X21,X5,X7,X7) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X7),X5,X21,X7,X7) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_420,plain,
! [X37,X28,X18,X19] :
( c_Type_Otyping(X18,X28,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X19,X18,X28,X37)),X19))
| ~ c_Type_Otyping(X18,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X37),X19) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_421,axiom,
! [X28,X26,X20] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X20),X26) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X20),X26) = X28 ),
c_0_34 ).
fof(c_0_422,axiom,
! [X28,X47,X26,X2] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X28) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X47,tc_Lambda_OdB,tc_Lambda_OdB),
c_0_35 ).
fof(c_0_423,axiom,
! [X47,X26,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X20)
| X26 = c_Lambda_OdB_OAbs(X20) ),
c_0_36 ).
fof(c_0_424,axiom,
! [X47,X26,X3] :
( c_Lambda_OdB_OVar(X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X3) = X26 ),
c_0_37 ).
fof(c_0_425,axiom,
! [X47,X26,X20] :
( c_Lambda_OdB_OAbs(X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X20) = X26 ),
c_0_38 ).
fof(c_0_426,axiom,
! [X47,X26,X3] :
( c_Lambda_OdB_OVar(X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X47 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_39 ).
fof(c_0_427,axiom,
! [X47,X26,X20] :
( c_Lambda_OdB_OAbs(X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X47 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_40 ).
fof(c_0_428,axiom,
! [X47,X26,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X47,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X20)
| X47 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_41 ).
fof(c_0_429,plain,
! [X9,X11,X20,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X9),X11))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X20,X7,X7),X7),X11),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_430,axiom,
! [X14,X18,X30,X19,X7] : c_Type_Oshift(c_Type_Oshift(X18,X14,X30,X7),c_HOL_Ozero__class_Ozero(tc_nat),X19,X7) = c_Type_Oshift(c_Type_Oshift(X18,c_HOL_Ozero__class_Ozero(tc_nat),X19,X7),c_Suc(X14),X30,X7),
c_0_43 ).
fof(c_0_431,plain,
! [X9,X11,X20,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X20,X7,X7),X7),X11),X9))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X9),X11)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_432,plain,
! [X37,X28,X14,X18,X55,X56,X57] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X57),X56)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X28,X37,X14)))
| ~ c_Type_Otyping(X18,X37,X57)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X37))
| ~ c_Type_Otyping(c_Type_Oshift(X18,X14,X57,tc_Type_Otype),X28,X55)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_433,plain,
! [X37,X28,X14,X18,X55,X56,X57] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X57),X56)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X28,X37,X14)))
| ~ c_Type_Otyping(X18,X37,X56)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X37))
| ~ c_Type_Otyping(c_Type_Oshift(X18,X14,X56,tc_Type_Otype),X28,X55)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_434,axiom,
! [X26,X20] : hAPP(hAPP(c_Lambda_OdB_OApp,X20),X26) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X20),X26),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_47 ).
fof(c_0_435,axiom,
! [X3] : c_Lambda_OdB_OVar(X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_48 ).
fof(c_0_436,axiom,
! [X20] : c_Lambda_OdB_OAbs(X20) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_49 ).
fof(c_0_437,axiom,
! [X20] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X20),
c_0_50 ).
fof(c_0_438,plain,
! [X37,X14,X18,X52] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X37,X14)))
| ~ c_Type_Otyping(X18,X37,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X37))
| ~ c_Type_Otyping(c_Type_Oshift(X18,X14,v_T____,tc_Type_Otype),v_a____,X52) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_439,axiom,
! [X22,X5,X23,X7] : c_List_Ofoldr(X22,c_List_Olist_ONil(X23),X5,X23,X7) = X5,
c_0_52 ).
fof(c_0_440,axiom,
! [X22,X5,X23,X7] : c_List_Ofoldl(X22,X5,c_List_Olist_ONil(X23),X7,X23) = X5,
c_0_53 ).
fof(c_0_441,plain,
! [X37,X28,X14,X59,X30,X19] :
( ~ c_Type_Otyping(X59,X37,X30)
| ~ c_Type_Otyping(c_Type_Oshift(X59,X14,X30,tc_Type_Otype),X28,X19)
| c_Type_Otyping(X59,c_Lambda_Osubst(X28,X37,X14),X19) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_442,plain,
! [X33,X28,X34,X26] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X33)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X33))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X34)) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_443,plain,
! [X28,X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X28,X20,X14)),c_Lambda_Osubst(X28,X26,X14)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_444,plain,
! [X28,X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X20,X28,X14)),c_Lambda_Osubst(X26,X28,X14)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_445,plain,
! [X28,X51,X30,X19] :
( c_Type_Otyping(X51,c_Lambda_OdB_OAbs(X28),hAPP(hAPP(c_Type_Otype_OFun,X19),X30))
| ~ c_Type_Otyping(c_Type_Oshift(X51,c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_Type_Otype),X28,X30) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_446,plain,
! [X16,X4,X6] :
( ~ hBOOL(hAPP(X6,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X16),X4,tc_nat)))
| hBOOL(hAPP(X6,X16)) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_447,plain,
! [X11,X4,X6] :
( ~ hBOOL(hAPP(X6,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X11),X4,tc_nat)))
| hBOOL(hAPP(X6,X11)) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_448,plain,
! [X28,X18,X19] :
( c_Type_Otyping(c_Type_Oshift(X18,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X19,X18,X28),tc_Type_Otype),X28,c_Type_Osko__Type__Xtyping__elims__3__2(X19,X18,X28))
| ~ c_Type_Otyping(X18,c_Lambda_OdB_OAbs(X28),X19) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_449,plain,
! [X28,X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X28,X20,X14)),c_Lambda_Osubst(X28,X26,X14)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_450,plain,
! [X20,X4,X5,X23,X7] :
( hBOOL(hAPP(hAPP(X20,X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X20,X7,X23),X5),X4)) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_451,plain,
! [X20,X45,X46,X23,X7] :
( hBOOL(hAPP(hAPP(X20,X45),X46))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X20,X7,X23),X46),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_452,plain,
! [X33,X28,X26] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X33)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X33)) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_453,plain,
! [X28,X34,X26] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X28)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X34)) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_454,plain,
! [X58] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X58) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_455,plain,
! [X28,X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X20,X28,X14)),c_Lambda_Osubst(X26,X28,X14)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_456,plain,
! [X43,X9,X11,X20,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X11),X43))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X9),X43))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X11),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_457,plain,
! [X37,X28,X18,X19] :
( c_Type_Otyping(X18,X37,c_Type_Osko__Type__Xtyping__elims__2__1(X19,X18,X28,X37))
| ~ c_Type_Otyping(X18,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X37),X19) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_458,plain,
! [X35,X37,X28,X13,X14] :
( c_Lambda_Osubst(c_Lambda_Osubst(X28,c_Lambda_Olift(X35,X14),c_Suc(X13)),c_Lambda_Osubst(X37,X35,X13),X14) = c_Lambda_Osubst(c_Lambda_Osubst(X28,X37,X14),X35,X13)
| ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_459,plain,
! [X16,X24,X4,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_460,plain,
! [X28,X18,X19] :
( c_Type_Otyping(c_Type_Oshift(X18,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X18,X28),tc_Type_Otype),X28,c_Type_Osko__Type__Xabs__typeE__1__2(X18,X28))
| ~ c_Type_Otyping(X18,c_Lambda_OdB_OAbs(X28),X19) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_461,plain,
! [X13,X14,X18,X19,X7] :
( hAPP(c_Type_Oshift(X18,X14,X19,X7),X13) = hAPP(X18,c_HOL_Ominus__class_Ominus(X13,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_462,axiom,
! [X28,X26] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X28)),c_Lambda_Osubst(X26,X28,c_HOL_Ozero__class_Ozero(tc_nat)))),
c_0_75 ).
fof(c_0_463,plain,
! [X28,X14,X18,X30,X19] :
( c_Type_Otyping(c_Type_Oshift(X18,X14,X30,tc_Type_Otype),c_Lambda_Olift(X28,X14),X19)
| ~ c_Type_Otyping(X18,X28,X19) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_464,plain,
! [X28,X26,X13,X14] :
( c_Lambda_Olift(c_Lambda_Osubst(X28,X26,X13),X14) = c_Lambda_Osubst(c_Lambda_Olift(X28,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Olift(X26,X14),X13)
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_465,plain,
! [X20,X4,X5,X23,X7] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X20,X7,X23),X5),X4))
| ~ hBOOL(hAPP(hAPP(X20,X4),X5)) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_466,plain,
! [X20,X4,X5,X23,X7] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X20,X7,X23),X4),X5))
| ~ hBOOL(hAPP(hAPP(X20,X5),X4)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_467,plain,
! [X37,X28,X26] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X37),X26)),hAPP(hAPP(c_Lambda_OdB_OApp,X37),X28)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_468,plain,
! [X37,X28,X26] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X37)),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X37)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_469,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_OAbs(v_r____)),v_a____),v_Ua____),
c_0_82 ).
fof(c_0_470,plain,
! [X20,X24,X4,X5,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X5),X24))
| ~ hBOOL(hAPP(hAPP(X20,X4),X24))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X5),X4)) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_471,plain,
! [X20,X24,X4,X5,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X5),X24))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X4),X24))
| ~ hBOOL(hAPP(hAPP(X20,X5),X4)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_472,plain,
! [X13,X14,X18,X19,X7] :
( hAPP(c_Type_Oshift(X18,X14,X19,X7),X13) = hAPP(X18,X13)
| ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_473,axiom,
! [X41,X42] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X42,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X41,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_86 ).
fof(c_0_474,axiom,
! [X38,X39] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X39),X38),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X39,tc_Type_Otype)),c_Nat_Osize__class_Osize(X38,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_87 ).
fof(c_0_475,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_88 ).
fof(c_0_476,plain,
! [X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X20,X14)),c_Lambda_Olift(X26,X14)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_477,plain,
! [X28,X26,X13,X14] :
( c_Lambda_Olift(c_Lambda_Osubst(X28,X26,X13),X14) = c_Lambda_Osubst(c_Lambda_Olift(X28,X14),c_Lambda_Olift(X26,X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_478,plain,
! [X24,X4,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_479,axiom,
! [X11,X18,X19,X7] : hAPP(c_Type_Oshift(X18,X11,X19,X7),X11) = X19,
c_0_92 ).
fof(c_0_480,plain,
! [X4,X5,X6] :
( hBOOL(hAPP(X6,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ hBOOL(hAPP(X6,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat))) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_481,axiom,
! [X37,X28,X26,X12] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X28),X37),X26,X12) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X28,X26,X12)),c_Lambda_Osubst(X37,X26,X12)),
c_0_94 ).
fof(c_0_482,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X7)
| c_HOL_Oord__class_Oless(X5,X4,X7)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X4),X7) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_483,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X7)
| c_HOL_Oord__class_Oless(X5,X4,X7)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24),X7) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_484,plain,
! [X28,X18,X19] :
( X19 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X19,X18,X28)),c_Type_Osko__Type__Xtyping__elims__3__2(X19,X18,X28))
| ~ c_Type_Otyping(X18,c_Lambda_OdB_OAbs(X28),X19) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_485,plain,
! [X34,X26] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X26)),c_Lambda_OdB_OAbs(X34)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X34)) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_486,plain,
! [X16,X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X16),X7)
| ~ c_HOL_Oord__class_Oless(X24,X16,X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_487,plain,
! [X20,X4,X5,X7] :
( c_Wellfounded_Oaccp(X20,X4,X7)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X4),X5))
| ~ c_Wellfounded_Oaccp(X20,X5,X7) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_488,plain,
! [X20,X4,X5,X7] :
( c_Wellfounded_Oaccp(X20,X4,X7)
| ~ c_Wellfounded_Oaccp(X20,X5,X7)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X4),X5)) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_489,plain,
! [X2,X3,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X2,tc_nat),c_HOL_Ominus__class_Ominus(X15,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_490,axiom,
! [X28,X26,X12] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X28),X26,X12) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X28,c_Lambda_Olift(X26,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)))),
c_0_103 ).
fof(c_0_491,plain,
! [X2,X3,X12] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X2),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_492,plain,
! [X24,X4,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_493,plain,
! [X16,X24,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)),X16) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_494,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Oab__semigroup__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24)) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_495,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24)) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_496,plain,
! [X43,X9,X11,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),X43)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X9)),X43) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_497,plain,
! [X28,X26,X51,X30,X19] :
( c_Type_Otyping(X51,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28),X30)
| ~ c_Type_Otyping(X51,X28,X19)
| ~ c_Type_Otyping(X51,X26,hAPP(hAPP(c_Type_Otype_OFun,X19),X30)) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_498,plain,
! [X15,X12,X13,X14] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_499,plain,
! [X21,X20,X7] : ~ c_ListOrder_Ostep1(X20,X21,c_List_Olist_ONil(X7),X7),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_500,plain,
! [X21,X20,X7] : ~ c_ListOrder_Ostep1(X20,c_List_Olist_ONil(X7),X21,X7),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_501,plain,
! [X33,X28,X18,X19] :
( c_Type_Otyping(X18,X33,X19)
| ~ c_Type_Otyping(X18,X28,X19)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X33)) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_502,plain,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X12),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_503,axiom,
! [X41,X42] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X42)),c_Lambda_OdB_OdB__size(X41))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_116 ).
fof(c_0_504,axiom,
! [X38,X39] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X39),X38)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X39)),c_Type_Otype_Otype__size(X38))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_117 ).
fof(c_0_505,plain,
! [X43,X9,X11,X37,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),X43)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),X37)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X43) = X37 ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_506,plain,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(X14,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X12),X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_507,axiom,
! [X2,X3,X12] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X12)),
c_0_120 ).
fof(c_0_508,plain,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X4,X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X5,X7) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_509,plain,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4),c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_510,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X4),X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_511,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X4),X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_512,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24),X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_513,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24),X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_514,plain,
! [X26,X20,X14] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X20,X14)),c_Lambda_Olift(X26,X14)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_515,plain,
! [X24,X4,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24),X7)
| ~ c_HOL_Oord__class_Oless(X4,X24,X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X5,X7) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_516,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_517,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_518,axiom,
! [X2,X3,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X2,tc_nat),c_Suc(X12),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X12,tc_nat),
c_0_131 ).
fof(c_0_519,plain,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(X5,X4,X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,X7),c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_520,plain,
! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_521,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_522,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X5,X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),X7) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_523,plain,
! [X28,X12,X14] :
( c_Lambda_Olift(c_Lambda_Olift(X28,X14),c_Suc(X12)) = c_Lambda_Olift(c_Lambda_Olift(X28,X12),X14)
| ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_524,plain,
! [X8,X9,X10,X11,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X11,X9,X7) != c_HOL_Ominus__class_Ominus(X10,X8,X7)
| c_HOL_Oord__class_Oless(X10,X8,X7)
| ~ c_HOL_Oord__class_Oless(X11,X9,X7) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_525,plain,
! [X8,X9,X10,X11,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X11,X9,X7) != c_HOL_Ominus__class_Ominus(X10,X8,X7)
| c_HOL_Oord__class_Oless(X11,X9,X7)
| ~ c_HOL_Oord__class_Oless(X10,X8,X7) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_526,plain,
! [X2,X3,X12] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_527,plain,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_528,plain,
! [X16,X24,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_529,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_530,plain,
! [X43,X9,X11,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),X43)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X43)) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_531,plain,
! [X9,X11,X20,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X11),X9))
| ~ hBOOL(hAPP(hAPP(X20,X11),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_532,axiom,
! [X12,X13,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X14,X12,tc_nat),X13,tc_nat),
c_0_145 ).
fof(c_0_533,plain,
! [X20,X13,X14] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X20,c_Lambda_OdB_OVar(X14),X13)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X20)) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_534,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_535,axiom,
! [X12,X13,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12),tc_nat),
c_0_148 ).
fof(c_0_536,axiom,
! [X2,X3,X12] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),
c_0_149 ).
fof(c_0_537,axiom,
! [X2,X3,X12] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X12),tc_nat) = c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),
c_0_150 ).
fof(c_0_538,plain,
! [X2,X3,X15,X12] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X2)
| ~ c_HOL_Oord__class_Oless(X12,X15,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_539,plain,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(X14,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X13),X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_540,plain,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ominus__class_Ominus(X5,X4,X7)),X4) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_541,axiom,
! [X43,X9,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X43)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X43)),
c_0_154 ).
fof(c_0_542,plain,
! [X20,X4,X5,X7] :
( c_Wellfounded_Oaccp(X20,X5,X7)
| ~ hBOOL(hAPP(hAPP(X20,X5),X4))
| ~ c_Wellfounded_Oaccp(X20,X4,X7) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_543,plain,
! [X9,X20,X5,X7] :
( c_Wellfounded_Oaccp(X20,X9,X7)
| ~ hBOOL(hAPP(hAPP(X20,X9),X5))
| ~ c_Wellfounded_Oaccp(X20,X5,X7) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_544,plain,
! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_545,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_546,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),X5,X7) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_547,plain,
! [X20] :
( hBOOL(hAPP(c_InductTermi_OIT,X20))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X20,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_548,plain,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,X7),c_HOL_Ozero__class_Ozero(X7),X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_549,plain,
! [X33,X28,X18,X19] :
( c_Type_Otyping(X18,X33,X19)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X33))
| ~ c_Type_Otyping(X18,X28,X19) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_550,plain,
! [X26,X12,X14] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X26,X12) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_551,plain,
! [X37,X13,X14] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X37,X14) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X13,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_552,plain,
! [X2,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,c_Suc(X14),tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_553,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_554,axiom,
! [X26,X12] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X26),X12) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X26,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)))),
c_0_167 ).
fof(c_0_555,plain,
! [X2,X3,X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_Nat_Osemiring__1__class_Oof__nat(X3,X7)),c_Nat_Osemiring__1__class_Oof__nat(X2,X7)) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_556,plain,
! [X2,X12,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X2,tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_557,axiom,
! [X3,X14] : c_HOL_Oord__class_Oless(X14,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X3)),tc_nat),
c_0_170 ).
fof(c_0_558,axiom,
! [X3,X14] : c_HOL_Oord__class_Oless(X14,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X14)),tc_nat),
c_0_171 ).
fof(c_0_559,axiom,
! [X11,X3] : c_HOL_Oord__class_Oless(X3,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X11)),tc_nat),
c_0_172 ).
fof(c_0_560,plain,
! [X28,X14] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X28),c_Lambda_OdB_OVar(X14))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_561,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_562,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_563,plain,
! [X43,X9,X11,X7] :
( ~ class_Orderings_Opreorder(X7)
| c_HOL_Oord__class_Oless(X11,X43,X7)
| ~ c_HOL_Oord__class_Oless(X9,X43,X7)
| ~ c_HOL_Oord__class_Oless(X11,X9,X7) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_564,plain,
! [X43,X9,X11,X7] :
( ~ class_Orderings_Oorder(X7)
| c_HOL_Oord__class_Oless(X43,X11,X7)
| ~ c_HOL_Oord__class_Oless(X43,X9,X7)
| ~ c_HOL_Oord__class_Oless(X9,X11,X7) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_565,plain,
! [X28,X26] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X26)),c_Lambda_OdB_OAbs(X28)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_566,plain,
! [X2,X3,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X7),c_Nat_Osemiring__1__class_Oof__nat(X2,X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_567,plain,
! [X43,X9,X11] :
( c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X43),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X9,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_568,plain,
! [X43,X9,X11] :
( c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X43),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X43,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_569,plain,
! [X3,X13,X14] :
( c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_570,plain,
! [X3,X13,X14] :
( c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_571,plain,
! [X12,X13,X14] :
( c_HOL_Oord__class_Oless(c_Suc(X14),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_572,plain,
! [X13,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X14),X14,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_573,plain,
! [X13,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X13),X14,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_574,plain,
! [X2] :
( c_Suc(c_HOL_Ominus__class_Ominus(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_575,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(X3,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
c_0_188 ).
fof(c_0_576,plain,
! [X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Oone__class_Oone(X7)),c_HOL_Oone__class_Oone(X7)),X7) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_577,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)) = X3
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
c_0_190 ).
fof(c_0_578,plain,
! [X2] :
( X2 = c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_579,plain,
! [X2] :
( c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_580,axiom,
! [X28,X26,X12] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28),X12) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X26,X12)),c_Lambda_Olift(X28,X12)),
c_0_193 ).
fof(c_0_581,plain,
! [X2,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),c_Nat_Osemiring__1__class_Oof__nat(X2,X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_582,plain,
! [X2,X3,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X7),c_Nat_Osemiring__1__class_Oof__nat(X2,X7),X7)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_583,plain,
! [X28] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X28,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_584,axiom,
! [X2,X3,X6] :
( hBOOL(hAPP(hAPP(X6,X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
c_0_197 ).
fof(c_0_585,axiom,
! [X20,X5,X7] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X5),X5)),
c_0_198 ).
fof(c_0_586,axiom,
! [X11,X20,X7] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X20,X7),X11),X11)),
c_0_199 ).
fof(c_0_587,plain,
! [X2,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),c_Nat_Osemiring__1__class_Oof__nat(X2,X7),X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_588,plain,
! [X43,X9,X11,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X43)
| X9 = X43 ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_589,plain,
! [X8,X10,X11,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X11,X11,X7) != c_HOL_Ominus__class_Ominus(X10,X8,X7)
| X10 = X8 ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_590,plain,
! [X9,X17,X11,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X17,X9,X7) != c_HOL_Ominus__class_Ominus(X11,X11,X7)
| X17 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_591,plain,
! [X4,X5,X7] :
( ~ class_Orderings_Opreorder(X7)
| ~ c_HOL_Oord__class_Oless(X4,X5,X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_592,plain,
! [X9,X11,X7] :
( ~ class_Orderings_Opreorder(X7)
| ~ c_HOL_Oord__class_Oless(X9,X11,X7)
| ~ c_HOL_Oord__class_Oless(X11,X9,X7) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_593,plain,
! [X9,X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| ~ c_HOL_Oord__class_Oless(X11,X9,X7)
| ~ c_HOL_Oord__class_Oless(X9,X11,X7) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_594,plain,
! [X4,X5,X7] :
( ~ class_Orderings_Oorder(X7)
| ~ c_HOL_Oord__class_Oless(X5,X4,X7)
| ~ c_HOL_Oord__class_Oless(X4,X5,X7) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_595,plain,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_596,axiom,
! [X2,X3] :
( c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = X2 ),
c_0_209 ).
fof(c_0_597,plain,
! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),c_HOL_Oone__class_Oone(X7)),X7) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_598,axiom,
! [X12,X14] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X14),X12) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X14,X12,tc_nat) ),
c_0_211 ).
fof(c_0_599,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X5)
| X4 = X24 ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_600,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)
| X4 = X24 ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_601,plain,
! [X24,X4,X5,X7] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24)
| X4 = X24 ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_602,plain,
! [X62,X63,X7] :
( X63 = X62
| ~ hBOOL(hAPP(hAPP(c_fequal(X7),X63),X62)) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_603,plain,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4),X4,X7) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_604,axiom,
! [X2,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_Suc(X3),tc_nat),
c_0_217 ).
fof(c_0_605,axiom,
! [X20,X23,X7] : c_Predicate_Oconversep(c_Predicate_Oconversep(X20,X7,X23),X23,X7) = X20,
c_0_218 ).
fof(c_0_606,plain,
! [X28,X14] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X14)),X28)),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_607,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X2),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_608,axiom,
! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X3)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)),
c_0_221 ).
fof(c_0_609,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_610,plain,
! [X11,X2] :
( c_HOL_Oord__class_Oless(c_Suc(X11),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_611,plain,
! [X2,X3] :
( X2 = X3
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_612,plain,
! [X2,X3] :
( X3 = X2
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_613,plain,
! [X2,X3] :
( X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X2),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_614,plain,
! [X37,X13,X14] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X37,X14) = c_Lambda_OdB_OVar(X13)
| ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_615,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_Suc(X3),X2,tc_nat)
| c_Suc(X3) = X2
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_616,axiom,
! [X2,X3,X12] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X2)
| X3 = X2 ),
c_0_229 ).
fof(c_0_617,axiom,
! [X2,X3,X12] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X12)
| X3 = X2 ),
c_0_230 ).
fof(c_0_618,axiom,
! [X43,X9,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X43)
| X9 = X43 ),
c_0_231 ).
fof(c_0_619,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_620,axiom,
! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)),
c_0_233 ).
fof(c_0_621,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_234 ).
fof(c_0_622,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat) = X3,
c_0_235 ).
fof(c_0_623,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X2,tc_nat) = X3,
c_0_236 ).
fof(c_0_624,plain,
! [X3,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X7),c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_625,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_626,axiom,
! [X40] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X40),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X40,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_239 ).
fof(c_0_627,plain,
! [X28,X14] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X28,X14)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_628,axiom,
! [X26,X12,X14] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X26,X12) = c_Lambda_OdB_OVar(X14)
| X14 = X12
| c_HOL_Oord__class_Oless(X12,X14,tc_nat) ),
c_0_241 ).
fof(c_0_629,plain,
! [X9,X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| X11 = X9
| c_HOL_Oord__class_Oless(X11,X9,X7)
| c_HOL_Oord__class_Oless(X9,X11,X7) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_630,plain,
! [X9,X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| c_HOL_Oord__class_Oless(X9,X11,X7)
| X11 = X9
| c_HOL_Oord__class_Oless(X11,X9,X7) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_631,plain,
! [X9,X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| c_HOL_Oord__class_Oless(X9,X11,X7)
| c_HOL_Oord__class_Oless(X11,X9,X7)
| X11 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_632,plain,
! [X9,X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| X11 = X9
| c_HOL_Oord__class_Oless(X9,X11,X7)
| c_HOL_Oord__class_Oless(X11,X9,X7) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_633,plain,
! [X9,X11,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X7)
| c_HOL_Oord__class_Oless(X9,X11,X7)
| c_HOL_Oord__class_Oless(X11,X9,X7)
| X11 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_634,axiom,
! [X53,X38,X54,X39] :
( hAPP(hAPP(c_Type_Otype_OFun,X39),X38) != hAPP(hAPP(c_Type_Otype_OFun,X54),X53)
| X39 = X54 ),
c_0_247 ).
fof(c_0_635,axiom,
! [X53,X38,X54,X39] :
( hAPP(hAPP(c_Type_Otype_OFun,X39),X38) != hAPP(hAPP(c_Type_Otype_OFun,X54),X53)
| X38 = X53 ),
c_0_248 ).
fof(c_0_636,axiom,
! [X48,X41,X49,X42] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41) != hAPP(hAPP(c_Lambda_OdB_OApp,X49),X48)
| X42 = X49 ),
c_0_249 ).
fof(c_0_637,axiom,
! [X48,X41,X49,X42] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41) != hAPP(hAPP(c_Lambda_OdB_OApp,X49),X48)
| X41 = X48 ),
c_0_250 ).
fof(c_0_638,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),
c_0_251 ).
fof(c_0_639,plain,
! [X3,X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X3),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Oone__class_Oone(X7)),c_Nat_Osemiring__1__class_Oof__nat(X3,X7)) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_640,axiom,
! [X11,X26] :
( c_HOL_Oord__class_Oless(X11,X11,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X26,X11) = X26 ),
c_0_253 ).
fof(c_0_641,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
c_0_254 ).
fof(c_0_642,axiom,
! [X11] :
( c_HOL_Oord__class_Oless(X11,X11,tc_nat)
| c_HOL_Oord__class_Oless(X11,c_Suc(X11),tc_nat) ),
c_0_255 ).
fof(c_0_643,plain,
! [X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X7),c_HOL_Ozero__class_Ozero(X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_644,plain,
! [X24,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X24),X5) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_645,plain,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X4),X5) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_646,plain,
! [X9,X11,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X9),X11) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_647,plain,
! [X14,X18,X19] :
( hAPP(X18,X14) = X19
| ~ c_Type_Otyping(X18,c_Lambda_OdB_OVar(X14),X19) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_648,axiom,
! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X3)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_Suc(X2)),
c_0_261 ).
fof(c_0_649,axiom,
! [X9,X11] :
( c_HOL_Oord__class_Oless(X9,X11,tc_nat)
| c_HOL_Oord__class_Oless(X11,X9,tc_nat)
| X11 = X9 ),
c_0_262 ).
fof(c_0_650,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| X3 = X2 ),
c_0_263 ).
fof(c_0_651,plain,
! [X9,X11,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| c_HOL_Ominus__class_Ominus(X11,X9,X7) != c_HOL_Ozero__class_Ozero(X7)
| X11 = X9 ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_652,plain,
! [X12,X14] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X14),X12) = c_Lambda_OdB_OVar(X14)
| ~ c_HOL_Oord__class_Oless(X14,X12,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_653,plain,
! [X2] :
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_654,axiom,
! [X11,X7] : hBOOL(hAPP(hAPP(c_fequal(X7),X11),X11)),
c_0_267 ).
fof(c_0_655,plain,
! [X11,X5,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| X11 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),X5)
| X5 = c_HOL_Ozero__class_Ozero(X7) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_656,plain,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X5,X4,X7) != c_HOL_Ozero__class_Ozero(X7)
| X5 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_657,plain,
! [X4,X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(X5,X4,X7) != c_HOL_Ozero__class_Ozero(X7)
| X5 = X4 ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_658,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),X5) != c_HOL_Ozero__class_Ozero(X7)
| X5 = c_HOL_Ozero__class_Ozero(X7) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_659,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_272 ).
fof(c_0_660,axiom,
! [X2,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_273 ).
fof(c_0_661,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_274 ).
fof(c_0_662,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_275 ).
fof(c_0_663,axiom,
! [X2,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_276 ).
fof(c_0_664,axiom,
! [X2,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_277 ).
fof(c_0_665,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_666,plain,
! [X11,X7] :
( ~ class_Orderings_Opreorder(X7)
| ~ c_HOL_Oord__class_Oless(X11,X11,X7) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_667,plain,
! [X11,X7] :
( ~ class_Orderings_Olinorder(X7)
| ~ c_HOL_Oord__class_Oless(X11,X11,X7) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_668,plain,
! [X11,X7] :
( ~ class_Orderings_Oorder(X7)
| ~ c_HOL_Oord__class_Oless(X11,X11,X7) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_669,axiom,
! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),
c_0_282 ).
fof(c_0_670,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_283 ).
fof(c_0_671,axiom,
! [X2,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_284 ).
fof(c_0_672,plain,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_673,plain,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_674,axiom,
! [X11,X51] : c_Type_Otyping(X51,c_Lambda_OdB_OVar(X11),hAPP(X51,X11)),
c_0_287 ).
fof(c_0_675,plain,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_676,plain,
! [X11] : ~ c_HOL_Oord__class_Oless(X11,X11,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_677,plain,
! [X20] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X20)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X20)) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_678,plain,
! [X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7)),c_HOL_Ozero__class_Ozero(X7)) = c_HOL_Ozero__class_Ozero(X7) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_679,axiom,
! [X28,X26,X12] : c_Lambda_Osubst(c_Lambda_Olift(X28,X12),X26,X12) = X28,
c_0_292 ).
fof(c_0_680,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_293 ).
fof(c_0_681,axiom,
! [X40] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X40)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X40)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_294 ).
fof(c_0_682,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_295 ).
fof(c_0_683,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_296 ).
fof(c_0_684,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_297 ).
fof(c_0_685,axiom,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != X3
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_298 ).
fof(c_0_686,axiom,
! [X11,X5] :
( X11 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X5)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_299 ).
fof(c_0_687,plain,
! [X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X7)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X7),c_HOL_Oone__class_Oone(X7),X7) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_688,plain,
! [X11,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| X11 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X11),c_HOL_Ozero__class_Ozero(X7)) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_689,plain,
! [X11,X7] :
( ~ class_Ring__and__Field_Oidom(X7)
| ~ class_Int_Onumber__ring(X7)
| c_HOL_Ominus__class_Ominus(X11,X11,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_690,plain,
! [X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7)),X5) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_691,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7)),X5) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_692,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7)),X5) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_693,plain,
! [X11,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_HOL_Ozero__class_Ozero(X7)),X11) = X11 ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_694,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_307 ).
fof(c_0_695,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_308 ).
fof(c_0_696,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X7),X7) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_697,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_310 ).
fof(c_0_698,plain,
! [X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),c_HOL_Ozero__class_Ozero(X7)) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_699,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),c_HOL_Ozero__class_Ozero(X7)) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_700,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X7)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),X5),c_HOL_Ozero__class_Ozero(X7)) = X5 ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_701,plain,
! [X11,X7] :
( ~ class_OrderedGroup_Oab__group__add(X7)
| c_HOL_Ominus__class_Ominus(X11,X11,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_702,plain,
! [X11,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(X11,X11,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_703,plain,
! [X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X7)
| c_HOL_Ominus__class_Ominus(X5,X5,X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_704,axiom,
! [X7] : c_Predicate_Oconversep(c_fequal(X7),X7,X7) = c_fequal(X7),
c_0_317 ).
fof(c_0_705,axiom,
! [X50,X41,X42] : hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41) != c_Lambda_OdB_OAbs(X50),
c_0_318 ).
fof(c_0_706,axiom,
! [X50,X41,X42] : c_Lambda_OdB_OAbs(X50) != hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41),
c_0_319 ).
fof(c_0_707,axiom,
! [X1,X48,X49] : c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X49),X48),
c_0_320 ).
fof(c_0_708,axiom,
! [X1,X48,X49] : hAPP(hAPP(c_Lambda_OdB_OApp,X49),X48) != c_Lambda_OdB_OVar(X1),
c_0_321 ).
fof(c_0_709,axiom,
! [X2] : c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2,
c_0_322 ).
fof(c_0_710,axiom,
! [X2] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X2),tc_nat),
c_0_323 ).
fof(c_0_711,axiom,
! [X11] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X11),tc_nat),
c_0_324 ).
fof(c_0_712,axiom,
! [X37,X12] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X37,X12) = X37,
c_0_325 ).
fof(c_0_713,axiom,
! [X44,X7] : c_List_Olistsp(X44,c_List_Olist_ONil(X7),X7),
c_0_326 ).
fof(c_0_714,axiom,
! [X2] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_327 ).
fof(c_0_715,axiom,
! [X11] : c_HOL_Oord__class_Oless(X11,c_Suc(X11),tc_nat),
c_0_328 ).
fof(c_0_716,axiom,
! [X2] : c_HOL_Oord__class_Oless(X2,c_Suc(X2),tc_nat),
c_0_329 ).
fof(c_0_717,axiom,
! [X2] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_330 ).
fof(c_0_718,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_331 ).
fof(c_0_719,axiom,
! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
c_0_332 ).
fof(c_0_720,axiom,
! [X2] : c_Suc(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X2),
c_0_333 ).
fof(c_0_721,axiom,
! [X3] : c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_334 ).
fof(c_0_722,axiom,
! [X20,X7] : c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X20,X7),X7) = c_Transitive__Closure_Ortranclp(X20,X7),
c_0_335 ).
fof(c_0_723,plain,
! [X2,X3,X7] :
( ~ class_Nat_Osemiring__char__0(X7)
| c_Nat_Osemiring__1__class_Oof__nat(X3,X7) != c_Nat_Osemiring__1__class_Oof__nat(X2,X7)
| X3 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_724,axiom,
! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2,
c_0_337 ).
fof(c_0_725,axiom,
! [X2] : c_Suc(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),
c_0_338 ).
fof(c_0_726,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
c_0_339 ).
fof(c_0_727,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
c_0_340 ).
fof(c_0_728,axiom,
! [X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ozero__class_Ozero(tc_nat)) = X3,
c_0_341 ).
fof(c_0_729,axiom,
! [X11] : X11 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_342 ).
fof(c_0_730,axiom,
! [X2] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X2))),
c_0_343 ).
fof(c_0_731,plain,
! [X60,X61] :
( class_Orderings_Oorder(tc_fun(X60,X61))
| ~ class_Orderings_Oorder(X61) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_732,plain,
! [X60,X61] :
( class_Orderings_Opreorder(tc_fun(X60,X61))
| ~ class_Orderings_Opreorder(X61) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_733,plain,
! [X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X7) = c_HOL_Oone__class_Oone(X7) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_734,plain,
! [X7] :
( ~ class_Ring__and__Field_Osemiring__1(X7)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X7) = c_HOL_Ozero__class_Ozero(X7) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_735,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
c_0_348 ).
fof(c_0_736,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
c_0_349 ).
fof(c_0_737,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
c_0_350 ).
fof(c_0_738,axiom,
! [X1] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_351 ).
fof(c_0_739,plain,
! [X7] :
( ~ class_Ring__and__Field_Ozero__neq__one(X7)
| c_HOL_Ozero__class_Ozero(X7) != c_HOL_Oone__class_Oone(X7) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_740,plain,
! [X7] :
( ~ class_Ring__and__Field_Ozero__neq__one(X7)
| c_HOL_Oone__class_Oone(X7) != c_HOL_Ozero__class_Ozero(X7) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_741,axiom,
! [X25,X1] :
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X25)
| X1 = X25 ),
c_0_354 ).
fof(c_0_742,axiom,
! [X50,X40] :
( c_Lambda_OdB_OAbs(X40) != c_Lambda_OdB_OAbs(X50)
| X40 = X50 ),
c_0_355 ).
fof(c_0_743,axiom,
! [X9,X11] :
( c_Suc(X11) != c_Suc(X9)
| X11 = X9 ),
c_0_356 ).
fof(c_0_744,axiom,
! [X25,X1] :
( c_Suc(X1) != c_Suc(X25)
| X1 = X25 ),
c_0_357 ).
fof(c_0_745,axiom,
! [X1,X50] : c_Lambda_OdB_OAbs(X50) != c_Lambda_OdB_OVar(X1),
c_0_358 ).
fof(c_0_746,axiom,
! [X1,X50] : c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X50),
c_0_359 ).
fof(c_0_747,axiom,
! [X1] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_360 ).
fof(c_0_748,axiom,
! [X25] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X25),
c_0_361 ).
fof(c_0_749,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X3),
c_0_362 ).
fof(c_0_750,axiom,
! [X3] : c_Suc(X3) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_363 ).
fof(c_0_751,axiom,
! [X25] : c_Suc(X25) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_364 ).
fof(c_0_752,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_365 ).
fof(c_0_753,axiom,
! [X2] : X2 != c_Suc(X2),
c_0_366 ).
fof(c_0_754,axiom,
! [X2] : c_Suc(X2) != X2,
c_0_367 ).
fof(c_0_755,axiom,
class_Orderings_Oorder(tc_bool),
c_0_368 ).
fof(c_0_756,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_369 ).
fof(c_0_757,axiom,
class_Orderings_Oorder(tc_nat),
c_0_370 ).
fof(c_0_758,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_371 ).
fof(c_0_759,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_372 ).
fof(c_0_760,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_373 ).
fof(c_0_761,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_374 ).
fof(c_0_762,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_375 ).
fof(c_0_763,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_376 ).
fof(c_0_764,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_377 ).
fof(c_0_765,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_378 ).
fof(c_0_766,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_379 ).
fof(c_0_767,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_380 ).
fof(c_0_768,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_381 ).
fof(c_0_769,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_382 ).
fof(c_0_770,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_383 ).
fof(c_0_771,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_384 ).
fof(c_0_772,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_385 ).
fof(c_0_773,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_386 ).
fof(c_0_774,plain,
! [X32,X33,X34,X35,X36,X37,X38] :
( X36 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X38,X36,X35,X32),X38,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X35,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X34),X33,tc_Lambda_OdB,tc_Lambda_OdB),X36)
| ~ c_Type_Otypings(X35,X33,X37)
| ~ c_Type_Otyping(X35,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X34),X33,tc_Lambda_OdB,tc_Lambda_OdB),X32,tc_Lambda_OdB,tc_Lambda_OdB),X38) ),
inference(variable_rename,[status(thm)],[c_0_387]) ).
fof(c_0_775,plain,
! [X37,X38,X39] :
( X37 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X39),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X39,X38,X37),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X39),X38,tc_Lambda_OdB,tc_Lambda_OdB)),X37)) ),
inference(variable_rename,[status(thm)],[c_0_388]) ).
fof(c_0_776,plain,
! [X32,X33,X34,X35,X36,X37,X38] :
( c_Type_Otypings(X35,X32,c_Type_Osko__Type__Xvar__app__types__1__1(X38,X36,X35,X32))
| ~ c_Type_Otyping(X35,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X34),X33,tc_Lambda_OdB,tc_Lambda_OdB),X36)
| ~ c_Type_Otypings(X35,X33,X37)
| ~ c_Type_Otyping(X35,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X34),X33,tc_Lambda_OdB,tc_Lambda_OdB),X32,tc_Lambda_OdB,tc_Lambda_OdB),X38) ),
inference(variable_rename,[status(thm)],[c_0_389]) ).
fof(c_0_777,plain,
! [X53,X54,X55,X56] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X53,X54)))
| ~ c_Type_Otyping(X55,X53,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X53))
| ~ c_Type_Otyping(c_Type_Oshift(X55,X54,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X56) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_390])])]) ).
fof(c_0_778,plain,
! [X37,X38,X39] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X38,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X39,X38,X37),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X39),X38,tc_Lambda_OdB,tc_Lambda_OdB)),X37)) ),
inference(variable_rename,[status(thm)],[c_0_391]) ).
fof(c_0_779,plain,
! [X48,X49,X50] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X50,X49,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X50,X48,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X49,X48,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_392])])]) ).
fof(c_0_780,plain,
! [X48,X49,X50] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X50,X48,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X49,X48,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X50),X49)) ),
inference(variable_rename,[status(thm)],[c_0_393]) ).
fof(c_0_781,plain,
! [X48,X49,X50] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X50,X48,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X49,X48,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X50),X49)) ),
inference(variable_rename,[status(thm)],[c_0_394]) ).
fof(c_0_782,plain,
! [X48,X49,X50] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X50)),X49),X48,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X49))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X50,X49,c_HOL_Ozero__class_Ozero(tc_nat)),X48,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(variable_rename,[status(thm)],[c_0_395]) ).
fof(c_0_783,plain,
! [X31,X32,X33,X34,X35] :
( X35 = X34
| ~ c_Type_Otyping(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB),X34)
| ~ c_Type_Otyping(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB),X35) ),
inference(variable_rename,[status(thm)],[c_0_396]) ).
fof(c_0_784,plain,
! [X48,X49,X50] :
( ~ 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(X50,X49,c_HOL_Ozero__class_Ozero(tc_nat)),X48,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X49,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X50)),X49),X48,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_397]) ).
fof(c_0_785,plain,
! [X28,X29,X30,X31] :
( c_Type_Otyping(X30,c_Lambda_OdB_OVar(X29),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X31,X30,X29,X28),X31,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X30,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X28,tc_Lambda_OdB,tc_Lambda_OdB),X31) ),
inference(variable_rename,[status(thm)],[c_0_398]) ).
fof(c_0_786,plain,
! [X29,X30,X31,X32] :
( c_Type_Otyping(X31,X30,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X32,X31,X30,X29),X32,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X29,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
inference(variable_rename,[status(thm)],[c_0_399]) ).
fof(c_0_787,plain,
! [X29,X30,X31,X32] :
( c_Type_Otyping(X31,X30,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X32,X31,X30,X29),X32,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X29,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
inference(variable_rename,[status(thm)],[c_0_400]) ).
fof(c_0_788,plain,
! [X32,X33,X34,X35,X36] :
( c_Type_Otyping(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X32,tc_Lambda_OdB,tc_Lambda_OdB),X36)
| ~ c_Type_Otypings(X34,X32,X35)
| ~ c_Type_Otyping(X34,X33,c_List_Ofoldr(c_Type_Otype_OFun,X35,X36,tc_Type_Otype,tc_Type_Otype)) ),
inference(variable_rename,[status(thm)],[c_0_401]) ).
fof(c_0_789,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_402 ).
fof(c_0_790,plain,
! [X37,X38] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X38),X37,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X37,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_403])])]) ).
fof(c_0_791,plain,
! [X28,X29,X30,X31] :
( c_Type_Otypings(X30,X28,c_Type_Osko__Type__Xvar__app__typesE__1__1(X31,X30,X29,X28))
| ~ c_Type_Otyping(X30,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X28,tc_Lambda_OdB,tc_Lambda_OdB),X31) ),
inference(variable_rename,[status(thm)],[c_0_404]) ).
fof(c_0_792,plain,
! [X29,X30,X31,X32] :
( c_Type_Otypings(X31,X29,c_Type_Osko__Type__Xlist__app__typeD__1__1(X32,X31,X30,X29))
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X29,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
inference(variable_rename,[status(thm)],[c_0_405]) ).
fof(c_0_793,plain,
! [X29,X30,X31,X32] :
( c_Type_Otypings(X31,X29,c_Type_Osko__Type__Xlist__app__typeE__1__1(X32,X31,X30,X29))
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X29,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
inference(variable_rename,[status(thm)],[c_0_406]) ).
fof(c_0_794,plain,
! [X48,X49,X50,X51] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X51),X49,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X50),X48,tc_Lambda_OdB,tc_Lambda_OdB)
| X51 = X50 ),
inference(variable_rename,[status(thm)],[c_0_407]) ).
fof(c_0_795,plain,
! [X48,X49,X50,X51] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X51),X49,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X50),X48,tc_Lambda_OdB,tc_Lambda_OdB)
| X49 = X48 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_408])])]) ).
fof(c_0_796,plain,
! [X48,X49,X50,X51] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X51),X50,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X49),X48,tc_Lambda_OdB,tc_Lambda_OdB)
| X51 = X49 ),
inference(variable_rename,[status(thm)],[c_0_409]) ).
fof(c_0_797,plain,
! [X48,X49,X50,X51] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X51),X50,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X49),X48,tc_Lambda_OdB,tc_Lambda_OdB)
| X50 = X48 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_410])])]) ).
fof(c_0_798,plain,
! [X33,X34,X35,X36] :
( ~ class_OrderedGroup_Osemigroup__add(X36)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),X34),X33,X36,X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X36),X34,X33,X36,X36)) ),
inference(variable_rename,[status(thm)],[c_0_411]) ).
fof(c_0_799,plain,
! [X48,X49,X50,X51] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X51),X48,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X50),X49,tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_412]) ).
fof(c_0_800,plain,
! [X28,X29,X30] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X28,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)
| X30 = X29 ),
inference(variable_rename,[status(thm)],[c_0_413]) ).
fof(c_0_801,plain,
! [X22,X23,X24] :
( ~ class_OrderedGroup_Omonoid__add(X24)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X24),X23,X22,X24,X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X24),X23),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X24),X22,c_HOL_Ozero__class_Ozero(X24),X24,X24)) ),
inference(variable_rename,[status(thm)],[c_0_414]) ).
fof(c_0_802,plain,
! [X33,X34,X35] :
( ~ class_OrderedGroup_Omonoid__add(X35)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X35),c_HOL_Ozero__class_Ozero(X35),X33,X35,X35)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X35),X34,X33,X35,X35) ),
inference(variable_rename,[status(thm)],[c_0_415]) ).
fof(c_0_803,axiom,
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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
c_0_416 ).
fof(c_0_804,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
c_0_417 ).
fof(c_0_805,plain,
! [X22,X23] :
( ~ class_OrderedGroup_Omonoid__add(X23)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X23),c_HOL_Ozero__class_Ozero(X23),X22,X23,X23) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X23),X22,c_HOL_Ozero__class_Ozero(X23),X23,X23) ),
inference(variable_rename,[status(thm)],[c_0_418]) ).
fof(c_0_806,plain,
! [X22,X23,X24] :
( ~ class_OrderedGroup_Oab__semigroup__add(X24)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X24),X22,X23,X24,X24) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X24),X23,X22,X24,X24) ),
inference(variable_rename,[status(thm)],[c_0_419]) ).
fof(c_0_807,plain,
! [X38,X39,X40,X41] :
( c_Type_Otyping(X40,X39,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X41,X40,X39,X38)),X41))
| ~ c_Type_Otyping(X40,hAPP(hAPP(c_Lambda_OdB_OApp,X39),X38),X41) ),
inference(variable_rename,[status(thm)],[c_0_420]) ).
fof(c_0_808,plain,
! [X29,X30,X31] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30) != c_List_Ofoldl(c_Lambda_OdB_OApp,X29,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30) = X29 ),
inference(variable_rename,[status(thm)],[c_0_421]) ).
fof(c_0_809,plain,
! [X48,X49,X50,X51] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X50)),X48) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X51),X49,tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_422]) ).
fof(c_0_810,plain,
! [X48,X49,X50] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X49,X48,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X50)
| X49 = c_Lambda_OdB_OAbs(X50) ),
inference(variable_rename,[status(thm)],[c_0_423]) ).
fof(c_0_811,plain,
! [X48,X49,X50] :
( c_Lambda_OdB_OVar(X50) != c_List_Ofoldl(c_Lambda_OdB_OApp,X49,X48,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X50) = X49 ),
inference(variable_rename,[status(thm)],[c_0_424]) ).
fof(c_0_812,plain,
! [X48,X49,X50] :
( c_Lambda_OdB_OAbs(X50) != c_List_Ofoldl(c_Lambda_OdB_OApp,X49,X48,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X50) = X49 ),
inference(variable_rename,[status(thm)],[c_0_425]) ).
fof(c_0_813,plain,
! [X48,X49,X50] :
( c_Lambda_OdB_OVar(X50) != c_List_Ofoldl(c_Lambda_OdB_OApp,X49,X48,tc_Lambda_OdB,tc_Lambda_OdB)
| X48 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_426])])]) ).
fof(c_0_814,plain,
! [X48,X49,X50] :
( c_Lambda_OdB_OAbs(X50) != c_List_Ofoldl(c_Lambda_OdB_OApp,X49,X48,tc_Lambda_OdB,tc_Lambda_OdB)
| X48 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_427])])]) ).
fof(c_0_815,plain,
! [X48,X49,X50] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X49,X48,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X50)
| X48 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_428])])]) ).
fof(c_0_816,plain,
! [X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X23,X24),X21),X22))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X23,X24,X24),X24),X22),X21)) ),
inference(variable_rename,[status(thm)],[c_0_429]) ).
fof(c_0_817,plain,
! [X31,X32,X33,X34,X35] : c_Type_Oshift(c_Type_Oshift(X32,X31,X33,X35),c_HOL_Ozero__class_Ozero(tc_nat),X34,X35) = c_Type_Oshift(c_Type_Oshift(X32,c_HOL_Ozero__class_Ozero(tc_nat),X34,X35),c_Suc(X31),X33,X35),
inference(variable_rename,[status(thm)],[c_0_430]) ).
fof(c_0_818,plain,
! [X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X23,X24,X24),X24),X22),X21))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X23,X24),X21),X22)) ),
inference(variable_rename,[status(thm)],[c_0_431]) ).
fof(c_0_819,plain,
! [X58,X59,X60,X61,X62,X63,X64] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X64),X63)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X59,X58,X60)))
| ~ c_Type_Otyping(X61,X58,X64)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X58))
| ~ c_Type_Otyping(c_Type_Oshift(X61,X60,X64,tc_Type_Otype),X59,X62)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X59)) ),
inference(variable_rename,[status(thm)],[c_0_432]) ).
fof(c_0_820,plain,
! [X58,X59,X60,X61,X62,X63,X64] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X64),X63)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X59,X58,X60)))
| ~ c_Type_Otyping(X61,X58,X63)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X58))
| ~ c_Type_Otyping(c_Type_Oshift(X61,X60,X63,tc_Type_Otype),X59,X62)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X59)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_433])])]) ).
fof(c_0_821,plain,
! [X27,X28] : hAPP(hAPP(c_Lambda_OdB_OApp,X28),X27) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X27),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_434]) ).
fof(c_0_822,plain,
! [X4] : c_Lambda_OdB_OVar(X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_435]) ).
fof(c_0_823,plain,
! [X21] : c_Lambda_OdB_OAbs(X21) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X21),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_436]) ).
fof(c_0_824,plain,
! [X21] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X21),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X21),
inference(variable_rename,[status(thm)],[c_0_437]) ).
fof(c_0_825,plain,
! [X53,X54,X55,X56] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X53,X54)))
| ~ c_Type_Otyping(X55,X53,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X53))
| ~ c_Type_Otyping(c_Type_Oshift(X55,X54,v_T____,tc_Type_Otype),v_a____,X56) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_438])])]) ).
fof(c_0_826,plain,
! [X24,X25,X26,X27] : c_List_Ofoldr(X24,c_List_Olist_ONil(X26),X25,X26,X27) = X25,
inference(variable_rename,[status(thm)],[c_0_439]) ).
fof(c_0_827,plain,
! [X24,X25,X26,X27] : c_List_Ofoldl(X24,X25,c_List_Olist_ONil(X26),X27,X26) = X25,
inference(variable_rename,[status(thm)],[c_0_440]) ).
fof(c_0_828,plain,
! [X60,X61,X62,X63,X64,X65] :
( ~ c_Type_Otyping(X63,X60,X64)
| ~ c_Type_Otyping(c_Type_Oshift(X63,X62,X64,tc_Type_Otype),X61,X65)
| c_Type_Otyping(X63,c_Lambda_Osubst(X61,X60,X62),X65) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_441])])]) ).
fof(c_0_829,plain,
! [X35,X36,X37,X38] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X38),X36)),hAPP(hAPP(c_Lambda_OdB_OApp,X37),X35)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X36),X35))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X38),X37)) ),
inference(variable_rename,[status(thm)],[c_0_442]) ).
fof(c_0_830,plain,
! [X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X29,X31,X32)),c_Lambda_Osubst(X29,X30,X32)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X31),X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_443])])]) ).
fof(c_0_831,plain,
! [X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X31,X29,X32)),c_Lambda_Osubst(X30,X29,X32)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X31),X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_444])])]) ).
fof(c_0_832,plain,
! [X52,X53,X54,X55] :
( c_Type_Otyping(X53,c_Lambda_OdB_OAbs(X52),hAPP(hAPP(c_Type_Otype_OFun,X55),X54))
| ~ c_Type_Otyping(c_Type_Oshift(X53,c_HOL_Ozero__class_Ozero(tc_nat),X55,tc_Type_Otype),X52,X54) ),
inference(variable_rename,[status(thm)],[c_0_445]) ).
fof(c_0_833,plain,
! [X17,X18,X19] :
( ~ hBOOL(hAPP(X19,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),X18,tc_nat)))
| hBOOL(hAPP(X19,X17)) ),
inference(variable_rename,[status(thm)],[c_0_446]) ).
fof(c_0_834,plain,
! [X12,X13,X14] :
( ~ hBOOL(hAPP(X14,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12),X13,tc_nat)))
| hBOOL(hAPP(X14,X12)) ),
inference(variable_rename,[status(thm)],[c_0_447]) ).
fof(c_0_835,plain,
! [X29,X30,X31] :
( c_Type_Otyping(c_Type_Oshift(X30,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X31,X30,X29),tc_Type_Otype),X29,c_Type_Osko__Type__Xtyping__elims__3__2(X31,X30,X29))
| ~ c_Type_Otyping(X30,c_Lambda_OdB_OAbs(X29),X31) ),
inference(variable_rename,[status(thm)],[c_0_448]) ).
fof(c_0_836,plain,
! [X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X29,X31,X32)),c_Lambda_Osubst(X29,X30,X32)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X31),X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_449])])]) ).
fof(c_0_837,plain,
! [X24,X25,X26,X27,X28] :
( hBOOL(hAPP(hAPP(X24,X25),X26))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X24,X28,X27),X26),X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_450])])]) ).
fof(c_0_838,plain,
! [X47,X48,X49,X50,X51] :
( hBOOL(hAPP(hAPP(X47,X48),X49))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X47,X51,X50),X49),X48)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_451])])]) ).
fof(c_0_839,plain,
! [X34,X35,X36] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X36),X35)),hAPP(hAPP(c_Lambda_OdB_OApp,X36),X34)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_452])])]) ).
fof(c_0_840,plain,
! [X35,X36,X37] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X37),X35)),hAPP(hAPP(c_Lambda_OdB_OApp,X36),X35)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X37),X36)) ),
inference(variable_rename,[status(thm)],[c_0_453]) ).
fof(c_0_841,plain,
! [X59] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X59) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_454])])]) ).
fof(c_0_842,plain,
! [X29,X30,X31,X32] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X31,X29,X32)),c_Lambda_Osubst(X30,X29,X32)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X31),X30)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_455])])]) ).
fof(c_0_843,plain,
! [X44,X45,X46,X47,X48] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X47,X48),X46),X44))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X47,X48),X45),X44))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X47,X48),X46),X45)) ),
inference(variable_rename,[status(thm)],[c_0_456]) ).
fof(c_0_844,plain,
! [X38,X39,X40,X41] :
( c_Type_Otyping(X40,X38,c_Type_Osko__Type__Xtyping__elims__2__1(X41,X40,X39,X38))
| ~ c_Type_Otyping(X40,hAPP(hAPP(c_Lambda_OdB_OApp,X39),X38),X41) ),
inference(variable_rename,[status(thm)],[c_0_457]) ).
fof(c_0_845,plain,
! [X38,X39,X40,X41,X42] :
( c_Lambda_Osubst(c_Lambda_Osubst(X40,c_Lambda_Olift(X38,X42),c_Suc(X41)),c_Lambda_Osubst(X39,X38,X41),X42) = c_Lambda_Osubst(c_Lambda_Osubst(X40,X39,X42),X38,X41)
| ~ c_HOL_Oord__class_Oless(X42,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X41),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_458]) ).
fof(c_0_846,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X28),X27)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X26),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X28),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X27),X25)) ),
inference(variable_rename,[status(thm)],[c_0_459]) ).
fof(c_0_847,plain,
! [X29,X30,X31] :
( c_Type_Otyping(c_Type_Oshift(X30,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X30,X29),tc_Type_Otype),X29,c_Type_Osko__Type__Xabs__typeE__1__2(X30,X29))
| ~ c_Type_Otyping(X30,c_Lambda_OdB_OAbs(X29),X31) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_460])])]) ).
fof(c_0_848,plain,
! [X20,X21,X22,X23,X24] :
( hAPP(c_Type_Oshift(X22,X21,X23,X24),X20) = hAPP(X22,c_HOL_Ominus__class_Ominus(X20,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_461])])]) ).
fof(c_0_849,plain,
! [X29,X30] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X30)),X29)),c_Lambda_Osubst(X30,X29,c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_462]) ).
fof(c_0_850,plain,
! [X31,X32,X33,X34,X35] :
( c_Type_Otyping(c_Type_Oshift(X33,X32,X34,tc_Type_Otype),c_Lambda_Olift(X31,X32),X35)
| ~ c_Type_Otyping(X33,X31,X35) ),
inference(variable_rename,[status(thm)],[c_0_463]) ).
fof(c_0_851,plain,
! [X29,X30,X31,X32] :
( c_Lambda_Olift(c_Lambda_Osubst(X29,X30,X31),X32) = c_Lambda_Osubst(c_Lambda_Olift(X29,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Olift(X30,X32),X31)
| ~ c_HOL_Oord__class_Oless(X31,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_464]) ).
fof(c_0_852,plain,
! [X24,X25,X26,X27,X28] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X24,X28,X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(X24,X25),X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_465])])]) ).
fof(c_0_853,plain,
! [X24,X25,X26,X27,X28] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X24,X28,X27),X25),X26))
| ~ hBOOL(hAPP(hAPP(X24,X26),X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_466])])]) ).
fof(c_0_854,plain,
! [X38,X39,X40] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X38),X40)),hAPP(hAPP(c_Lambda_OdB_OApp,X38),X39)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X40),X39)) ),
inference(variable_rename,[status(thm)],[c_0_467]) ).
fof(c_0_855,plain,
! [X38,X39,X40] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X40),X38)),hAPP(hAPP(c_Lambda_OdB_OApp,X39),X38)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X40),X39)) ),
inference(variable_rename,[status(thm)],[c_0_468]) ).
fof(c_0_856,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_OAbs(v_r____)),v_a____),v_Ua____),
c_0_469 ).
fof(c_0_857,plain,
! [X25,X26,X27,X28,X29] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X25,X29),X28),X26))
| ~ hBOOL(hAPP(hAPP(X25,X27),X26))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X25,X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_470]) ).
fof(c_0_858,plain,
! [X25,X26,X27,X28,X29] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X25,X29),X28),X26))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X25,X29),X27),X26))
| ~ hBOOL(hAPP(hAPP(X25,X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_471]) ).
fof(c_0_859,plain,
! [X20,X21,X22,X23,X24] :
( hAPP(c_Type_Oshift(X22,X21,X23,X24),X20) = hAPP(X22,X20)
| ~ c_HOL_Oord__class_Oless(X20,X21,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_472])])]) ).
fof(c_0_860,plain,
! [X43,X44] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X44),X43),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X44,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X43,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_473]) ).
fof(c_0_861,plain,
! [X40,X41] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X41),X40),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X41,tc_Type_Otype)),c_Nat_Osize__class_Osize(X40,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_474]) ).
fof(c_0_862,plain,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X4))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_475]) ).
fof(c_0_863,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X28,X29)),c_Lambda_Olift(X27,X29)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_476])])]) ).
fof(c_0_864,plain,
! [X29,X30,X31,X32] :
( c_Lambda_Olift(c_Lambda_Osubst(X29,X30,X31),X32) = c_Lambda_Osubst(c_Lambda_Olift(X29,X32),c_Lambda_Olift(X30,X32),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X31),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X32,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X31),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_477]) ).
fof(c_0_865,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X26)),X25) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X25)),X26) ),
inference(variable_rename,[status(thm)],[c_0_478]) ).
fof(c_0_866,plain,
! [X20,X21,X22,X23] : hAPP(c_Type_Oshift(X21,X20,X22,X23),X20) = X22,
inference(variable_rename,[status(thm)],[c_0_479]) ).
fof(c_0_867,plain,
! [X7,X8,X9] :
( hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X8,X7,tc_nat)
| ~ hBOOL(hAPP(X9,c_HOL_Ominus__class_Ominus(X8,X7,tc_nat))) ),
inference(variable_rename,[status(thm)],[c_0_480]) ).
fof(c_0_868,plain,
! [X38,X39,X40,X41] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X39),X38),X40,X41) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X39,X40,X41)),c_Lambda_Osubst(X38,X40,X41)),
inference(variable_rename,[status(thm)],[c_0_481]) ).
fof(c_0_869,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X28)
| c_HOL_Oord__class_Oless(X27,X26,X28)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X25),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X25),X26),X28) ),
inference(variable_rename,[status(thm)],[c_0_482]) ).
fof(c_0_870,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X28)
| c_HOL_Oord__class_Oless(X27,X26,X28)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25),X28) ),
inference(variable_rename,[status(thm)],[c_0_483]) ).
fof(c_0_871,plain,
! [X29,X30,X31] :
( X31 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X31,X30,X29)),c_Type_Osko__Type__Xtyping__elims__3__2(X31,X30,X29))
| ~ c_Type_Otyping(X30,c_Lambda_OdB_OAbs(X29),X31) ),
inference(variable_rename,[status(thm)],[c_0_484]) ).
fof(c_0_872,plain,
! [X35,X36] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X36)),c_Lambda_OdB_OAbs(X35)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X36),X35)) ),
inference(variable_rename,[status(thm)],[c_0_485]) ).
fof(c_0_873,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X29)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X28),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X27),X25),X29)
| ~ c_HOL_Oord__class_Oless(X26,X25,X29)
| ~ c_HOL_Oord__class_Oless(X28,X27,X29) ),
inference(variable_rename,[status(thm)],[c_0_486]) ).
fof(c_0_874,plain,
! [X21,X22,X23,X24] :
( c_Wellfounded_Oaccp(X21,X22,X24)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X21,X24),X22),X23))
| ~ c_Wellfounded_Oaccp(X21,X23,X24) ),
inference(variable_rename,[status(thm)],[c_0_487]) ).
fof(c_0_875,plain,
! [X21,X22,X23,X24] :
( c_Wellfounded_Oaccp(X21,X22,X24)
| ~ c_Wellfounded_Oaccp(X21,X23,X24)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X21,X24),X22),X23)) ),
inference(variable_rename,[status(thm)],[c_0_488]) ).
fof(c_0_876,plain,
! [X16,X17,X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X16,tc_nat),c_HOL_Ominus__class_Ominus(X18,X17,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X18,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_489]) ).
fof(c_0_877,plain,
! [X29,X30,X31] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X29),X30,X31) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X29,c_Lambda_Olift(X30,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X31),c_HOL_Oone__class_Oone(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_490]) ).
fof(c_0_878,plain,
! [X13,X14,X15] :
( c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X13),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_491])])]) ).
fof(c_0_879,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X26)),X25) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_492]) ).
fof(c_0_880,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X26)),X25) ),
inference(variable_rename,[status(thm)],[c_0_493]) ).
fof(c_0_881,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Oab__semigroup__add(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X26)),X25) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_882,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X26)),X25) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_883,plain,
! [X44,X45,X46,X47] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X47)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X45),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45)),X44) ),
inference(variable_rename,[status(thm)],[c_0_496]) ).
fof(c_0_884,plain,
! [X52,X53,X54,X55,X56] :
( c_Type_Otyping(X54,hAPP(hAPP(c_Lambda_OdB_OApp,X53),X52),X55)
| ~ c_Type_Otyping(X54,X52,X56)
| ~ c_Type_Otyping(X54,X53,hAPP(hAPP(c_Type_Otype_OFun,X56),X55)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_497])])]) ).
fof(c_0_885,plain,
! [X16,X17,X18,X19] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X16),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_498]) ).
fof(c_0_886,plain,
! [X22,X23,X24] : ~ c_ListOrder_Ostep1(X23,X22,c_List_Olist_ONil(X24),X24),
inference(variable_rename,[status(thm)],[c_0_499]) ).
fof(c_0_887,plain,
! [X22,X23,X24] : ~ c_ListOrder_Ostep1(X23,c_List_Olist_ONil(X24),X22,X24),
inference(variable_rename,[status(thm)],[c_0_500]) ).
fof(c_0_888,plain,
! [X34,X35,X36,X37] :
( c_Type_Otyping(X36,X34,X37)
| ~ c_Type_Otyping(X36,X35,X37)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X34)) ),
inference(variable_rename,[status(thm)],[c_0_501]) ).
fof(c_0_889,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_502]) ).
fof(c_0_890,plain,
! [X43,X44] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X44),X43)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X44)),c_Lambda_OdB_OdB__size(X43))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_503]) ).
fof(c_0_891,plain,
! [X40,X41] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X41),X40)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X41)),c_Type_Otype_Otype__size(X40))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_504]) ).
fof(c_0_892,plain,
! [X44,X45,X46,X47,X48] :
( ~ class_OrderedGroup_Oab__group__add(X48)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X45),X44)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X45),X47)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X46),X44) = X47 ),
inference(variable_rename,[status(thm)],[c_0_505]) ).
fof(c_0_893,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_506]) ).
fof(c_0_894,plain,
! [X13,X14,X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X13)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15)),
inference(variable_rename,[status(thm)],[c_0_507]) ).
fof(c_0_895,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X8),X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X8,X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_508]) ).
fof(c_0_896,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X10)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X8),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_509]) ).
fof(c_0_897,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X28)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X25),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X25),X26),X28)
| ~ c_HOL_Oord__class_Oless(X27,X26,X28) ),
inference(variable_rename,[status(thm)],[c_0_510]) ).
fof(c_0_898,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X28)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X25),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X25),X26),X28)
| ~ c_HOL_Oord__class_Oless(X27,X26,X28) ),
inference(variable_rename,[status(thm)],[c_0_511]) ).
fof(c_0_899,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X28)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25),X28)
| ~ c_HOL_Oord__class_Oless(X27,X26,X28) ),
inference(variable_rename,[status(thm)],[c_0_512]) ).
fof(c_0_900,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X28)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25),X28)
| ~ c_HOL_Oord__class_Oless(X27,X26,X28) ),
inference(variable_rename,[status(thm)],[c_0_513]) ).
fof(c_0_901,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X28,X29)),c_Lambda_Olift(X27,X29)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_514])])]) ).
fof(c_0_902,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Oordered__semidom(X28)
| c_HOL_Oord__class_Oless(X26,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X25),X28)
| ~ c_HOL_Oord__class_Oless(X26,X25,X28)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X28),X27,X28) ),
inference(variable_rename,[status(thm)],[c_0_515]) ).
fof(c_0_903,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_516])])]) ).
fof(c_0_904,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_517]) ).
fof(c_0_905,plain,
! [X13,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X14),X13,tc_nat),c_Suc(X15),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),X15,tc_nat),
inference(variable_rename,[status(thm)],[c_0_518]) ).
fof(c_0_906,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| c_HOL_Oord__class_Oless(X9,X8,X10)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X9,X8,X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_519]) ).
fof(c_0_907,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X9)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),X8),c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_520]) ).
fof(c_0_908,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),X8),c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_521]) ).
fof(c_0_909,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X8,X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),X8),X9) ),
inference(variable_rename,[status(thm)],[c_0_522]) ).
fof(c_0_910,plain,
! [X29,X30,X31] :
( c_Lambda_Olift(c_Lambda_Olift(X29,X31),c_Suc(X30)) = c_Lambda_Olift(c_Lambda_Olift(X29,X30),X31)
| ~ c_HOL_Oord__class_Oless(X31,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_523]) ).
fof(c_0_911,plain,
! [X12,X13,X14,X15,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| c_HOL_Ominus__class_Ominus(X15,X13,X16) != c_HOL_Ominus__class_Ominus(X14,X12,X16)
| c_HOL_Oord__class_Oless(X14,X12,X16)
| ~ c_HOL_Oord__class_Oless(X15,X13,X16) ),
inference(variable_rename,[status(thm)],[c_0_524]) ).
fof(c_0_912,plain,
! [X12,X13,X14,X15,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| c_HOL_Ominus__class_Ominus(X15,X13,X16) != c_HOL_Ominus__class_Ominus(X14,X12,X16)
| c_HOL_Oord__class_Oless(X15,X13,X16)
| ~ c_HOL_Oord__class_Oless(X14,X12,X16) ),
inference(variable_rename,[status(thm)],[c_0_525]) ).
fof(c_0_913,plain,
! [X13,X14,X15] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_526])])]) ).
fof(c_0_914,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_527]) ).
fof(c_0_915,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X25)) ),
inference(variable_rename,[status(thm)],[c_0_528]) ).
fof(c_0_916,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X25)) ),
inference(variable_rename,[status(thm)],[c_0_529]) ).
fof(c_0_917,plain,
! [X44,X45,X46,X47] :
( ~ class_OrderedGroup_Oab__group__add(X47)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X45),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X44)) ),
inference(variable_rename,[status(thm)],[c_0_530]) ).
fof(c_0_918,plain,
! [X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X23,X24),X22),X21))
| ~ hBOOL(hAPP(hAPP(X23,X22),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_531])])]) ).
fof(c_0_919,plain,
! [X15,X16,X17] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X17,X15,tc_nat),X16,tc_nat),
inference(variable_rename,[status(thm)],[c_0_532]) ).
fof(c_0_920,plain,
! [X21,X22,X23] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X21,c_Lambda_OdB_OVar(X23),X22)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_533])])]) ).
fof(c_0_921,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_534]) ).
fof(c_0_922,plain,
! [X15,X16,X17] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),tc_nat),
inference(variable_rename,[status(thm)],[c_0_535]) ).
fof(c_0_923,plain,
! [X13,X14,X15] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X13),tc_nat) = c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),
inference(variable_rename,[status(thm)],[c_0_536]) ).
fof(c_0_924,plain,
! [X13,X14,X15] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),tc_nat) = c_HOL_Ominus__class_Ominus(X14,X13,tc_nat),
inference(variable_rename,[status(thm)],[c_0_537]) ).
fof(c_0_925,plain,
! [X16,X17,X18,X19] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X16)
| ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
| c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_538]) ).
fof(c_0_926,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X17,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_539]) ).
fof(c_0_927,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),c_HOL_Ominus__class_Ominus(X9,X8,X10)),X8) = X9 ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_928,plain,
! [X44,X45,X46] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X45),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X46),X44)),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_929,plain,
! [X21,X22,X23,X24] :
( c_Wellfounded_Oaccp(X21,X23,X24)
| ~ hBOOL(hAPP(hAPP(X21,X23),X22))
| ~ c_Wellfounded_Oaccp(X21,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_930,plain,
! [X21,X22,X23,X24] :
( c_Wellfounded_Oaccp(X22,X21,X24)
| ~ hBOOL(hAPP(hAPP(X22,X21),X23))
| ~ c_Wellfounded_Oaccp(X22,X23,X24) ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_931,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),X8),c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_932,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),X8),c_HOL_Ozero__class_Ozero(X9),X9)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_933,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),X8),X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),X8,X9) ),
inference(variable_rename,[status(thm)],[c_0_546]) ).
fof(c_0_934,plain,
! [X21] :
( hBOOL(hAPP(c_InductTermi_OIT,X21))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X21,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_935,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X9,X8,X10),c_HOL_Ozero__class_Ozero(X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_936,plain,
! [X34,X35,X36,X37] :
( c_Type_Otyping(X36,X34,X37)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X34))
| ~ c_Type_Otyping(X36,X35,X37) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_937,plain,
! [X27,X28,X29] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X29),X27,X28) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X29,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X28,X29,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_938,plain,
! [X38,X39,X40] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X39),X38,X40) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X39,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X40,X39,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_939,plain,
! [X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,c_Suc(X16),tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_552])])]) ).
fof(c_0_940,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_941,plain,
! [X27,X28] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X27),X28) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),c_HOL_Oone__class_Oone(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_942,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Osemiring__1(X10)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),c_Nat_Osemiring__1__class_Oof__nat(X9,X10)),c_Nat_Osemiring__1__class_Oof__nat(X8,X10)) ),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_943,plain,
! [X14,X15,X16] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X16,X14,tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_944,plain,
! [X15,X16] : c_HOL_Oord__class_Oless(X16,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_945,plain,
! [X15,X16] : c_HOL_Oord__class_Oless(X16,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_946,plain,
! [X12,X13] : c_HOL_Oord__class_Oless(X13,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_947,plain,
! [X29,X30] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X29),c_Lambda_OdB_OVar(X30))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_560])])]) ).
fof(c_0_948,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_561])])]) ).
fof(c_0_949,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_950,plain,
! [X44,X45,X46,X47] :
( ~ class_Orderings_Opreorder(X47)
| c_HOL_Oord__class_Oless(X46,X44,X47)
| ~ c_HOL_Oord__class_Oless(X45,X44,X47)
| ~ c_HOL_Oord__class_Oless(X46,X45,X47) ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_951,plain,
! [X44,X45,X46,X47] :
( ~ class_Orderings_Oorder(X47)
| c_HOL_Oord__class_Oless(X44,X46,X47)
| ~ c_HOL_Oord__class_Oless(X44,X45,X47)
| ~ c_HOL_Oord__class_Oless(X45,X46,X47) ),
inference(variable_rename,[status(thm)],[c_0_564]) ).
fof(c_0_952,plain,
! [X29,X30] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X30)),c_Lambda_OdB_OAbs(X29)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X29)) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_953,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X10)
| c_HOL_Oord__class_Oless(X9,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X9,X10),c_Nat_Osemiring__1__class_Oof__nat(X8,X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_954,plain,
! [X44,X45,X46] :
( c_HOL_Oord__class_Oless(X46,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X45),X44),tc_nat)
| ~ c_HOL_Oord__class_Oless(X46,X45,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_955,plain,
! [X44,X45,X46] :
( c_HOL_Oord__class_Oless(X46,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X45),X44),tc_nat)
| ~ c_HOL_Oord__class_Oless(X46,X44,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_568]) ).
fof(c_0_956,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_957,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_958,plain,
! [X15,X16,X17] :
( c_HOL_Oord__class_Oless(c_Suc(X17),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_959,plain,
! [X15,X16] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X16,tc_nat),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_960,plain,
! [X15,X16] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),X16,tc_nat),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_961,plain,
! [X3] :
( c_Suc(c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_962,plain,
! [X4,X5] : c_HOL_Ominus__class_Ominus(X5,c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_963,plain,
! [X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Oone__class_Oone(X8)),c_HOL_Oone__class_Oone(X8)),X8) ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_964,plain,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Ominus__class_Ominus(X5,X4,tc_nat)) = X5
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_577]) ).
fof(c_0_965,plain,
! [X3] :
( X3 = c_Suc(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_578]) ).
fof(c_0_966,plain,
! [X3] :
( c_Suc(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_579]) ).
fof(c_0_967,plain,
! [X29,X30,X31] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X30),X29),X31) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X30,X31)),c_Lambda_Olift(X29,X31)),
inference(variable_rename,[status(thm)],[c_0_580]) ).
fof(c_0_968,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),c_Nat_Osemiring__1__class_Oof__nat(X8,X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_581]) ).
fof(c_0_969,plain,
! [X8,X9,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X10)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X9,X10),c_Nat_Osemiring__1__class_Oof__nat(X8,X10),X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_582]) ).
fof(c_0_970,plain,
! [X29] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X29,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
inference(variable_rename,[status(thm)],[c_0_583]) ).
fof(c_0_971,plain,
! [X7,X8,X9] :
( hBOOL(hAPP(hAPP(X9,X7),X8))
| c_HOL_Oord__class_Oless(X7,X8,tc_nat)
| X8 = X7
| c_HOL_Oord__class_Oless(X8,X7,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_584])])]) ).
fof(c_0_972,plain,
! [X21,X22,X23] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X21,X23),X22),X22)),
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_973,plain,
! [X21,X22,X23] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X22,X23),X21),X21)),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_974,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X9),c_Nat_Osemiring__1__class_Oof__nat(X8,X9),X9)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_975,plain,
! [X44,X45,X46,X47] :
( ~ class_Ring__and__Field_Oidom(X47)
| ~ class_Int_Onumber__ring(X47)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X45) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X44)
| X45 = X44 ),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_976,plain,
! [X12,X13,X14,X15] :
( ~ class_OrderedGroup_Oab__group__add(X15)
| c_HOL_Ominus__class_Ominus(X14,X14,X15) != c_HOL_Ominus__class_Ominus(X13,X12,X15)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_977,plain,
! [X18,X19,X20,X21] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_HOL_Ominus__class_Ominus(X19,X18,X21) != c_HOL_Ominus__class_Ominus(X20,X20,X21)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_978,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Opreorder(X10)
| ~ c_HOL_Oord__class_Oless(X8,X9,X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_979,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ c_HOL_Oord__class_Oless(X12,X13,X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_592]) ).
fof(c_0_980,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,X14)
| ~ c_HOL_Oord__class_Oless(X12,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_593]) ).
fof(c_0_981,plain,
! [X8,X9,X10] :
( ~ class_Orderings_Oorder(X10)
| ~ c_HOL_Oord__class_Oless(X9,X8,X10)
| ~ c_HOL_Oord__class_Oless(X8,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_982,plain,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_595]) ).
fof(c_0_983,plain,
! [X4,X5] :
( c_HOL_Ominus__class_Ominus(X4,X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_596]) ).
fof(c_0_984,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| c_HOL_Oord__class_Oless(X8,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),c_HOL_Oone__class_Oone(X9)),X9) ),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_985,plain,
! [X15,X16] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X16),X15) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_598]) ).
fof(c_0_986,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X27) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X25),X27)
| X26 = X25 ),
inference(variable_rename,[status(thm)],[c_0_599]) ).
fof(c_0_987,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X26) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X25)
| X26 = X25 ),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_988,plain,
! [X25,X26,X27,X28] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X26) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X25)
| X26 = X25 ),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_989,plain,
! [X64,X65,X66] :
( X65 = X64
| ~ hBOOL(hAPP(hAPP(c_fequal(X66),X65),X64)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_602])])]) ).
fof(c_0_990,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X8),X8,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_603]) ).
fof(c_0_991,plain,
! [X4,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),c_Suc(X5),tc_nat),
inference(variable_rename,[status(thm)],[c_0_604]) ).
fof(c_0_992,plain,
! [X24,X25,X26] : c_Predicate_Oconversep(c_Predicate_Oconversep(X24,X26,X25),X25,X26) = X24,
inference(variable_rename,[status(thm)],[c_0_605]) ).
fof(c_0_993,plain,
! [X29,X30] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X30)),X29)),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_994,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_995,plain,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X5)),X4) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)),
inference(variable_rename,[status(thm)],[c_0_608]) ).
fof(c_0_996,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_609]) ).
fof(c_0_997,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(c_Suc(X12),c_Suc(X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_998,plain,
! [X4,X5] :
( X4 = X5
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_611]) ).
fof(c_0_999,plain,
! [X4,X5] :
( X5 = X4
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_612]) ).
fof(c_0_1000,plain,
! [X4,X5] :
( X5 = X4
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_1001,plain,
! [X38,X39,X40] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X39),X38,X40) = c_Lambda_OdB_OVar(X39)
| ~ c_HOL_Oord__class_Oless(X39,X40,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_1002,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat)
| c_Suc(X5) = X4
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_615]) ).
fof(c_0_1003,plain,
! [X13,X14,X15] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X13)
| X14 = X13 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_616])])]) ).
fof(c_0_1004,plain,
! [X13,X14,X15] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15)
| X14 = X13 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_617])])]) ).
fof(c_0_1005,plain,
! [X44,X45,X46] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X46),X45) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X46),X44)
| X45 = X44 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_618])])]) ).
fof(c_0_1006,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_1007,plain,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_Suc(X4)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_1008,plain,
! [X4,X5] : c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1009,plain,
! [X4,X5] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),X4,tc_nat) = X5,
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1010,plain,
! [X4,X5] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4),X4,tc_nat) = X5,
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1011,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X9)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X8,X9),c_HOL_Ozero__class_Ozero(X9),X9) ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_1012,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_625]) ).
fof(c_0_1013,plain,
! [X41] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X41),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X41,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_626]) ).
fof(c_0_1014,plain,
! [X29,X30] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X29,X30)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_627])])]) ).
fof(c_0_1015,plain,
! [X27,X28,X29] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X29),X27,X28) = c_Lambda_OdB_OVar(X29)
| X29 = X28
| c_HOL_Oord__class_Oless(X28,X29,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1016,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| X13 = X12
| c_HOL_Oord__class_Oless(X13,X12,X14)
| c_HOL_Oord__class_Oless(X12,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_1017,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_HOL_Oord__class_Oless(X12,X13,X14)
| X13 = X12
| c_HOL_Oord__class_Oless(X13,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1018,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| c_HOL_Oord__class_Oless(X12,X13,X14)
| c_HOL_Oord__class_Oless(X13,X12,X14)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_1019,plain,
! [X12,X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| X13 = X12
| c_HOL_Oord__class_Oless(X12,X13,X14)
| c_HOL_Oord__class_Oless(X13,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1020,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X14)
| c_HOL_Oord__class_Oless(X12,X13,X14)
| c_HOL_Oord__class_Oless(X13,X12,X14)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_1021,plain,
! [X55,X56,X57,X58] :
( hAPP(hAPP(c_Type_Otype_OFun,X58),X56) != hAPP(hAPP(c_Type_Otype_OFun,X57),X55)
| X58 = X57 ),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1022,plain,
! [X55,X56,X57,X58] :
( hAPP(hAPP(c_Type_Otype_OFun,X58),X56) != hAPP(hAPP(c_Type_Otype_OFun,X57),X55)
| X56 = X55 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_635])])]) ).
fof(c_0_1023,plain,
! [X50,X51,X52,X53] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X53),X51) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X50)
| X53 = X52 ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1024,plain,
! [X50,X51,X52,X53] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X53),X51) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X50)
| X51 = X50 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_637])])]) ).
fof(c_0_1025,plain,
! [X4,X5] : c_HOL_Ominus__class_Ominus(c_Suc(X5),c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1026,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Osemiring__1(X9)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X8),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Oone__class_Oone(X9)),c_Nat_Osemiring__1__class_Oof__nat(X8,X9)) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1027,plain,
! [X27,X28] :
( c_HOL_Oord__class_Oless(X27,X27,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X27),X28,X27) = X28 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_640])])]) ).
fof(c_0_1028,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1029,plain,
! [X12] :
( c_HOL_Oord__class_Oless(X12,X12,tc_nat)
| c_HOL_Oord__class_Oless(X12,c_Suc(X12),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1030,plain,
! [X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X8),c_HOL_Ozero__class_Ozero(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1031,plain,
! [X25,X26,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X26) ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1032,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X8),X9) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1033,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X12),X13) ),
inference(variable_rename,[status(thm)],[c_0_646]) ).
fof(c_0_1034,plain,
! [X20,X21,X22] :
( hAPP(X21,X20) = X22
| ~ c_Type_Otyping(X21,c_Lambda_OdB_OVar(X20),X22) ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1035,plain,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X5)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_Suc(X4)),
inference(variable_rename,[status(thm)],[c_0_648]) ).
fof(c_0_1036,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(X12,X13,tc_nat)
| c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1037,plain,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,X5,tc_nat)
| c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| X5 = X4 ),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1038,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oidom(X14)
| ~ class_Int_Onumber__ring(X14)
| c_HOL_Ominus__class_Ominus(X13,X12,X14) != c_HOL_Ozero__class_Ozero(X14)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1039,plain,
! [X15,X16] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X16),X15) = c_Lambda_OdB_OVar(X16)
| ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1040,plain,
! [X3] :
( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1041,plain,
! [X12,X13] : hBOOL(hAPP(hAPP(c_fequal(X13),X12),X12)),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1042,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oidom(X14)
| ~ class_Int_Onumber__ring(X14)
| X12 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X12),X13)
| X13 = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1043,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Oab__group__add(X10)
| c_HOL_Ominus__class_Ominus(X9,X8,X10) != c_HOL_Ozero__class_Ozero(X10)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1044,plain,
! [X8,X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Ominus__class_Ominus(X9,X8,X10) != c_HOL_Ozero__class_Ozero(X10)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1045,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),X8) != c_HOL_Ozero__class_Ozero(X9)
| X8 = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1046,plain,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_659]) ).
fof(c_0_1047,plain,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1048,plain,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1049,plain,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_662])])]) ).
fof(c_0_1050,plain,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_663]) ).
fof(c_0_1051,plain,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_664])])]) ).
fof(c_0_1052,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_665 ).
fof(c_0_1053,plain,
! [X12,X13] :
( ~ class_Orderings_Opreorder(X13)
| ~ c_HOL_Oord__class_Oless(X12,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1054,plain,
! [X12,X13] :
( ~ class_Orderings_Olinorder(X13)
| ~ c_HOL_Oord__class_Oless(X12,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1055,plain,
! [X12,X13] :
( ~ class_Orderings_Oorder(X13)
| ~ c_HOL_Oord__class_Oless(X12,X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1056,plain,
! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1057,plain,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_670]) ).
fof(c_0_1058,plain,
! [X4,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1059,plain,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1060,plain,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1061,plain,
! [X52,X53] : c_Type_Otyping(X53,c_Lambda_OdB_OVar(X52),hAPP(X53,X52)),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1062,plain,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_nat),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1063,plain,
! [X12] : ~ c_HOL_Oord__class_Oless(X12,X12,tc_nat),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1064,plain,
! [X21] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X21)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X21)) ),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1065,plain,
! [X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8)),c_HOL_Ozero__class_Ozero(X8)) = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1066,plain,
! [X29,X30,X31] : c_Lambda_Osubst(c_Lambda_Olift(X29,X31),X30,X31) = X29,
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1067,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_680 ).
fof(c_0_1068,plain,
! [X41] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X41)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(variable_rename,[status(thm)],[c_0_681]) ).
fof(c_0_1069,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_682 ).
fof(c_0_1070,plain,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_683]) ).
fof(c_0_1071,plain,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != c_HOL_Ozero__class_Ozero(tc_nat)
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_684])])]) ).
fof(c_0_1072,plain,
! [X4,X5] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X4) != X5
| X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_685])])]) ).
fof(c_0_1073,plain,
! [X12,X13] :
( X12 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X13)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1074,plain,
! [X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_HOL_Oone__class_Oone(X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1075,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| ~ class_Int_Onumber__ring(X13)
| X12 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),c_HOL_Ozero__class_Ozero(X13)) ),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1076,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Oidom(X13)
| ~ class_Int_Onumber__ring(X13)
| c_HOL_Ominus__class_Ominus(X12,X12,X13) = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1077,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X8) = X8 ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1078,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X8) = X8 ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1079,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),c_HOL_Ozero__class_Ozero(X9)),X8) = X8 ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1080,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),c_HOL_Ozero__class_Ozero(X13)),X12) = X12 ),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1081,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
c_0_694 ).
fof(c_0_1082,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_695 ).
fof(c_0_1083,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X8,c_HOL_Ozero__class_Ozero(X9),X9) = X8 ),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1084,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_697 ).
fof(c_0_1085,plain,
! [X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),c_HOL_Ozero__class_Ozero(X9)) = X8 ),
inference(variable_rename,[status(thm)],[c_0_698]) ).
fof(c_0_1086,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Omonoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),c_HOL_Ozero__class_Ozero(X9)) = X8 ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1087,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X9)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X9),X8),c_HOL_Ozero__class_Ozero(X9)) = X8 ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1088,plain,
! [X12,X13] :
( ~ class_OrderedGroup_Oab__group__add(X13)
| c_HOL_Ominus__class_Ominus(X12,X12,X13) = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1089,plain,
! [X12,X13] :
( ~ class_OrderedGroup_Ogroup__add(X13)
| c_HOL_Ominus__class_Ominus(X12,X12,X13) = c_HOL_Ozero__class_Ozero(X13) ),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1090,plain,
! [X8,X9] :
( ~ class_OrderedGroup_Ogroup__add(X9)
| c_HOL_Ominus__class_Ominus(X8,X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1091,plain,
! [X8] : c_Predicate_Oconversep(c_fequal(X8),X8,X8) = c_fequal(X8),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1092,plain,
! [X51,X52,X53] : hAPP(hAPP(c_Lambda_OdB_OApp,X53),X52) != c_Lambda_OdB_OAbs(X51),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1093,plain,
! [X51,X52,X53] : c_Lambda_OdB_OAbs(X51) != hAPP(hAPP(c_Lambda_OdB_OApp,X53),X52),
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1094,plain,
! [X50,X51,X52] : c_Lambda_OdB_OVar(X50) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X51),
inference(variable_rename,[status(thm)],[c_0_707]) ).
fof(c_0_1095,plain,
! [X50,X51,X52] : hAPP(hAPP(c_Lambda_OdB_OApp,X52),X51) != c_Lambda_OdB_OVar(X50),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1096,plain,
! [X3] : c_HOL_Ominus__class_Ominus(c_Suc(X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3,
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1097,plain,
! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X3),tc_nat),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1098,plain,
! [X12] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X12),tc_nat),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1099,plain,
! [X38,X39] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X39),X38,X39) = X38,
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1100,plain,
! [X45,X46] : c_List_Olistsp(X45,c_List_Olist_ONil(X46),X46),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1101,plain,
! [X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1102,plain,
! [X12] : c_HOL_Oord__class_Oless(X12,c_Suc(X12),tc_nat),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1103,plain,
! [X3] : c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1104,plain,
! [X3] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1105,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_718 ).
fof(c_0_1106,plain,
! [X4] : c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4,
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1107,plain,
! [X3] : c_Suc(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X3),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1108,plain,
! [X4] : c_HOL_Ominus__class_Ominus(X4,X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1109,plain,
! [X21,X22] : c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X21,X22),X22) = c_Transitive__Closure_Ortranclp(X21,X22),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1110,plain,
! [X8,X9,X10] :
( ~ class_Nat_Osemiring__char__0(X10)
| c_Nat_Osemiring__1__class_Oof__nat(X9,X10) != c_Nat_Osemiring__1__class_Oof__nat(X8,X10)
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1111,plain,
! [X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3) = X3,
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1112,plain,
! [X3] : c_Suc(X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_725]) ).
fof(c_0_1113,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
c_0_726 ).
fof(c_0_1114,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
c_0_727 ).
fof(c_0_1115,plain,
! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Ozero__class_Ozero(tc_nat)) = X4,
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1116,plain,
! [X12] : X12 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1117,plain,
! [X3] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X3))),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1118,plain,
! [X62,X63] :
( class_Orderings_Oorder(tc_fun(X62,X63))
| ~ class_Orderings_Oorder(X63) ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1119,plain,
! [X62,X63] :
( class_Orderings_Opreorder(tc_fun(X62,X63))
| ~ class_Orderings_Opreorder(X63) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1120,plain,
! [X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X8) = c_HOL_Oone__class_Oone(X8) ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1121,plain,
! [X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X8) = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1122,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
c_0_735 ).
fof(c_0_1123,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
c_0_736 ).
fof(c_0_1124,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
c_0_737 ).
fof(c_0_1125,plain,
! [X2] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X2),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1126,plain,
! [X8] :
( ~ class_Ring__and__Field_Ozero__neq__one(X8)
| c_HOL_Ozero__class_Ozero(X8) != c_HOL_Oone__class_Oone(X8) ),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1127,plain,
! [X8] :
( ~ class_Ring__and__Field_Ozero__neq__one(X8)
| c_HOL_Oone__class_Oone(X8) != c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1128,plain,
! [X26,X27] :
( c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OVar(X26)
| X27 = X26 ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1129,plain,
! [X51,X52] :
( c_Lambda_OdB_OAbs(X52) != c_Lambda_OdB_OAbs(X51)
| X52 = X51 ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1130,plain,
! [X12,X13] :
( c_Suc(X13) != c_Suc(X12)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1131,plain,
! [X26,X27] :
( c_Suc(X27) != c_Suc(X26)
| X27 = X26 ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1132,plain,
! [X51,X52] : c_Lambda_OdB_OAbs(X52) != c_Lambda_OdB_OVar(X51),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1133,plain,
! [X51,X52] : c_Lambda_OdB_OVar(X51) != c_Lambda_OdB_OAbs(X52),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1134,plain,
! [X2] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X2)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1135,plain,
! [X26] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X26),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1136,plain,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X4),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1137,plain,
! [X4] : c_Suc(X4) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1138,plain,
! [X26] : c_Suc(X26) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1139,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_752 ).
fof(c_0_1140,plain,
! [X3] : X3 != c_Suc(X3),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1141,plain,
! [X3] : c_Suc(X3) != X3,
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1142,axiom,
class_Orderings_Oorder(tc_bool),
c_0_755 ).
fof(c_0_1143,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_756 ).
fof(c_0_1144,axiom,
class_Orderings_Oorder(tc_nat),
c_0_757 ).
fof(c_0_1145,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_758 ).
fof(c_0_1146,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_759 ).
fof(c_0_1147,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_760 ).
fof(c_0_1148,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_761 ).
fof(c_0_1149,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_762 ).
fof(c_0_1150,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_763 ).
fof(c_0_1151,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_764 ).
fof(c_0_1152,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_765 ).
fof(c_0_1153,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_766 ).
fof(c_0_1154,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_767 ).
fof(c_0_1155,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_768 ).
fof(c_0_1156,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_769 ).
fof(c_0_1157,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_770 ).
fof(c_0_1158,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_771 ).
fof(c_0_1159,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_772 ).
fof(c_0_1160,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_773 ).
cnf(c_0_1161,plain,
( X7 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(split_conjunct,[status(thm)],[c_0_774]) ).
cnf(c_0_1162,plain,
( X3 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_775]) ).
cnf(c_0_1163,plain,
( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(split_conjunct,[status(thm)],[c_0_776]) ).
cnf(c_0_1164,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X4,X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(split_conjunct,[status(thm)],[c_0_777]) ).
cnf(c_0_1165,plain,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_778]) ).
cnf(c_0_1166,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_779]) ).
cnf(c_0_1167,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_780]) ).
cnf(c_0_1168,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_781]) ).
cnf(c_0_1169,plain,
( 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,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)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_782]) ).
cnf(c_0_1170,plain,
( X4 = X5
| ~ 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_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(split_conjunct,[status(thm)],[c_0_783]) ).
cnf(c_0_1171,plain,
( 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),X2,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) ),
inference(split_conjunct,[status(thm)],[c_0_784]) ).
cnf(c_0_1172,plain,
( 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))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_785]) ).
cnf(c_0_1173,plain,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_786]) ).
cnf(c_0_1174,plain,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_787]) ).
cnf(c_0_1175,plain,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X1,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_788]) ).
cnf(c_0_1176,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(split_conjunct,[status(thm)],[c_0_789]) ).
cnf(c_0_1177,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_790]) ).
cnf(c_0_1178,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_791]) ).
cnf(c_0_1179,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_792]) ).
cnf(c_0_1180,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_793]) ).
cnf(c_0_1181,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_794]) ).
cnf(c_0_1182,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_795]) ).
cnf(c_0_1183,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_796]) ).
cnf(c_0_1184,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_797]) ).
cnf(c_0_1185,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_798]) ).
cnf(c_0_1186,plain,
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),
inference(split_conjunct,[status(thm)],[c_0_799]) ).
cnf(c_0_1187,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_800]) ).
cnf(c_0_1188,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1))
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_801]) ).
cnf(c_0_1189,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_802]) ).
cnf(c_0_1190,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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(split_conjunct,[status(thm)],[c_0_803]) ).
cnf(c_0_1191,plain,
c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
inference(split_conjunct,[status(thm)],[c_0_804]) ).
cnf(c_0_1192,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_805]) ).
cnf(c_0_1193,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_806]) ).
cnf(c_0_1194,plain,
( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_807]) ).
cnf(c_0_1195,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_808]) ).
cnf(c_0_1196,plain,
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),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1197,plain,
( X1 = c_Lambda_OdB_OAbs(X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_810]) ).
cnf(c_0_1198,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_811]) ).
cnf(c_0_1199,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_812]) ).
cnf(c_0_1200,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(split_conjunct,[status(thm)],[c_0_813]) ).
cnf(c_0_1201,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(split_conjunct,[status(thm)],[c_0_814]) ).
cnf(c_0_1202,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(split_conjunct,[status(thm)],[c_0_815]) ).
cnf(c_0_1203,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1204,plain,
c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4) = c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4),
inference(split_conjunct,[status(thm)],[c_0_817]) ).
cnf(c_0_1205,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_818]) ).
cnf(c_0_1206,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X4),X7) ),
inference(split_conjunct,[status(thm)],[c_0_819]) ).
cnf(c_0_1207,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X7),X4) ),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1208,plain,
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),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1209,plain,
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),
inference(split_conjunct,[status(thm)],[c_0_822]) ).
cnf(c_0_1210,plain,
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),
inference(split_conjunct,[status(thm)],[c_0_823]) ).
cnf(c_0_1211,plain,
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),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1212,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X4,X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(split_conjunct,[status(thm)],[c_0_825]) ).
cnf(c_0_1213,plain,
c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_826]) ).
cnf(c_0_1214,plain,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
inference(split_conjunct,[status(thm)],[c_0_827]) ).
cnf(c_0_1215,plain,
( c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(split_conjunct,[status(thm)],[c_0_828]) ).
cnf(c_0_1216,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ 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),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_829]) ).
cnf(c_0_1217,plain,
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_830]) ).
cnf(c_0_1218,plain,
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_831]) ).
cnf(c_0_1219,plain,
( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_832]) ).
cnf(c_0_1220,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_833]) ).
cnf(c_0_1221,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_834]) ).
cnf(c_0_1222,plain,
( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_835]) ).
cnf(c_0_1223,plain,
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_836]) ).
cnf(c_0_1224,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_837]) ).
cnf(c_0_1225,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_838]) ).
cnf(c_0_1226,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_839]) ).
cnf(c_0_1227,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_840]) ).
cnf(c_0_1228,plain,
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1) ),
inference(split_conjunct,[status(thm)],[c_0_841]) ).
cnf(c_0_1229,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_842]) ).
cnf(c_0_1230,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_843]) ).
cnf(c_0_1231,plain,
( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_844]) ).
cnf(c_0_1232,plain,
( c_Lambda_Osubst(c_Lambda_Osubst(X3,c_Lambda_Olift(X4,X1),c_Suc(X2)),c_Lambda_Osubst(X5,X4,X2),X1) = c_Lambda_Osubst(c_Lambda_Osubst(X3,X5,X1),X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_845]) ).
cnf(c_0_1233,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_846]) ).
cnf(c_0_1234,plain,
( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_847]) ).
cnf(c_0_1235,plain,
( hAPP(c_Type_Oshift(X3,X1,X4,X5),X2) = hAPP(X3,c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_848]) ).
cnf(c_0_1236,plain,
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)))),
inference(split_conjunct,[status(thm)],[c_0_849]) ).
cnf(c_0_1237,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_850]) ).
cnf(c_0_1238,plain,
( c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X1),X2) = c_Lambda_Osubst(c_Lambda_Olift(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Olift(X4,X2),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_851]) ).
cnf(c_0_1239,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_852]) ).
cnf(c_0_1240,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_853]) ).
cnf(c_0_1241,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_854]) ).
cnf(c_0_1242,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_855]) ).
cnf(c_0_1243,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____),
inference(split_conjunct,[status(thm)],[c_0_856]) ).
cnf(c_0_1244,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_857]) ).
cnf(c_0_1245,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_858]) ).
cnf(c_0_1246,plain,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_859]) ).
cnf(c_0_1247,plain,
c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_860]) ).
cnf(c_0_1248,plain,
c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_861]) ).
cnf(c_0_1249,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_862]) ).
cnf(c_0_1250,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_863]) ).
cnf(c_0_1251,plain,
( c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X2),X1) = c_Lambda_Osubst(c_Lambda_Olift(X3,X1),c_Lambda_Olift(X4,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_864]) ).
cnf(c_0_1252,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1253,plain,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
inference(split_conjunct,[status(thm)],[c_0_866]) ).
cnf(c_0_1254,plain,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1255,plain,
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)),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1256,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_869]) ).
cnf(c_0_1257,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_870]) ).
cnf(c_0_1258,plain,
( X3 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_871]) ).
cnf(c_0_1259,plain,
( 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)) ),
inference(split_conjunct,[status(thm)],[c_0_872]) ).
cnf(c_0_1260,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_873]) ).
cnf(c_0_1261,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_874]) ).
cnf(c_0_1262,plain,
( c_Wellfounded_Oaccp(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_875]) ).
cnf(c_0_1263,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_876]) ).
cnf(c_0_1264,plain,
c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
inference(split_conjunct,[status(thm)],[c_0_877]) ).
cnf(c_0_1265,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_878]) ).
cnf(c_0_1266,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_879]) ).
cnf(c_0_1267,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_880]) ).
cnf(c_0_1268,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_881]) ).
cnf(c_0_1269,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_882]) ).
cnf(c_0_1270,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_883]) ).
cnf(c_0_1271,plain,
( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
| ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
| ~ c_Type_Otyping(X1,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_884]) ).
cnf(c_0_1272,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_885]) ).
cnf(c_0_1273,plain,
~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
inference(split_conjunct,[status(thm)],[c_0_886]) ).
cnf(c_0_1274,plain,
~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
inference(split_conjunct,[status(thm)],[c_0_887]) ).
cnf(c_0_1275,plain,
( c_Type_Otyping(X3,X2,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ c_Type_Otyping(X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_888]) ).
cnf(c_0_1276,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_889]) ).
cnf(c_0_1277,plain,
c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_890]) ).
cnf(c_0_1278,plain,
c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_891]) ).
cnf(c_0_1279,plain,
( 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),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_892]) ).
cnf(c_0_1280,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_893]) ).
cnf(c_0_1281,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_894]) ).
cnf(c_0_1282,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_895]) ).
cnf(c_0_1283,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_896]) ).
cnf(c_0_1284,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_897]) ).
cnf(c_0_1285,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_898]) ).
cnf(c_0_1286,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_899]) ).
cnf(c_0_1287,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_900]) ).
cnf(c_0_1288,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_901]) ).
cnf(c_0_1289,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_902]) ).
cnf(c_0_1290,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(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_903]) ).
cnf(c_0_1291,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_904]) ).
cnf(c_0_1292,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_905]) ).
cnf(c_0_1293,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_906]) ).
cnf(c_0_1294,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_907]) ).
cnf(c_0_1295,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_908]) ).
cnf(c_0_1296,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_909]) ).
cnf(c_0_1297,plain,
( c_Lambda_Olift(c_Lambda_Olift(X3,X1),c_Suc(X2)) = c_Lambda_Olift(c_Lambda_Olift(X3,X2),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_910]) ).
cnf(c_0_1298,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_911]) ).
cnf(c_0_1299,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_912]) ).
cnf(c_0_1300,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_913]) ).
cnf(c_0_1301,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_914]) ).
cnf(c_0_1302,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_915]) ).
cnf(c_0_1303,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_916]) ).
cnf(c_0_1304,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_917]) ).
cnf(c_0_1305,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_918]) ).
cnf(c_0_1306,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_919]) ).
cnf(c_0_1307,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_920]) ).
cnf(c_0_1308,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_921]) ).
cnf(c_0_1309,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_922]) ).
cnf(c_0_1310,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_923]) ).
cnf(c_0_1311,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_924]) ).
cnf(c_0_1312,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_925]) ).
cnf(c_0_1313,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_926]) ).
cnf(c_0_1314,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_927]) ).
cnf(c_0_1315,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_928]) ).
cnf(c_0_1316,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_929]) ).
cnf(c_0_1317,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_930]) ).
cnf(c_0_1318,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_931]) ).
cnf(c_0_1319,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_932]) ).
cnf(c_0_1320,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_933]) ).
cnf(c_0_1321,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(split_conjunct,[status(thm)],[c_0_934]) ).
cnf(c_0_1322,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_935]) ).
cnf(c_0_1323,plain,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_936]) ).
cnf(c_0_1324,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_937]) ).
cnf(c_0_1325,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_938]) ).
cnf(c_0_1326,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_939]) ).
cnf(c_0_1327,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_940]) ).
cnf(c_0_1328,plain,
c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X2) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),
inference(split_conjunct,[status(thm)],[c_0_941]) ).
cnf(c_0_1329,plain,
( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3))
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_942]) ).
cnf(c_0_1330,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_943]) ).
cnf(c_0_1331,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_944]) ).
cnf(c_0_1332,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_945]) ).
cnf(c_0_1333,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_946]) ).
cnf(c_0_1334,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_947]) ).
cnf(c_0_1335,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_948]) ).
cnf(c_0_1336,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_949]) ).
cnf(c_0_1337,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_950]) ).
cnf(c_0_1338,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_951]) ).
cnf(c_0_1339,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_952]) ).
cnf(c_0_1340,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_953]) ).
cnf(c_0_1341,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_954]) ).
cnf(c_0_1342,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_955]) ).
cnf(c_0_1343,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_956]) ).
cnf(c_0_1344,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_957]) ).
cnf(c_0_1345,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_958]) ).
cnf(c_0_1346,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_959]) ).
cnf(c_0_1347,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_960]) ).
cnf(c_0_1348,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_961]) ).
cnf(c_0_1349,plain,
c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_962]) ).
cnf(c_0_1350,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_963]) ).
cnf(c_0_1351,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_964]) ).
cnf(c_0_1352,plain,
( X1 = c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_965]) ).
cnf(c_0_1353,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_966]) ).
cnf(c_0_1354,plain,
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)),
inference(split_conjunct,[status(thm)],[c_0_967]) ).
cnf(c_0_1355,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_968]) ).
cnf(c_0_1356,plain,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_969]) ).
cnf(c_0_1357,plain,
( 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)) ),
inference(split_conjunct,[status(thm)],[c_0_970]) ).
cnf(c_0_1358,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_971]) ).
cnf(c_0_1359,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(split_conjunct,[status(thm)],[c_0_972]) ).
cnf(c_0_1360,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(split_conjunct,[status(thm)],[c_0_973]) ).
cnf(c_0_1361,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_974]) ).
cnf(c_0_1362,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_975]) ).
cnf(c_0_1363,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_976]) ).
cnf(c_0_1364,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_977]) ).
cnf(c_0_1365,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_978]) ).
cnf(c_0_1366,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_979]) ).
cnf(c_0_1367,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_980]) ).
cnf(c_0_1368,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_981]) ).
cnf(c_0_1369,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_982]) ).
cnf(c_0_1370,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_983]) ).
cnf(c_0_1371,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_984]) ).
cnf(c_0_1372,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
inference(split_conjunct,[status(thm)],[c_0_985]) ).
cnf(c_0_1373,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_986]) ).
cnf(c_0_1374,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_987]) ).
cnf(c_0_1375,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1376,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_989]) ).
cnf(c_0_1377,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_990]) ).
cnf(c_0_1378,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_991]) ).
cnf(c_0_1379,plain,
c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_992]) ).
cnf(c_0_1380,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
inference(split_conjunct,[status(thm)],[c_0_993]) ).
cnf(c_0_1381,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_994]) ).
cnf(c_0_1382,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_995]) ).
cnf(c_0_1383,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1384,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1385,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_998]) ).
cnf(c_0_1386,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_999]) ).
cnf(c_0_1387,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1000]) ).
cnf(c_0_1388,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1001]) ).
cnf(c_0_1389,plain,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1002]) ).
cnf(c_0_1390,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1003]) ).
cnf(c_0_1391,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1004]) ).
cnf(c_0_1392,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1005]) ).
cnf(c_0_1393,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1394,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1395,plain,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1396,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1397,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1010]) ).
cnf(c_0_1398,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1011]) ).
cnf(c_0_1399,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1012]) ).
cnf(c_0_1400,plain,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_1013]) ).
cnf(c_0_1401,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1014]) ).
cnf(c_0_1402,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1015]) ).
cnf(c_0_1403,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1016]) ).
cnf(c_0_1404,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1017]) ).
cnf(c_0_1405,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1018]) ).
cnf(c_0_1406,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1019]) ).
cnf(c_0_1407,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1020]) ).
cnf(c_0_1408,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1021]) ).
cnf(c_0_1409,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1022]) ).
cnf(c_0_1410,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1023]) ).
cnf(c_0_1411,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1024]) ).
cnf(c_0_1412,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1025]) ).
cnf(c_0_1413,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2))
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1026]) ).
cnf(c_0_1414,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1027]) ).
cnf(c_0_1415,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1028]) ).
cnf(c_0_1416,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1029]) ).
cnf(c_0_1417,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1030]) ).
cnf(c_0_1418,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_1031]) ).
cnf(c_0_1419,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_1032]) ).
cnf(c_0_1420,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_1033]) ).
cnf(c_0_1421,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1034]) ).
cnf(c_0_1422,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
inference(split_conjunct,[status(thm)],[c_0_1035]) ).
cnf(c_0_1423,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1036]) ).
cnf(c_0_1424,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1037]) ).
cnf(c_0_1425,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1038]) ).
cnf(c_0_1426,plain,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1039]) ).
cnf(c_0_1427,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1040]) ).
cnf(c_0_1428,plain,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
inference(split_conjunct,[status(thm)],[c_0_1041]) ).
cnf(c_0_1429,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1042]) ).
cnf(c_0_1430,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1043]) ).
cnf(c_0_1431,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1044]) ).
cnf(c_0_1432,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1045]) ).
cnf(c_0_1433,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1046]) ).
cnf(c_0_1434,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1047]) ).
cnf(c_0_1435,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1048]) ).
cnf(c_0_1436,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1049]) ).
cnf(c_0_1437,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1050]) ).
cnf(c_0_1438,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1051]) ).
cnf(c_0_1439,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1052]) ).
cnf(c_0_1440,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1053]) ).
cnf(c_0_1441,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1054]) ).
cnf(c_0_1442,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1055]) ).
cnf(c_0_1443,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_1056]) ).
cnf(c_0_1444,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(split_conjunct,[status(thm)],[c_0_1057]) ).
cnf(c_0_1445,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1058]) ).
cnf(c_0_1446,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1059]) ).
cnf(c_0_1447,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1060]) ).
cnf(c_0_1448,plain,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1061]) ).
cnf(c_0_1449,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1062]) ).
cnf(c_0_1450,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1063]) ).
cnf(c_0_1451,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1064]) ).
cnf(c_0_1452,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_1065]) ).
cnf(c_0_1453,plain,
c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1454,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1455,plain,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_1068]) ).
cnf(c_0_1456,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1069]) ).
cnf(c_0_1457,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1070]) ).
cnf(c_0_1458,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1071]) ).
cnf(c_0_1459,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1072]) ).
cnf(c_0_1460,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1073]) ).
cnf(c_0_1461,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1074]) ).
cnf(c_0_1462,plain,
( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1075]) ).
cnf(c_0_1463,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1076]) ).
cnf(c_0_1464,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1077]) ).
cnf(c_0_1465,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1078]) ).
cnf(c_0_1466,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1079]) ).
cnf(c_0_1467,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1080]) ).
cnf(c_0_1468,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
inference(split_conjunct,[status(thm)],[c_0_1081]) ).
cnf(c_0_1469,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1082]) ).
cnf(c_0_1470,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1083]) ).
cnf(c_0_1471,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1084]) ).
cnf(c_0_1472,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1085]) ).
cnf(c_0_1473,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1086]) ).
cnf(c_0_1474,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1087]) ).
cnf(c_0_1475,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1088]) ).
cnf(c_0_1476,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1089]) ).
cnf(c_0_1477,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1090]) ).
cnf(c_0_1478,plain,
c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
inference(split_conjunct,[status(thm)],[c_0_1091]) ).
cnf(c_0_1479,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
inference(split_conjunct,[status(thm)],[c_0_1092]) ).
cnf(c_0_1480,plain,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1093]) ).
cnf(c_0_1481,plain,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1482,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
inference(split_conjunct,[status(thm)],[c_0_1095]) ).
cnf(c_0_1483,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1096]) ).
cnf(c_0_1484,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1097]) ).
cnf(c_0_1485,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1098]) ).
cnf(c_0_1486,plain,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1099]) ).
cnf(c_0_1487,plain,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
inference(split_conjunct,[status(thm)],[c_0_1100]) ).
cnf(c_0_1488,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1101]) ).
cnf(c_0_1489,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1490,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1103]) ).
cnf(c_0_1491,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1492,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1493,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1494,plain,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1495,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1496,plain,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1497,plain,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1498,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1499,plain,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1500,plain,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
inference(split_conjunct,[status(thm)],[c_0_1113]) ).
cnf(c_0_1501,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(split_conjunct,[status(thm)],[c_0_1114]) ).
cnf(c_0_1502,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1503,plain,
X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1504,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
inference(split_conjunct,[status(thm)],[c_0_1117]) ).
cnf(c_0_1505,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1118]) ).
cnf(c_0_1506,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1507,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1120]) ).
cnf(c_0_1508,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1509,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1510,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1511,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1512,plain,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1513,plain,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1514,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1515,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1516,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1517,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1518,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1519,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1520,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(split_conjunct,[status(thm)],[c_0_1133]) ).
cnf(c_0_1521,plain,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1134]) ).
cnf(c_0_1522,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1523,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1136]) ).
cnf(c_0_1524,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1137]) ).
cnf(c_0_1525,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1138]) ).
cnf(c_0_1526,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1139]) ).
cnf(c_0_1527,plain,
X1 != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1140]) ).
cnf(c_0_1528,plain,
c_Suc(X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_1141]) ).
cnf(c_0_1529,plain,
class_Orderings_Oorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1142]) ).
cnf(c_0_1530,plain,
class_Orderings_Opreorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1143]) ).
cnf(c_0_1531,plain,
class_Orderings_Oorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1144]) ).
cnf(c_0_1532,plain,
class_Orderings_Olinorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1145]) ).
cnf(c_0_1533,plain,
class_Orderings_Opreorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1146]) ).
cnf(c_0_1534,plain,
class_Nat_Osemiring__char__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1147]) ).
cnf(c_0_1535,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1148]) ).
cnf(c_0_1536,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1149]) ).
cnf(c_0_1537,plain,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1150]) ).
cnf(c_0_1538,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1151]) ).
cnf(c_0_1539,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1152]) ).
cnf(c_0_1540,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1153]) ).
cnf(c_0_1541,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1154]) ).
cnf(c_0_1542,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1543,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1544,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1157]) ).
cnf(c_0_1545,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1158]) ).
cnf(c_0_1546,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1159]) ).
cnf(c_0_1547,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1160]) ).
cnf(c_0_1548,plain,
( c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
c_0_1161,
[final] ).
cnf(c_0_1549,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
c_0_1162,
[final] ).
cnf(c_0_1550,plain,
( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
c_0_1163,
[final] ).
cnf(c_0_1551,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X4,X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
c_0_1164,
[final] ).
cnf(c_0_1552,plain,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
c_0_1165,
[final] ).
cnf(c_0_1553,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
c_0_1166,
[final] ).
cnf(c_0_1554,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1167,
[final] ).
cnf(c_0_1555,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1168,
[final] ).
cnf(c_0_1556,plain,
( 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,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)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
c_0_1169,
[final] ).
cnf(c_0_1557,plain,
( X4 = X5
| ~ 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_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
c_0_1170,
[final] ).
cnf(c_0_1558,plain,
( 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),X2,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_0_1171,
[final] ).
cnf(c_0_1559,plain,
( 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))
| ~ 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_0_1172,
[final] ).
cnf(c_0_1560,plain,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_1173,
[final] ).
cnf(c_0_1561,plain,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_1174,
[final] ).
cnf(c_0_1562,plain,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X1,X5,X3) ),
c_0_1175,
[final] ).
cnf(c_0_1563,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_1176,
[final] ).
cnf(c_0_1564,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
c_0_1177,
[final] ).
cnf(c_0_1565,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
| ~ 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_0_1178,
[final] ).
cnf(c_0_1566,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_1179,
[final] ).
cnf(c_0_1567,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_1180,
[final] ).
cnf(c_0_1568,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1181,
[final] ).
cnf(c_0_1569,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1182,
[final] ).
cnf(c_0_1570,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1183,
[final] ).
cnf(c_0_1571,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1184,
[final] ).
cnf(c_0_1572,plain,
( 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) ),
c_0_1185,
[final] ).
cnf(c_0_1573,plain,
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),
c_0_1186,
[final] ).
cnf(c_0_1574,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1187,
[final] ).
cnf(c_0_1575,plain,
( 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)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1188,
[final] ).
cnf(c_0_1576,plain,
( 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) ),
c_0_1189,
[final] ).
cnf(c_0_1577,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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
c_0_1190,
[final] ).
cnf(c_0_1578,plain,
c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
c_0_1191,
[final] ).
cnf(c_0_1579,plain,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1192,
[final] ).
cnf(c_0_1580,plain,
( 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) ),
c_0_1193,
[final] ).
cnf(c_0_1581,plain,
( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
c_0_1194,
[final] ).
cnf(c_0_1582,plain,
( 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) ),
c_0_1195,
[final] ).
cnf(c_0_1583,plain,
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),
c_0_1196,
[final] ).
cnf(c_0_1584,plain,
( X1 = c_Lambda_OdB_OAbs(X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
c_0_1197,
[final] ).
cnf(c_0_1585,plain,
( 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) ),
c_0_1198,
[final] ).
cnf(c_0_1586,plain,
( 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) ),
c_0_1199,
[final] ).
cnf(c_0_1587,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) ),
c_0_1200,
[final] ).
cnf(c_0_1588,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) ),
c_0_1201,
[final] ).
cnf(c_0_1589,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) ),
c_0_1202,
[final] ).
cnf(c_0_1590,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
c_0_1203,
[final] ).
cnf(c_0_1591,plain,
c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4) = c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),
c_0_1204,
[final] ).
cnf(c_0_1592,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
c_0_1205,
[final] ).
cnf(c_0_1593,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
c_0_1206,
[final] ).
cnf(c_0_1594,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
c_0_1207,
[final] ).
cnf(c_0_1595,plain,
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) = hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
c_0_1208,
[final] ).
cnf(c_0_1596,plain,
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) = c_Lambda_OdB_OVar(X1),
c_0_1209,
[final] ).
cnf(c_0_1597,plain,
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),
c_0_1210,
[final] ).
cnf(c_0_1598,plain,
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),
c_0_1211,
[final] ).
cnf(c_0_1599,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X4,X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
c_0_1212,
[final] ).
cnf(c_0_1600,plain,
c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
c_0_1213,
[final] ).
cnf(c_0_1601,plain,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
c_0_1214,
[final] ).
cnf(c_0_1602,plain,
( c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
c_0_1215,
[final] ).
cnf(c_0_1603,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ 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),X3),X4)) ),
c_0_1216,
[final] ).
cnf(c_0_1604,plain,
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1217,
[final] ).
cnf(c_0_1605,plain,
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1218,
[final] ).
cnf(c_0_1606,plain,
( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4) ),
c_0_1219,
[final] ).
cnf(c_0_1607,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
c_0_1220,
[final] ).
cnf(c_0_1608,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
c_0_1221,
[final] ).
cnf(c_0_1609,plain,
( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
c_0_1222,
[final] ).
cnf(c_0_1610,plain,
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1223,
[final] ).
cnf(c_0_1611,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
c_0_1224,
[final] ).
cnf(c_0_1612,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
c_0_1225,
[final] ).
cnf(c_0_1613,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1226,
[final] ).
cnf(c_0_1614,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1227,
[final] ).
cnf(c_0_1615,plain,
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1) ),
c_0_1228,
[final] ).
cnf(c_0_1616,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1229,
[final] ).
cnf(c_0_1617,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
c_0_1230,
[final] ).
cnf(c_0_1618,plain,
( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
c_0_1231,
[final] ).
cnf(c_0_1619,plain,
( c_Lambda_Osubst(c_Lambda_Osubst(X3,c_Lambda_Olift(X4,X1),c_Suc(X2)),c_Lambda_Osubst(X5,X4,X2),X1) = c_Lambda_Osubst(c_Lambda_Osubst(X3,X5,X1),X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
c_0_1232,
[final] ).
cnf(c_0_1620,plain,
( 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) ),
c_0_1233,
[final] ).
cnf(c_0_1621,plain,
( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
c_0_1234,
[final] ).
cnf(c_0_1622,plain,
( hAPP(c_Type_Oshift(X3,X1,X4,X5),X2) = hAPP(X3,c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1235,
[final] ).
cnf(c_0_1623,plain,
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)))),
c_0_1236,
[final] ).
cnf(c_0_1624,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
c_0_1237,
[final] ).
cnf(c_0_1625,plain,
( c_Lambda_Osubst(c_Lambda_Olift(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Olift(X4,X2),X1) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
c_0_1238,
[final] ).
cnf(c_0_1626,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1239,
[final] ).
cnf(c_0_1627,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1240,
[final] ).
cnf(c_0_1628,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1241,
[final] ).
cnf(c_0_1629,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1242,
[final] ).
cnf(c_0_1630,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____),
c_0_1243,
[final] ).
cnf(c_0_1631,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
c_0_1244,
[final] ).
cnf(c_0_1632,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
c_0_1245,
[final] ).
cnf(c_0_1633,plain,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1246,
[final] ).
cnf(c_0_1634,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB),
c_0_1247,
[final] ).
cnf(c_0_1635,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype),
c_0_1248,
[final] ).
cnf(c_0_1636,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
c_0_1249,
[final] ).
cnf(c_0_1637,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1250,
[final] ).
cnf(c_0_1638,plain,
( c_Lambda_Osubst(c_Lambda_Olift(X3,X1),c_Lambda_Olift(X4,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X2),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
c_0_1251,
[final] ).
cnf(c_0_1639,plain,
( 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) ),
c_0_1252,
[final] ).
cnf(c_0_1640,plain,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
c_0_1253,
[final] ).
cnf(c_0_1641,plain,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1254,
[final] ).
cnf(c_0_1642,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)) = c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4),
c_0_1255,
[final] ).
cnf(c_0_1643,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ 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_0_1256,
[final] ).
cnf(c_0_1644,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ 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_0_1257,
[final] ).
cnf(c_0_1645,plain,
( hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
c_0_1258,
[final] ).
cnf(c_0_1646,plain,
( 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)) ),
c_0_1259,
[final] ).
cnf(c_0_1647,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1260,
[final] ).
cnf(c_0_1648,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
c_0_1261,
[final] ).
cnf(c_0_1649,plain,
( c_Wellfounded_Oaccp(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
c_0_1262,
[final] ).
cnf(c_0_1650,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
c_0_1263,
[final] ).
cnf(c_0_1651,plain,
c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))) = c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3),
c_0_1264,
[final] ).
cnf(c_0_1652,plain,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
c_0_1265,
[final] ).
cnf(c_0_1653,plain,
( 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) ),
c_0_1266,
[final] ).
cnf(c_0_1654,plain,
( 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) ),
c_0_1267,
[final] ).
cnf(c_0_1655,plain,
( 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) ),
c_0_1268,
[final] ).
cnf(c_0_1656,plain,
( 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) ),
c_0_1269,
[final] ).
cnf(c_0_1657,plain,
( 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) ),
c_0_1270,
[final] ).
cnf(c_0_1658,plain,
( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
| ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
| ~ c_Type_Otyping(X1,X5,X3) ),
c_0_1271,
[final] ).
cnf(c_0_1659,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
c_0_1272,
[final] ).
cnf(c_0_1660,plain,
~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
c_0_1273,
[final] ).
cnf(c_0_1661,plain,
~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
c_0_1274,
[final] ).
cnf(c_0_1662,plain,
( c_Type_Otyping(X3,X2,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ c_Type_Otyping(X3,X1,X4) ),
c_0_1275,
[final] ).
cnf(c_0_1663,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
c_0_1276,
[final] ).
cnf(c_0_1664,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),
c_0_1277,
[final] ).
cnf(c_0_1665,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)),
c_0_1278,
[final] ).
cnf(c_0_1666,plain,
( 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),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_1279,
[final] ).
cnf(c_0_1667,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
c_0_1280,
[final] ).
cnf(c_0_1668,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
c_0_1281,
[final] ).
cnf(c_0_1669,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_1282,
[final] ).
cnf(c_0_1670,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_1283,
[final] ).
cnf(c_0_1671,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_1284,
[final] ).
cnf(c_0_1672,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1285,
[final] ).
cnf(c_0_1673,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_1286,
[final] ).
cnf(c_0_1674,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_1287,
[final] ).
cnf(c_0_1675,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1288,
[final] ).
cnf(c_0_1676,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1289,
[final] ).
cnf(c_0_1677,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(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
c_0_1290,
[final] ).
cnf(c_0_1678,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
c_0_1291,
[final] ).
cnf(c_0_1679,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
c_0_1292,
[final] ).
cnf(c_0_1680,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1293,
[final] ).
cnf(c_0_1681,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ 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_0_1294,
[final] ).
cnf(c_0_1682,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ 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_0_1295,
[final] ).
cnf(c_0_1683,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ 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_0_1296,
[final] ).
cnf(c_0_1684,plain,
( c_Lambda_Olift(c_Lambda_Olift(X3,X1),c_Suc(X2)) = c_Lambda_Olift(c_Lambda_Olift(X3,X2),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
c_0_1297,
[final] ).
cnf(c_0_1685,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1298,
[final] ).
cnf(c_0_1686,plain,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1299,
[final] ).
cnf(c_0_1687,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1300,
[final] ).
cnf(c_0_1688,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1301,
[final] ).
cnf(c_0_1689,plain,
( 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) ),
c_0_1302,
[final] ).
cnf(c_0_1690,plain,
( 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) ),
c_0_1303,
[final] ).
cnf(c_0_1691,plain,
( 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) ),
c_0_1304,
[final] ).
cnf(c_0_1692,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1305,
[final] ).
cnf(c_0_1693,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
c_0_1306,
[final] ).
cnf(c_0_1694,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1307,
[final] ).
cnf(c_0_1695,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
c_0_1308,
[final] ).
cnf(c_0_1696,plain,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
c_0_1309,
[final] ).
cnf(c_0_1697,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
c_0_1310,
[final] ).
cnf(c_0_1698,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
c_0_1311,
[final] ).
cnf(c_0_1699,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
c_0_1312,
[final] ).
cnf(c_0_1700,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
c_0_1313,
[final] ).
cnf(c_0_1701,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1314,
[final] ).
cnf(c_0_1702,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
c_0_1315,
[final] ).
cnf(c_0_1703,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
c_0_1316,
[final] ).
cnf(c_0_1704,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
c_0_1317,
[final] ).
cnf(c_0_1705,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_1318,
[final] ).
cnf(c_0_1706,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1319,
[final] ).
cnf(c_0_1707,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1320,
[final] ).
cnf(c_0_1708,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) ),
c_0_1321,
[final] ).
cnf(c_0_1709,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
c_0_1322,
[final] ).
cnf(c_0_1710,plain,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
c_0_1323,
[final] ).
cnf(c_0_1711,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1324,
[final] ).
cnf(c_0_1712,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1325,
[final] ).
cnf(c_0_1713,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1326,
[final] ).
cnf(c_0_1714,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1327,
[final] ).
cnf(c_0_1715,plain,
c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))) = c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X2),
c_0_1328,
[final] ).
cnf(c_0_1716,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
c_0_1329,
[final] ).
cnf(c_0_1717,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1330,
[final] ).
cnf(c_0_1718,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
c_0_1331,
[final] ).
cnf(c_0_1719,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
c_0_1332,
[final] ).
cnf(c_0_1720,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
c_0_1333,
[final] ).
cnf(c_0_1721,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1334,
[final] ).
cnf(c_0_1722,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1335,
[final] ).
cnf(c_0_1723,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1336,
[final] ).
cnf(c_0_1724,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1337,
[final] ).
cnf(c_0_1725,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1338,
[final] ).
cnf(c_0_1726,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1339,
[final] ).
cnf(c_0_1727,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1340,
[final] ).
cnf(c_0_1728,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1341,
[final] ).
cnf(c_0_1729,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1342,
[final] ).
cnf(c_0_1730,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1343,
[final] ).
cnf(c_0_1731,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1344,
[final] ).
cnf(c_0_1732,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
c_0_1345,
[final] ).
cnf(c_0_1733,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
c_0_1346,
[final] ).
cnf(c_0_1734,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
c_0_1347,
[final] ).
cnf(c_0_1735,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1348,
[final] ).
cnf(c_0_1736,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),
c_0_1349,
[final] ).
cnf(c_0_1737,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1350,
[final] ).
cnf(c_0_1738,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ),
c_0_1351,
[final] ).
cnf(c_0_1739,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1352,
[final] ).
cnf(c_0_1740,plain,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1353,
[final] ).
cnf(c_0_1741,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)) = c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3),
c_0_1354,
[final] ).
cnf(c_0_1742,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1355,
[final] ).
cnf(c_0_1743,plain,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_1356,
[final] ).
cnf(c_0_1744,plain,
( 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)) ),
c_0_1357,
[final] ).
cnf(c_0_1745,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
c_0_1358,
[final] ).
cnf(c_0_1746,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
c_0_1359,
[final] ).
cnf(c_0_1747,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
c_0_1360,
[final] ).
cnf(c_0_1748,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1361,
[final] ).
cnf(c_0_1749,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1362,
[final] ).
cnf(c_0_1750,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
c_0_1363,
[final] ).
cnf(c_0_1751,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1364,
[final] ).
cnf(c_0_1752,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1365,
[final] ).
cnf(c_0_1753,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1366,
[final] ).
cnf(c_0_1754,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1367,
[final] ).
cnf(c_0_1755,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1368,
[final] ).
cnf(c_0_1756,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1369,
[final] ).
cnf(c_0_1757,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1370,
[final] ).
cnf(c_0_1758,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1371,
[final] ).
cnf(c_0_1759,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
c_0_1372,
[final] ).
cnf(c_0_1760,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
c_0_1373,
[final] ).
cnf(c_0_1761,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
c_0_1374,
[final] ).
cnf(c_0_1762,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
c_0_1375,
[final] ).
cnf(c_0_1763,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
c_0_1376,
[final] ).
cnf(c_0_1764,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_1377,
[final] ).
cnf(c_0_1765,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
c_0_1378,
[final] ).
cnf(c_0_1766,plain,
c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
c_0_1379,
[final] ).
cnf(c_0_1767,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
c_0_1380,
[final] ).
cnf(c_0_1768,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
c_0_1381,
[final] ).
cnf(c_0_1769,plain,
c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2),
c_0_1382,
[final] ).
cnf(c_0_1770,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1383,
[final] ).
cnf(c_0_1771,plain,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1384,
[final] ).
cnf(c_0_1772,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1385,
[final] ).
cnf(c_0_1773,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1386,
[final] ).
cnf(c_0_1774,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
c_0_1387,
[final] ).
cnf(c_0_1775,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1388,
[final] ).
cnf(c_0_1776,plain,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1389,
[final] ).
cnf(c_0_1777,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
c_0_1390,
[final] ).
cnf(c_0_1778,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
c_0_1391,
[final] ).
cnf(c_0_1779,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
c_0_1392,
[final] ).
cnf(c_0_1780,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
c_0_1393,
[final] ).
cnf(c_0_1781,plain,
c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
c_0_1394,
[final] ).
cnf(c_0_1782,plain,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1395,
[final] ).
cnf(c_0_1783,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
c_0_1396,
[final] ).
cnf(c_0_1784,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
c_0_1397,
[final] ).
cnf(c_0_1785,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_1398,
[final] ).
cnf(c_0_1786,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1399,
[final] ).
cnf(c_0_1787,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB),
c_0_1400,
[final] ).
cnf(c_0_1788,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1401,
[final] ).
cnf(c_0_1789,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
c_0_1402,
[final] ).
cnf(c_0_1790,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
c_0_1403,
[final] ).
cnf(c_0_1791,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1404,
[final] ).
cnf(c_0_1792,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1405,
[final] ).
cnf(c_0_1793,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
c_0_1406,
[final] ).
cnf(c_0_1794,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1407,
[final] ).
cnf(c_0_1795,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
c_0_1408,
[final] ).
cnf(c_0_1796,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
c_0_1409,
[final] ).
cnf(c_0_1797,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
c_0_1410,
[final] ).
cnf(c_0_1798,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
c_0_1411,
[final] ).
cnf(c_0_1799,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
c_0_1412,
[final] ).
cnf(c_0_1800,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
c_0_1413,
[final] ).
cnf(c_0_1801,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1414,
[final] ).
cnf(c_0_1802,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
c_0_1415,
[final] ).
cnf(c_0_1803,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1416,
[final] ).
cnf(c_0_1804,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1417,
[final] ).
cnf(c_0_1805,plain,
( 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) ),
c_0_1418,
[final] ).
cnf(c_0_1806,plain,
( 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) ),
c_0_1419,
[final] ).
cnf(c_0_1807,plain,
( 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) ),
c_0_1420,
[final] ).
cnf(c_0_1808,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
c_0_1421,
[final] ).
cnf(c_0_1809,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
c_0_1422,
[final] ).
cnf(c_0_1810,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1423,
[final] ).
cnf(c_0_1811,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1424,
[final] ).
cnf(c_0_1812,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1425,
[final] ).
cnf(c_0_1813,plain,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1426,
[final] ).
cnf(c_0_1814,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
c_0_1427,
[final] ).
cnf(c_0_1815,plain,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
c_0_1428,
[final] ).
cnf(c_0_1816,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1429,
[final] ).
cnf(c_0_1817,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_1430,
[final] ).
cnf(c_0_1818,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_1431,
[final] ).
cnf(c_0_1819,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1432,
[final] ).
cnf(c_0_1820,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1433,
[final] ).
cnf(c_0_1821,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1434,
[final] ).
cnf(c_0_1822,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1435,
[final] ).
cnf(c_0_1823,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1436,
[final] ).
cnf(c_0_1824,plain,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1437,
[final] ).
cnf(c_0_1825,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1438,
[final] ).
cnf(c_0_1826,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1439,
[final] ).
cnf(c_0_1827,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1440,
[final] ).
cnf(c_0_1828,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1441,
[final] ).
cnf(c_0_1829,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1442,
[final] ).
cnf(c_0_1830,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
c_0_1443,
[final] ).
cnf(c_0_1831,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1444,
[final] ).
cnf(c_0_1832,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_1445,
[final] ).
cnf(c_0_1833,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1446,
[final] ).
cnf(c_0_1834,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1447,
[final] ).
cnf(c_0_1835,plain,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
c_0_1448,
[final] ).
cnf(c_0_1836,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_1449,
[final] ).
cnf(c_0_1837,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_1450,
[final] ).
cnf(c_0_1838,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1451,
[final] ).
cnf(c_0_1839,plain,
( 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) ),
c_0_1452,
[final] ).
cnf(c_0_1840,plain,
c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
c_0_1453,
[final] ).
cnf(c_0_1841,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1454,
[final] ).
cnf(c_0_1842,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)),
c_0_1455,
[final] ).
cnf(c_0_1843,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1456,
[final] ).
cnf(c_0_1844,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1457,
[final] ).
cnf(c_0_1845,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1458,
[final] ).
cnf(c_0_1846,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_1459,
[final] ).
cnf(c_0_1847,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_1460,
[final] ).
cnf(c_0_1848,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1461,
[final] ).
cnf(c_0_1849,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1462,
[final] ).
cnf(c_0_1850,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1463,
[final] ).
cnf(c_0_1851,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1464,
[final] ).
cnf(c_0_1852,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1465,
[final] ).
cnf(c_0_1853,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1466,
[final] ).
cnf(c_0_1854,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1467,
[final] ).
cnf(c_0_1855,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1468,
[final] ).
cnf(c_0_1856,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1469,
[final] ).
cnf(c_0_1857,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1470,
[final] ).
cnf(c_0_1858,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
c_0_1471,
[final] ).
cnf(c_0_1859,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1472,
[final] ).
cnf(c_0_1860,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1473,
[final] ).
cnf(c_0_1861,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1474,
[final] ).
cnf(c_0_1862,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_1475,
[final] ).
cnf(c_0_1863,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1476,
[final] ).
cnf(c_0_1864,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_1477,
[final] ).
cnf(c_0_1865,plain,
c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
c_0_1478,
[final] ).
cnf(c_0_1866,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
c_0_1479,
[final] ).
cnf(c_0_1867,plain,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
c_0_1480,
[final] ).
cnf(c_0_1868,plain,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
c_0_1481,
[final] ).
cnf(c_0_1869,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
c_0_1482,
[final] ).
cnf(c_0_1870,plain,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
c_0_1483,
[final] ).
cnf(c_0_1871,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_1484,
[final] ).
cnf(c_0_1872,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_1485,
[final] ).
cnf(c_0_1873,plain,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
c_0_1486,
[final] ).
cnf(c_0_1874,plain,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
c_0_1487,
[final] ).
cnf(c_0_1875,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1488,
[final] ).
cnf(c_0_1876,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_1489,
[final] ).
cnf(c_0_1877,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_1490,
[final] ).
cnf(c_0_1878,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1491,
[final] ).
cnf(c_0_1879,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1492,
[final] ).
cnf(c_0_1880,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_1493,
[final] ).
cnf(c_0_1881,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1) = c_Suc(X1),
c_0_1494,
[final] ).
cnf(c_0_1882,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1495,
[final] ).
cnf(c_0_1883,plain,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
c_0_1496,
[final] ).
cnf(c_0_1884,plain,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
c_0_1497,
[final] ).
cnf(c_0_1885,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
c_0_1498,
[final] ).
cnf(c_0_1886,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = c_Suc(X1),
c_0_1499,
[final] ).
cnf(c_0_1887,plain,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
c_0_1500,
[final] ).
cnf(c_0_1888,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
c_0_1501,
[final] ).
cnf(c_0_1889,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
c_0_1502,
[final] ).
cnf(c_0_1890,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
c_0_1503,
[final] ).
cnf(c_0_1891,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
c_0_1504,
[final] ).
cnf(c_0_1892,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_1505,
[final] ).
cnf(c_0_1893,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1506,
[final] ).
cnf(c_0_1894,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
c_0_1507,
[final] ).
cnf(c_0_1895,plain,
( 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) ),
c_0_1508,
[final] ).
cnf(c_0_1896,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
c_0_1509,
[final] ).
cnf(c_0_1897,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
c_0_1510,
[final] ).
cnf(c_0_1898,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
c_0_1511,
[final] ).
cnf(c_0_1899,plain,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1512,
[final] ).
cnf(c_0_1900,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_1513,
[final] ).
cnf(c_0_1901,plain,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_1514,
[final] ).
cnf(c_0_1902,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
c_0_1515,
[final] ).
cnf(c_0_1903,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
c_0_1516,
[final] ).
cnf(c_0_1904,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_1517,
[final] ).
cnf(c_0_1905,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_1518,
[final] ).
cnf(c_0_1906,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
c_0_1519,
[final] ).
cnf(c_0_1907,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
c_0_1520,
[final] ).
cnf(c_0_1908,plain,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1521,
[final] ).
cnf(c_0_1909,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1522,
[final] ).
cnf(c_0_1910,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1523,
[final] ).
cnf(c_0_1911,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1524,
[final] ).
cnf(c_0_1912,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1525,
[final] ).
cnf(c_0_1913,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
c_0_1526,
[final] ).
cnf(c_0_1914,plain,
c_Suc(X1) != X1,
c_0_1527,
[final] ).
cnf(c_0_1915,plain,
c_Suc(X1) != X1,
c_0_1528,
[final] ).
cnf(c_0_1916,plain,
class_Orderings_Oorder(tc_bool),
c_0_1529,
[final] ).
cnf(c_0_1917,plain,
class_Orderings_Opreorder(tc_bool),
c_0_1530,
[final] ).
cnf(c_0_1918,plain,
class_Orderings_Oorder(tc_nat),
c_0_1531,
[final] ).
cnf(c_0_1919,plain,
class_Orderings_Olinorder(tc_nat),
c_0_1532,
[final] ).
cnf(c_0_1920,plain,
class_Orderings_Opreorder(tc_nat),
c_0_1533,
[final] ).
cnf(c_0_1921,plain,
class_Nat_Osemiring__char__0(tc_nat),
c_0_1534,
[final] ).
cnf(c_0_1922,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_1535,
[final] ).
cnf(c_0_1923,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_1536,
[final] ).
cnf(c_0_1924,plain,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_1537,
[final] ).
cnf(c_0_1925,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_1538,
[final] ).
cnf(c_0_1926,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_1539,
[final] ).
cnf(c_0_1927,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_1540,
[final] ).
cnf(c_0_1928,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_1541,
[final] ).
cnf(c_0_1929,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_1542,
[final] ).
cnf(c_0_1930,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_1543,
[final] ).
cnf(c_0_1931,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_1544,
[final] ).
cnf(c_0_1932,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_1545,
[final] ).
cnf(c_0_1933,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_1546,
[final] ).
cnf(c_0_1934,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_1547,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1548_0,axiom,
( c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1548]) ).
cnf(c_0_1548_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1548]) ).
cnf(c_0_1548_2,axiom,
( ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1548]) ).
cnf(c_0_1548_3,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1548]) ).
cnf(c_0_1549_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1549]) ).
cnf(c_0_1549_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1549]) ).
cnf(c_0_1550_0,axiom,
( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1550_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1550_2,axiom,
( ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1550_3,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1550]) ).
cnf(c_0_1551_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X4,X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1551_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X4,X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1551_2,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X4,X2)))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1551_3,axiom,
( ~ c_Type_Otyping(X1,X4,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1551]) ).
cnf(c_0_1552_0,axiom,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1552]) ).
cnf(c_0_1552_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1552]) ).
cnf(c_0_1553_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1553]) ).
cnf(c_0_1553_1,axiom,
( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB)
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1553]) ).
cnf(c_0_1554_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1554]) ).
cnf(c_0_1554_1,axiom,
( ~ 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_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1554]) ).
cnf(c_0_1555_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1555]) ).
cnf(c_0_1555_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1555]) ).
cnf(c_0_1556_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,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)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1556]) ).
cnf(c_0_1556_1,axiom,
( ~ 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)))
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_1556]) ).
cnf(c_0_1556_2,axiom,
( ~ 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)))
| 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))) ),
inference(literals_permutation,[status(thm)],[c_0_1556]) ).
cnf(c_0_1557_0,axiom,
( X4 = X5
| ~ 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_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1557]) ).
cnf(c_0_1557_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1557]) ).
cnf(c_0_1557_2,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_1557]) ).
cnf(c_0_1558_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),X2,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) ),
inference(literals_permutation,[status(thm)],[c_0_1558]) ).
cnf(c_0_1558_1,axiom,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(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) ),
inference(literals_permutation,[status(thm)],[c_0_1558]) ).
cnf(c_0_1558_2,axiom,
( ~ 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)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_1558]) ).
cnf(c_0_1559_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(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1559]) ).
cnf(c_0_1559_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1559]) ).
cnf(c_0_1560_0,axiom,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1560_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)) ),
inference(literals_permutation,[status(thm)],[c_0_1560]) ).
cnf(c_0_1561_0,axiom,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1561_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)) ),
inference(literals_permutation,[status(thm)],[c_0_1561]) ).
cnf(c_0_1562_0,axiom,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X1,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1562_2,axiom,
( ~ c_Type_Otypings(X1,X5,X3)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_1562]) ).
cnf(c_0_1564_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1564_1,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1564]) ).
cnf(c_0_1565_0,axiom,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1565_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1565]) ).
cnf(c_0_1566_0,axiom,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1566_1,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,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1566]) ).
cnf(c_0_1567_0,axiom,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1567_1,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,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1567]) ).
cnf(c_0_1568_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1568_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1568]) ).
cnf(c_0_1569_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1569_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1569]) ).
cnf(c_0_1570_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1570_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1570]) ).
cnf(c_0_1571_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1571_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1571]) ).
cnf(c_0_1572_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) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1572_1,axiom,
( ~ class_OrderedGroup_Osemigroup__add(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_1572]) ).
cnf(c_0_1574_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1574_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1574]) ).
cnf(c_0_1575_0,axiom,
( 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)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1575_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(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)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1575]) ).
cnf(c_0_1576_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) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1576_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_1576]) ).
cnf(c_0_1579_0,axiom,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1579_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1579]) ).
cnf(c_0_1580_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) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1580_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_1580]) ).
cnf(c_0_1581_0,axiom,
( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1581_1,axiom,
( ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
| c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1581]) ).
cnf(c_0_1582_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) ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1582_1,axiom,
( 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)
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1582]) ).
cnf(c_0_1584_0,axiom,
( X1 = c_Lambda_OdB_OAbs(X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1584_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2)
| X1 = c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1584]) ).
cnf(c_0_1585_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) ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1585_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1585]) ).
cnf(c_0_1586_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) ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1586_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1586]) ).
cnf(c_0_1587_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1587_1,axiom,
( c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1587]) ).
cnf(c_0_1588_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1588_1,axiom,
( c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1588]) ).
cnf(c_0_1589_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1589_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1589]) ).
cnf(c_0_1590_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1590_1,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)) ),
inference(literals_permutation,[status(thm)],[c_0_1590]) ).
cnf(c_0_1592_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1592_1,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)) ),
inference(literals_permutation,[status(thm)],[c_0_1592]) ).
cnf(c_0_1593_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_2,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_4,axiom,
( ~ c_Type_Otyping(X2,X6,X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1593_5,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____
| ~ c_Type_Otyping(X2,X6,X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1593]) ).
cnf(c_0_1594_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_2,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_4,axiom,
( ~ c_Type_Otyping(X2,X6,X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1594_5,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____
| ~ c_Type_Otyping(X2,X6,X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1594]) ).
cnf(c_0_1599_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X4,X2)))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X4,X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_2,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X4,X2)))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1599_3,axiom,
( ~ c_Type_Otyping(X1,X4,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X4,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1599]) ).
cnf(c_0_1602_0,axiom,
( c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1602_2,axiom,
( ~ c_Type_Otyping(X1,X3,X6)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1602]) ).
cnf(c_0_1603_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ 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),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_1,axiom,
( ~ 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),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1603_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4))
| ~ 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),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1603]) ).
cnf(c_0_1604_0,axiom,
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1604_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1604]) ).
cnf(c_0_1605_0,axiom,
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1605_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1605]) ).
cnf(c_0_1606_0,axiom,
( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1606_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1606]) ).
cnf(c_0_1607_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1607_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1607]) ).
cnf(c_0_1608_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1608_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X3,tc_nat)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1608]) ).
cnf(c_0_1609_0,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1609_1,axiom,
( ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3)
| c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1609]) ).
cnf(c_0_1610_0,axiom,
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1610_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1610]) ).
cnf(c_0_1611_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1611_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1611]) ).
cnf(c_0_1612_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1612_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1612]) ).
cnf(c_0_1613_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1613_1,axiom,
( ~ 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),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1613]) ).
cnf(c_0_1614_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1614_1,axiom,
( ~ 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),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1614]) ).
cnf(c_0_1615_0,axiom,
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1615_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1)
| v_thesis____ ),
inference(literals_permutation,[status(thm)],[c_0_1615]) ).
cnf(c_0_1616_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1616_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1616]) ).
cnf(c_0_1617_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_1,axiom,
( ~ 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(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1617_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1617]) ).
cnf(c_0_1618_0,axiom,
( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1618_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1618]) ).
cnf(c_0_1619_0,axiom,
( c_Lambda_Osubst(c_Lambda_Osubst(X3,c_Lambda_Olift(X4,X1),c_Suc(X2)),c_Lambda_Osubst(X5,X4,X2),X1) = c_Lambda_Osubst(c_Lambda_Osubst(X3,X5,X1),X4,X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1619_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| c_Lambda_Osubst(c_Lambda_Osubst(X3,c_Lambda_Olift(X4,X1),c_Suc(X2)),c_Lambda_Osubst(X5,X4,X2),X1) = c_Lambda_Osubst(c_Lambda_Osubst(X3,X5,X1),X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1619]) ).
cnf(c_0_1620_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) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1620_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_1620]) ).
cnf(c_0_1621_0,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2))
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1621_1,axiom,
( ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3)
| c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1621]) ).
cnf(c_0_1622_0,axiom,
( hAPP(c_Type_Oshift(X3,X1,X4,X5),X2) = hAPP(X3,c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1622_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(c_Type_Oshift(X3,X1,X4,X5),X2) = hAPP(X3,c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1622]) ).
cnf(c_0_1624_0,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1624_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1624]) ).
cnf(c_0_1625_0,axiom,
( c_Lambda_Osubst(c_Lambda_Olift(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Olift(X4,X2),X1) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X1),X2)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1625_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| c_Lambda_Osubst(c_Lambda_Olift(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Olift(X4,X2),X1) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1625]) ).
cnf(c_0_1626_0,axiom,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1626_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1626]) ).
cnf(c_0_1627_0,axiom,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1627_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1627]) ).
cnf(c_0_1628_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1628_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1628]) ).
cnf(c_0_1629_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1629_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1629]) ).
cnf(c_0_1631_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1631]) ).
cnf(c_0_1631_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1631]) ).
cnf(c_0_1631_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1631]) ).
cnf(c_0_1632_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1632_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1632_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1632]) ).
cnf(c_0_1633_0,axiom,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1633_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1633]) ).
cnf(c_0_1636_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1636_1,axiom,
( c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1636]) ).
cnf(c_0_1637_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1637_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1637]) ).
cnf(c_0_1638_0,axiom,
( c_Lambda_Osubst(c_Lambda_Olift(X3,X1),c_Lambda_Olift(X4,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X2),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1638_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| c_Lambda_Osubst(c_Lambda_Olift(X3,X1),c_Lambda_Olift(X4,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1638]) ).
cnf(c_0_1639_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) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1639_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_1639]) ).
cnf(c_0_1641_0,axiom,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_1,axiom,
( ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1641_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)))
| hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_1641]) ).
cnf(c_0_1643_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1643_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)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1643_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ 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)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1643]) ).
cnf(c_0_1644_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1644_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)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1644_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ 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)
| c_HOL_Oord__class_Oless(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1644]) ).
cnf(c_0_1645_0,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1645_1,axiom,
( ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3)
| hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1645]) ).
cnf(c_0_1646_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)) ),
inference(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1646_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1646]) ).
cnf(c_0_1647_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1647_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1647_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1647_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1647]) ).
cnf(c_0_1648_0,axiom,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1648]) ).
cnf(c_0_1648_1,axiom,
( ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1648]) ).
cnf(c_0_1648_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2))
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1648]) ).
cnf(c_0_1649_0,axiom,
( c_Wellfounded_Oaccp(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1649_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| c_Wellfounded_Oaccp(X1,X3,X2)
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1649_2,axiom,
( ~ c_Wellfounded_Oaccp(X1,X4,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| c_Wellfounded_Oaccp(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1649]) ).
cnf(c_0_1650_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1650_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1650_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1650]) ).
cnf(c_0_1652_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1652_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1652]) ).
cnf(c_0_1653_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) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1653_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_1653]) ).
cnf(c_0_1654_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) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1654_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_1654]) ).
cnf(c_0_1655_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) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1655_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_1655]) ).
cnf(c_0_1656_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) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1656_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_1656]) ).
cnf(c_0_1657_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) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1657_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| 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)) ),
inference(literals_permutation,[status(thm)],[c_0_1657]) ).
cnf(c_0_1658_0,axiom,
( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
| ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
| ~ c_Type_Otyping(X1,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1658_2,axiom,
( ~ c_Type_Otyping(X1,X5,X3)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_1658]) ).
cnf(c_0_1659_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1659_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1659_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1659]) ).
cnf(c_0_1662_0,axiom,
( c_Type_Otyping(X3,X2,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ c_Type_Otyping(X3,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1662_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1662_2,axiom,
( ~ c_Type_Otyping(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| c_Type_Otyping(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1662]) ).
cnf(c_0_1663_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1663_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1663]) ).
cnf(c_0_1666_0,axiom,
( 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),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1666_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1666]) ).
cnf(c_0_1667_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1667_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1667]) ).
cnf(c_0_1669_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1669_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1669_2,axiom,
( ~ 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)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1669_3,axiom,
( ~ 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)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1669]) ).
cnf(c_0_1670_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1670_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1670_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1670_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1670]) ).
cnf(c_0_1671_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1671_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1671]) ).
cnf(c_0_1672_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1672_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1672_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1672]) ).
cnf(c_0_1673_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1673_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1673]) ).
cnf(c_0_1674_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1674_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1674]) ).
cnf(c_0_1675_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1675_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1675]) ).
cnf(c_0_1676_0,axiom,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1676_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1676]) ).
cnf(c_0_1677_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1677_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1677]) ).
cnf(c_0_1678_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1678_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1678]) ).
cnf(c_0_1680_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1680_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1680]) ).
cnf(c_0_1681_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1681_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1681_2,axiom,
( ~ 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)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1681]) ).
cnf(c_0_1682_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1682_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1682_2,axiom,
( ~ 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)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1682]) ).
cnf(c_0_1683_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1683_2,axiom,
( ~ 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)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1683]) ).
cnf(c_0_1684_0,axiom,
( c_Lambda_Olift(c_Lambda_Olift(X3,X1),c_Suc(X2)) = c_Lambda_Olift(c_Lambda_Olift(X3,X2),X1)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1684_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| c_Lambda_Olift(c_Lambda_Olift(X3,X1),c_Suc(X2)) = c_Lambda_Olift(c_Lambda_Olift(X3,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1684]) ).
cnf(c_0_1685_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_2,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1685_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1685]) ).
cnf(c_0_1686_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_2,axiom,
( c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1686_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1686]) ).
cnf(c_0_1687_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1687_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1687]) ).
cnf(c_0_1688_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1688_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1688]) ).
cnf(c_0_1689_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) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1689_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1689]) ).
cnf(c_0_1690_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) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1690_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1690]) ).
cnf(c_0_1691_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_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1691_1,axiom,
( ~ 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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1691]) ).
cnf(c_0_1692_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1692_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1692]) ).
cnf(c_0_1694_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1694_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1694]) ).
cnf(c_0_1695_0,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1695_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1695]) ).
cnf(c_0_1699_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_1,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1700_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1700_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1701_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1703_0,axiom,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_1,axiom,
( ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1704_0,axiom,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_1,axiom,
( ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1705_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1705_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1705_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1706_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1707_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1708_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) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1708_1,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)) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1709_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1710_0,axiom,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4))
| ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1711_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1712_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1712_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1713_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1713_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1714_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1716_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3)
| ~ class_Ring__and__Field_Osemiring__1(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1717_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1721_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)) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1721_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1722_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1722_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1723_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1723_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1724_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1725_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1726_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)) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1726_1,axiom,
( ~ 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(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1727_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1728_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1728_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1729_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1730_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1731_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1732_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1735_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1737_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1738_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1739_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1740_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1740_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1742_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_2,axiom,
( ~ 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)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1743_0,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1744_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)) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1744_1,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) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1745_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1745]) ).
cnf(c_0_1745_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1745]) ).
cnf(c_0_1745_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1745]) ).
cnf(c_0_1745_3,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1745]) ).
cnf(c_0_1748_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ 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) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1749_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1750_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1750_1,axiom,
( c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1750_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X4)
| c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1751_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1751_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1751_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1752_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1752_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1752_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1753_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1753_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1753_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1754_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1754_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1754_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1755_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1755_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1755_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1756_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1756_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1757_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1757_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1757_2,axiom,
( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1758_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1758_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1759_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_1,axiom,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1760_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1761_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1762_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_2,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1763_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1763_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1764_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1764_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1768_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1768_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1770_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1770_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1771_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1772_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1773_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1774_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1774_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1774_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1775_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1775]) ).
cnf(c_0_1775_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1775]) ).
cnf(c_0_1776_0,axiom,
( c_Suc(X1) = X2
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1776_1,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1776_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1777_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1777_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1778_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1778_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1779_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1779]) ).
cnf(c_0_1779_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1779]) ).
cnf(c_0_1780_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1780_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1785_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1786_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1788_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1789_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_2,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1790_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_2,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1791_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1792_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1793_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_2,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1794_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1795_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_1,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1796_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_1,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1797_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_1,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1798_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_1,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1800_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2)
| ~ class_Ring__and__Field_Osemiring__1(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1800_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1801_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1801_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1802_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1802_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1803_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1804_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1804_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1805_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) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1805_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1806_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) ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1806_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1807_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) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1807_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1808_0,axiom,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1808]) ).
cnf(c_0_1808_1,axiom,
( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1808]) ).
cnf(c_0_1810_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1810_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1810_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1811_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1812_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1812_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1812_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1812_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1813_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) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1813_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1814_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1814_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1816_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_2,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1817_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1818_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1818_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1818_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1819_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1819_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1819_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1820_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1820_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1820_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1821_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1821_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1821_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1822_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1823_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1823_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1823_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1824_0,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_1,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1825_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_1,axiom,
( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1827_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1828_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1829_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1831_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1832_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1832_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1832_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1838_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1839_0,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) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| 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) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1844_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1845_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1846_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1847_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1848_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1849_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1850_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1851_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) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1851_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1852_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1852_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1853_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1853_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1854_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) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1857_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1857_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1859_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) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1860_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1860_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1861_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1861_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1862_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1863_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1864_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1864_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1875_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1875_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1884_0,axiom,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_1,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| X1 = X2
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_2,axiom,
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1892_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1893_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1893_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1894_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X1)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1895_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) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X1)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1900_0,axiom,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1900_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1901_0,axiom,
( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1902_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1903_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1903_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1904_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1905_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1573_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),
inference(literals_permutation,[status(thm)],[c_0_1573]) ).
cnf(c_0_1583_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),
inference(literals_permutation,[status(thm)],[c_0_1583]) ).
cnf(c_0_1660_0,axiom,
~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
inference(literals_permutation,[status(thm)],[c_0_1660]) ).
cnf(c_0_1661_0,axiom,
~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
inference(literals_permutation,[status(thm)],[c_0_1661]) ).
cnf(c_0_1733_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1734_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1767_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1826_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1833_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1834_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1836_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1837_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1866_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1867_0,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1868_0,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1869_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1906_0,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1907_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1909_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1910_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1911_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1912_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1914_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1915_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1563_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(literals_permutation,[status(thm)],[c_0_1563]) ).
cnf(c_0_1577_0,axiom,
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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(literals_permutation,[status(thm)],[c_0_1577]) ).
cnf(c_0_1578_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
inference(literals_permutation,[status(thm)],[c_0_1578]) ).
cnf(c_0_1591_0,axiom,
c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4) = c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),
inference(literals_permutation,[status(thm)],[c_0_1591]) ).
cnf(c_0_1595_0,axiom,
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) = hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),
inference(literals_permutation,[status(thm)],[c_0_1595]) ).
cnf(c_0_1596_0,axiom,
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) = c_Lambda_OdB_OVar(X1),
inference(literals_permutation,[status(thm)],[c_0_1596]) ).
cnf(c_0_1597_0,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),
inference(literals_permutation,[status(thm)],[c_0_1597]) ).
cnf(c_0_1598_0,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),
inference(literals_permutation,[status(thm)],[c_0_1598]) ).
cnf(c_0_1600_0,axiom,
c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
inference(literals_permutation,[status(thm)],[c_0_1600]) ).
cnf(c_0_1601_0,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
inference(literals_permutation,[status(thm)],[c_0_1601]) ).
cnf(c_0_1623_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)))),
inference(literals_permutation,[status(thm)],[c_0_1623]) ).
cnf(c_0_1630_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_OAbs(v_r____)),v_a____),v_Ua____),
inference(literals_permutation,[status(thm)],[c_0_1630]) ).
cnf(c_0_1634_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),tc_Lambda_OdB),
inference(literals_permutation,[status(thm)],[c_0_1634]) ).
cnf(c_0_1635_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype),
inference(literals_permutation,[status(thm)],[c_0_1635]) ).
cnf(c_0_1640_0,axiom,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
inference(literals_permutation,[status(thm)],[c_0_1640]) ).
cnf(c_0_1642_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)) = c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4),
inference(literals_permutation,[status(thm)],[c_0_1642]) ).
cnf(c_0_1651_0,axiom,
c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))) = c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_1651]) ).
cnf(c_0_1664_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_1664]) ).
cnf(c_0_1665_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)),
inference(literals_permutation,[status(thm)],[c_0_1665]) ).
cnf(c_0_1668_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
inference(literals_permutation,[status(thm)],[c_0_1668]) ).
cnf(c_0_1679_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1679]) ).
cnf(c_0_1693_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1693]) ).
cnf(c_0_1696_0,axiom,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1697_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1698_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1702_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1715_0,axiom,
c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))) = c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X2),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1718_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1719_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1720_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1736_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1741_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)) = c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1746_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1747_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1765_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1766_0,axiom,
c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1769_0,axiom,
c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1781_0,axiom,
c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1782_0,axiom,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1783_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1784_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1787_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1799_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1809_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1815_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1830_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1835_0,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1840_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(X1,X2),X3,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1841_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1842_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1843_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1855_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1856_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1858_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1865_0,axiom,
c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1870_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1871_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1872_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1873_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1874_0,axiom,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1876_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1877_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1878_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1879_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1880_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1881_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1) = c_Suc(X1),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1882_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1883_0,axiom,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1885_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1886_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = c_Suc(X1),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1887_0,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1888_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1889_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1890_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1891_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1896_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1897_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1898_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(literals_permutation,[status(thm)],[c_0_1898]) ).
cnf(c_0_1899_0,axiom,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1908_0,axiom,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1913_0,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1916_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1917_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1918_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1919_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1920_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1921_0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1922_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1923_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1924_0,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1925_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1926_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1927_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1928_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1929_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1930_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1931_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1932_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1933_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1934_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
! [X1] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1) ),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_1_002,negated_conjecture,
~ v_thesis____,
file('<stdin>',cls_conjecture_0) ).
fof(c_0_2_003,negated_conjecture,
! [X1] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_3_004,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_4_005,negated_conjecture,
! [X2] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X2) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2])])]) ).
fof(c_0_5_006,negated_conjecture,
~ v_thesis____,
c_0_3 ).
cnf(c_0_6_007,negated_conjecture,
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7_008,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8_009,negated_conjecture,
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X1) ),
c_0_6,
[final] ).
cnf(c_0_9_010,negated_conjecture,
~ v_thesis____,
c_0_7,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_640,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
| v_thesis____ ),
file('/export/starexec/sandbox/tmp/iprover_modulo_da4f08.p',c_0_1615_0) ).
cnf(c_1685,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
| v_thesis____ ),
inference(copy,[status(esa)],[c_640]) ).
cnf(c_57822,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(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____))
| v_thesis____ ),
inference(instantiation,[status(thm)],[c_1685]) ).
cnf(c_632,plain,
( c_Type_Otyping(X0,X1,c_Type_Osko__Type__Xtyping__elims__2__1(X2,X0,X3,X1))
| ~ c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1),X2) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_da4f08.p',c_0_1618_1) ).
cnf(c_1677,plain,
( c_Type_Otyping(X0,X1,c_Type_Osko__Type__Xtyping__elims__2__1(X2,X0,X3,X1))
| ~ c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1),X2) ),
inference(copy,[status(esa)],[c_632]) ).
cnf(c_23394,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____)
| 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(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)) ),
inference(instantiation,[status(thm)],[c_1677]) ).
cnf(c_88,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____),
file('/export/starexec/sandbox/tmp/iprover_modulo_da4f08.p',c_0_1630_0) ).
cnf(c_774,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/tmp/iprover_modulo_da4f08.p',c_0_9) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_57822,c_23394,c_88,c_774]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL839-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : iprover_modulo %s %d
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 3 10:48:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running in mono-core mode
% 0.21/0.47 % Orienting using strategy Equiv(ClausalAll)
% 0.21/0.47 % Orientation found
% 0.21/0.47 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_509f88.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_da4f08.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_beba14 | grep -v "SZS"
% 0.21/0.50
% 0.21/0.50 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.21/0.50
% 0.21/0.50 %
% 0.21/0.50 % ------ iProver source info
% 0.21/0.50
% 0.21/0.50 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.21/0.50 % git: non_committed_changes: true
% 0.21/0.50 % git: last_make_outside_of_git: true
% 0.21/0.50
% 0.21/0.50 %
% 0.21/0.50 % ------ Input Options
% 0.21/0.50
% 0.21/0.50 % --out_options all
% 0.21/0.50 % --tptp_safe_out true
% 0.21/0.50 % --problem_path ""
% 0.21/0.50 % --include_path ""
% 0.21/0.50 % --clausifier .//eprover
% 0.21/0.50 % --clausifier_options --tstp-format
% 0.21/0.50 % --stdin false
% 0.21/0.50 % --dbg_backtrace false
% 0.21/0.50 % --dbg_dump_prop_clauses false
% 0.21/0.50 % --dbg_dump_prop_clauses_file -
% 0.21/0.50 % --dbg_out_stat false
% 0.21/0.50
% 0.21/0.50 % ------ General Options
% 0.21/0.50
% 0.21/0.50 % --fof false
% 0.21/0.50 % --time_out_real 150.
% 0.21/0.50 % --time_out_prep_mult 0.2
% 0.21/0.50 % --time_out_virtual -1.
% 0.21/0.50 % --schedule none
% 0.21/0.50 % --ground_splitting input
% 0.21/0.50 % --splitting_nvd 16
% 0.21/0.50 % --non_eq_to_eq false
% 0.21/0.50 % --prep_gs_sim true
% 0.21/0.50 % --prep_unflatten false
% 0.21/0.50 % --prep_res_sim true
% 0.21/0.50 % --prep_upred true
% 0.21/0.50 % --res_sim_input true
% 0.21/0.50 % --clause_weak_htbl true
% 0.21/0.50 % --gc_record_bc_elim false
% 0.21/0.50 % --symbol_type_check false
% 0.21/0.50 % --clausify_out false
% 0.21/0.50 % --large_theory_mode false
% 0.21/0.50 % --prep_sem_filter none
% 0.21/0.50 % --prep_sem_filter_out false
% 0.21/0.50 % --preprocessed_out false
% 0.21/0.50 % --sub_typing false
% 0.21/0.50 % --brand_transform false
% 0.21/0.50 % --pure_diseq_elim true
% 0.21/0.50 % --min_unsat_core false
% 0.21/0.50 % --pred_elim true
% 0.21/0.50 % --add_important_lit false
% 0.21/0.50 % --soft_assumptions false
% 0.21/0.50 % --reset_solvers false
% 0.21/0.50 % --bc_imp_inh []
% 0.21/0.50 % --conj_cone_tolerance 1.5
% 0.21/0.50 % --prolific_symb_bound 500
% 0.21/0.50 % --lt_threshold 2000
% 0.21/0.50
% 0.21/0.50 % ------ SAT Options
% 0.21/0.50
% 0.21/0.50 % --sat_mode false
% 0.21/0.50 % --sat_fm_restart_options ""
% 0.21/0.50 % --sat_gr_def false
% 0.21/0.50 % --sat_epr_types true
% 0.21/0.50 % --sat_non_cyclic_types false
% 0.21/0.50 % --sat_finite_models false
% 0.21/0.50 % --sat_fm_lemmas false
% 0.21/0.50 % --sat_fm_prep false
% 0.21/0.50 % --sat_fm_uc_incr true
% 0.21/0.50 % --sat_out_model small
% 0.21/0.50 % --sat_out_clauses false
% 0.21/0.50
% 0.21/0.50 % ------ QBF Options
% 0.21/0.50
% 0.21/0.50 % --qbf_mode false
% 0.21/0.50 % --qbf_elim_univ true
% 0.21/0.50 % --qbf_sk_in true
% 0.21/0.50 % --qbf_pred_elim true
% 0.21/0.50 % --qbf_split 32
% 0.21/0.50
% 0.21/0.50 % ------ BMC1 Options
% 0.21/0.50
% 0.21/0.50 % --bmc1_incremental false
% 0.21/0.50 % --bmc1_axioms reachable_all
% 0.21/0.50 % --bmc1_min_bound 0
% 0.21/0.50 % --bmc1_max_bound -1
% 0.21/0.50 % --bmc1_max_bound_default -1
% 0.21/0.50 % --bmc1_symbol_reachability true
% 0.21/0.50 % --bmc1_property_lemmas false
% 0.21/0.50 % --bmc1_k_induction false
% 0.21/0.50 % --bmc1_non_equiv_states false
% 0.21/0.50 % --bmc1_deadlock false
% 0.21/0.50 % --bmc1_ucm false
% 0.21/0.50 % --bmc1_add_unsat_core none
% 0.21/0.50 % --bmc1_unsat_core_children false
% 0.21/0.50 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.50 % --bmc1_out_stat full
% 0.21/0.50 % --bmc1_ground_init false
% 0.21/0.50 % --bmc1_pre_inst_next_state false
% 0.21/0.50 % --bmc1_pre_inst_state false
% 0.21/0.50 % --bmc1_pre_inst_reach_state false
% 0.21/0.50 % --bmc1_out_unsat_core false
% 0.21/0.50 % --bmc1_aig_witness_out false
% 0.21/0.50 % --bmc1_verbose false
% 0.21/0.50 % --bmc1_dump_clauses_tptp false
% 150.35/150.57 % --bmc1_dump_unsat_core_tptp false
% 150.35/150.57 % --bmc1_dump_file -
% 150.35/150.57 % --bmc1_ucm_expand_uc_limit 128
% 150.35/150.57 % --bmc1_ucm_n_expand_iterations 6
% 150.35/150.57 % --bmc1_ucm_extend_mode 1
% 150.35/150.57 % --bmc1_ucm_init_mode 2
% 150.35/150.57 % --bmc1_ucm_cone_mode none
% 150.35/150.57 % --bmc1_ucm_reduced_relation_type 0
% 150.35/150.57 % --bmc1_ucm_relax_model 4
% 150.35/150.57 % --bmc1_ucm_full_tr_after_sat true
% 150.35/150.57 % --bmc1_ucm_expand_neg_assumptions false
% 150.35/150.57 % --bmc1_ucm_layered_model none
% 150.35/150.57 % --bmc1_ucm_max_lemma_size 10
% 150.35/150.57
% 150.35/150.57 % ------ AIG Options
% 150.35/150.57
% 150.35/150.57 % --aig_mode false
% 150.35/150.57
% 150.35/150.57 % ------ Instantiation Options
% 150.35/150.57
% 150.35/150.57 % --instantiation_flag true
% 150.35/150.57 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.35/150.57 % --inst_solver_per_active 750
% 150.35/150.57 % --inst_solver_calls_frac 0.5
% 150.35/150.57 % --inst_passive_queue_type priority_queues
% 150.35/150.57 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.35/150.57 % --inst_passive_queues_freq [25;2]
% 150.35/150.57 % --inst_dismatching true
% 150.35/150.57 % --inst_eager_unprocessed_to_passive true
% 150.35/150.57 % --inst_prop_sim_given true
% 150.35/150.57 % --inst_prop_sim_new false
% 150.35/150.57 % --inst_orphan_elimination true
% 150.35/150.57 % --inst_learning_loop_flag true
% 150.35/150.57 % --inst_learning_start 3000
% 150.35/150.57 % --inst_learning_factor 2
% 150.35/150.57 % --inst_start_prop_sim_after_learn 3
% 150.35/150.57 % --inst_sel_renew solver
% 150.35/150.57 % --inst_lit_activity_flag true
% 150.35/150.57 % --inst_out_proof true
% 150.35/150.57
% 150.35/150.57 % ------ Resolution Options
% 150.35/150.57
% 150.35/150.57 % --resolution_flag true
% 150.35/150.57 % --res_lit_sel kbo_max
% 150.35/150.57 % --res_to_prop_solver none
% 150.35/150.57 % --res_prop_simpl_new false
% 150.35/150.57 % --res_prop_simpl_given false
% 150.35/150.57 % --res_passive_queue_type priority_queues
% 150.35/150.57 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.35/150.57 % --res_passive_queues_freq [15;5]
% 150.35/150.57 % --res_forward_subs full
% 150.35/150.57 % --res_backward_subs full
% 150.35/150.57 % --res_forward_subs_resolution true
% 150.35/150.57 % --res_backward_subs_resolution true
% 150.35/150.57 % --res_orphan_elimination false
% 150.35/150.57 % --res_time_limit 1000.
% 150.35/150.57 % --res_out_proof true
% 150.35/150.57 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_509f88.s
% 150.35/150.57 % --modulo true
% 150.35/150.57
% 150.35/150.57 % ------ Combination Options
% 150.35/150.57
% 150.35/150.57 % --comb_res_mult 1000
% 150.35/150.57 % --comb_inst_mult 300
% 150.35/150.57 % ------
% 150.35/150.57
% 150.35/150.57 % ------ Parsing...% successful
% 150.35/150.57
% 150.35/150.57 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 150.35/150.57
% 150.35/150.57 % ------ Proving...
% 150.35/150.57 % ------ Problem Properties
% 150.35/150.57
% 150.35/150.57 %
% 150.35/150.57 % EPR false
% 150.35/150.57 % Horn false
% 150.35/150.57 % Has equality true
% 150.35/150.57
% 150.35/150.57 % % ------ Input Options Time Limit: Unbounded
% 150.35/150.57
% 150.35/150.57
% 150.35/150.57 % warning: Clause {~(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0));v_thesis____} has no selected literals
% 150.35/150.57 cnf(c_773,negated_conjecture,
% 150.35/150.57 ( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
% 150.35/150.57 | v_thesis____ ),
% 150.35/150.57 file('/export/starexec/sandbox/tmp/iprover_modulo_da4f08.p', c_0_8) ).
% 150.35/150.57
% 150.35/150.57 % warning: Clause {~(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0));v_thesis____} has no selected literals
% 150.35/150.57 cnf(c_773,negated_conjecture,
% 150.35/150.57 ( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
% 150.35/150.57 | v_thesis____ ),
% 150.35/150.57 file('/export/starexec/sandbox/tmp/iprover_modulo_da4f08.p', c_0_8) ).
% 150.35/150.57
% 150.35/150.57 Compiling...
% 150.35/150.57 Loading plugin: done.
% 150.35/150.57 %
% 150.35/150.57
% 150.35/150.57
% 150.35/150.57 % Time Out Real
% 150.35/150.57
% 150.35/150.57 % ------ Statistics
% 150.35/150.57
% 150.35/150.57 % ------ General
% 150.35/150.57
% 150.35/150.57 % num_of_input_clauses: 775
% 150.35/150.57 % num_of_input_neg_conjectures: 2
% 150.35/150.57 % num_of_splits: 0
% 150.35/150.57 % num_of_split_atoms: 0
% 150.35/150.57 % num_of_sem_filtered_clauses: 0
% 150.35/150.57 % num_of_subtypes: 0
% 150.35/150.57 % monotx_restored_types: 0
% 150.35/150.57 % sat_num_of_epr_types: 0
% 150.35/150.57 % sat_num_of_non_cyclic_types: 0
% 150.35/150.57 % sat_guarded_non_collapsed_types: 0
% 150.35/150.57 % is_epr: 0
% 150.35/150.57 % is_horn: 0
% 150.35/150.57 % has_eq: 1
% 150.35/150.57 % num_pure_diseq_elim: 0
% 150.35/150.57 % simp_replaced_by: 0
% 150.35/150.57 % res_preprocessed: 2
% 150.35/150.57 % prep_upred: 0
% 150.35/150.57 % prep_unflattend: 0
% 150.35/150.57 % pred_elim_cands: 0
% 150.35/150.57 % pred_elim: 0
% 150.35/150.57 % pred_elim_cl: 0
% 150.35/150.57 % pred_elim_cycles: 0
% 150.35/150.57 % forced_gc_time: 0
% 150.35/150.57 % gc_basic_clause_elim: 0
% 150.35/150.57 % parsing_time: 0.045
% 150.35/150.57 % sem_filter_time: 0.
% 150.35/150.57 % pred_elim_time: 0.
% 150.35/150.57 % out_proof_time: 0.
% 150.35/150.57 % monotx_time: 0.
% 150.35/150.57 % subtype_inf_time: 0.
% 150.35/150.57 % unif_index_cands_time: 0.
% 150.35/150.57 % unif_index_add_time: 0.
% 150.35/150.57 % total_time: 150.088
% 150.35/150.57 % num_of_symbols: 110
% 150.35/150.57 % num_of_terms: 3033
% 150.35/150.57
% 150.35/150.57 % ------ Propositional Solver
% 150.35/150.57
% 150.35/150.57 % prop_solver_calls: 1
% 150.35/150.57 % prop_fast_solver_calls: 3
% 150.35/150.57 % prop_num_of_clauses: 731
% 150.35/150.57 % prop_preprocess_simplified: 2307
% 150.35/150.57 % prop_fo_subsumed: 0
% 150.35/150.57 % prop_solver_time: 0.
% 150.35/150.57 % prop_fast_solver_time: 0.
% 150.35/150.57 % prop_unsat_core_time: 0.
% 150.35/150.57
% 150.35/150.57 % ------ QBF
% 150.35/150.57
% 150.35/150.57 % qbf_q_res: 0
% 150.35/150.57 % qbf_num_tautologies: 0
% 150.35/150.57 % qbf_prep_cycles: 0
% 150.35/150.57
% 150.35/150.57 % ------ BMC1
% 150.35/150.57
% 150.35/150.57 % bmc1_current_bound: -1
% 150.35/150.57 % bmc1_last_solved_bound: -1
% 150.35/150.57 % bmc1_unsat_core_size: -1
% 150.35/150.57 % bmc1_unsat_core_parents_size: -1
% 150.35/150.57 % bmc1_merge_next_fun: 0
% 150.35/150.57 % bmc1_unsat_core_clauses_time: 0.
% 150.35/150.57
% 150.35/150.57 % ------ Instantiation
% 150.35/150.57
% 150.35/150.57 % inst_num_of_clauses: 699
% 150.35/150.57 % inst_num_in_passive: 0
% 150.35/150.57 % inst_num_in_active: 0
% 150.35/150.57 % inst_num_in_unprocessed: 776
% 150.35/150.57 % inst_num_of_loops: 0
% 150.35/150.57 % inst_num_of_learning_restarts: 0
% 150.35/150.57 % inst_num_moves_active_passive: 0
% 150.35/150.57 % inst_lit_activity: 0
% 150.35/150.57 % inst_lit_activity_moves: 0
% 150.35/150.57 % inst_num_tautologies: 0
% 150.35/150.57 % inst_num_prop_implied: 0
% 150.35/150.57 % inst_num_existing_simplified: 0
% 150.35/150.57 % inst_num_eq_res_simplified: 0
% 150.35/150.57 % inst_num_child_elim: 0
% 150.35/150.57 % inst_num_of_dismatching_blockings: 0
% 150.35/150.57 % inst_num_of_non_proper_insts: 0
% 150.35/150.57 % inst_num_of_duplicates: 0
% 150.35/150.57 % inst_inst_num_from_inst_to_res: 0
% 150.35/150.57 % inst_dismatching_checking_time: 0.
% 150.35/150.57
% 150.35/150.57 % ------ Resolution
% 150.35/150.57
% 150.35/150.57 % res_num_of_clauses: 641
% 150.35/150.57 % res_num_in_passive: 0
% 150.35/150.57 % res_num_in_active: 268
% 150.35/150.57 % res_num_of_loops: 0
% 150.35/150.57 % res_forward_subset_subsumed: 381
% 150.35/150.57 % res_backward_subset_subsumed: 0
% 150.35/150.57 % res_forward_subsumed: 0
% 150.35/150.57 % res_backward_subsumed: 0
% 150.35/150.57 % res_forward_subsumption_resolution: 0
% 150.35/150.57 % res_backward_subsumption_resolution: 0
% 150.35/150.57 % res_clause_to_clause_subsumption: 0
% 150.35/150.57 % res_orphan_elimination: 0
% 150.35/150.57 % res_tautology_del: 0
% 150.35/150.57 % res_num_eq_res_simplified: 0
% 150.35/150.57 % res_num_sel_changes: 0
% 150.35/150.57 % res_moves_from_active_to_pass: 0
% 150.35/150.57
% 150.35/150.57 % Status Unknown
% 150.43/150.67 % Orienting using strategy ClausalAll
% 150.43/150.67 % Orientation found
% 150.43/150.67 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_509f88.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_da4f08.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_a30628 | grep -v "SZS"
% 150.43/150.69
% 150.43/150.69 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.43/150.69
% 150.43/150.69 %
% 150.43/150.69 % ------ iProver source info
% 150.43/150.69
% 150.43/150.69 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.43/150.69 % git: non_committed_changes: true
% 150.43/150.69 % git: last_make_outside_of_git: true
% 150.43/150.69
% 150.43/150.69 %
% 150.43/150.69 % ------ Input Options
% 150.43/150.69
% 150.43/150.69 % --out_options all
% 150.43/150.69 % --tptp_safe_out true
% 150.43/150.69 % --problem_path ""
% 150.43/150.69 % --include_path ""
% 150.43/150.69 % --clausifier .//eprover
% 150.43/150.69 % --clausifier_options --tstp-format
% 150.43/150.69 % --stdin false
% 150.43/150.69 % --dbg_backtrace false
% 150.43/150.69 % --dbg_dump_prop_clauses false
% 150.43/150.69 % --dbg_dump_prop_clauses_file -
% 150.43/150.69 % --dbg_out_stat false
% 150.43/150.69
% 150.43/150.69 % ------ General Options
% 150.43/150.69
% 150.43/150.69 % --fof false
% 150.43/150.69 % --time_out_real 150.
% 150.43/150.69 % --time_out_prep_mult 0.2
% 150.43/150.69 % --time_out_virtual -1.
% 150.43/150.69 % --schedule none
% 150.43/150.69 % --ground_splitting input
% 150.43/150.69 % --splitting_nvd 16
% 150.43/150.69 % --non_eq_to_eq false
% 150.43/150.69 % --prep_gs_sim true
% 150.43/150.69 % --prep_unflatten false
% 150.43/150.69 % --prep_res_sim true
% 150.43/150.69 % --prep_upred true
% 150.43/150.69 % --res_sim_input true
% 150.43/150.69 % --clause_weak_htbl true
% 150.43/150.69 % --gc_record_bc_elim false
% 150.43/150.69 % --symbol_type_check false
% 150.43/150.69 % --clausify_out false
% 150.43/150.69 % --large_theory_mode false
% 150.43/150.69 % --prep_sem_filter none
% 150.43/150.69 % --prep_sem_filter_out false
% 150.43/150.69 % --preprocessed_out false
% 150.43/150.69 % --sub_typing false
% 150.43/150.69 % --brand_transform false
% 150.43/150.69 % --pure_diseq_elim true
% 150.43/150.69 % --min_unsat_core false
% 150.43/150.69 % --pred_elim true
% 150.43/150.69 % --add_important_lit false
% 150.43/150.69 % --soft_assumptions false
% 150.43/150.69 % --reset_solvers false
% 150.43/150.69 % --bc_imp_inh []
% 150.43/150.69 % --conj_cone_tolerance 1.5
% 150.43/150.69 % --prolific_symb_bound 500
% 150.43/150.69 % --lt_threshold 2000
% 150.43/150.69
% 150.43/150.69 % ------ SAT Options
% 150.43/150.69
% 150.43/150.69 % --sat_mode false
% 150.43/150.69 % --sat_fm_restart_options ""
% 150.43/150.69 % --sat_gr_def false
% 150.43/150.69 % --sat_epr_types true
% 150.43/150.69 % --sat_non_cyclic_types false
% 150.43/150.69 % --sat_finite_models false
% 150.43/150.69 % --sat_fm_lemmas false
% 150.43/150.69 % --sat_fm_prep false
% 150.43/150.69 % --sat_fm_uc_incr true
% 150.43/150.69 % --sat_out_model small
% 150.43/150.69 % --sat_out_clauses false
% 150.43/150.69
% 150.43/150.69 % ------ QBF Options
% 150.43/150.69
% 150.43/150.69 % --qbf_mode false
% 150.43/150.69 % --qbf_elim_univ true
% 150.43/150.69 % --qbf_sk_in true
% 150.43/150.69 % --qbf_pred_elim true
% 150.43/150.69 % --qbf_split 32
% 150.43/150.69
% 150.43/150.69 % ------ BMC1 Options
% 150.43/150.69
% 150.43/150.69 % --bmc1_incremental false
% 150.43/150.69 % --bmc1_axioms reachable_all
% 150.43/150.69 % --bmc1_min_bound 0
% 150.43/150.69 % --bmc1_max_bound -1
% 150.43/150.69 % --bmc1_max_bound_default -1
% 150.43/150.69 % --bmc1_symbol_reachability true
% 150.43/150.69 % --bmc1_property_lemmas false
% 150.43/150.69 % --bmc1_k_induction false
% 150.43/150.69 % --bmc1_non_equiv_states false
% 150.43/150.69 % --bmc1_deadlock false
% 150.43/150.69 % --bmc1_ucm false
% 150.43/150.69 % --bmc1_add_unsat_core none
% 150.43/150.69 % --bmc1_unsat_core_children false
% 150.43/150.69 % --bmc1_unsat_core_extrapolate_axioms false
% 150.43/150.69 % --bmc1_out_stat full
% 150.43/150.69 % --bmc1_ground_init false
% 150.43/150.69 % --bmc1_pre_inst_next_state false
% 150.43/150.69 % --bmc1_pre_inst_state false
% 150.43/150.69 % --bmc1_pre_inst_reach_state false
% 150.43/150.69 % --bmc1_out_unsat_core false
% 150.43/150.69 % --bmc1_aig_witness_out false
% 150.43/150.69 % --bmc1_verbose false
% 150.43/150.69 % --bmc1_dump_clauses_tptp false
% 151.55/151.91 % --bmc1_dump_unsat_core_tptp false
% 151.55/151.91 % --bmc1_dump_file -
% 151.55/151.91 % --bmc1_ucm_expand_uc_limit 128
% 151.55/151.91 % --bmc1_ucm_n_expand_iterations 6
% 151.55/151.91 % --bmc1_ucm_extend_mode 1
% 151.55/151.91 % --bmc1_ucm_init_mode 2
% 151.55/151.91 % --bmc1_ucm_cone_mode none
% 151.55/151.91 % --bmc1_ucm_reduced_relation_type 0
% 151.55/151.91 % --bmc1_ucm_relax_model 4
% 151.55/151.91 % --bmc1_ucm_full_tr_after_sat true
% 151.55/151.91 % --bmc1_ucm_expand_neg_assumptions false
% 151.55/151.91 % --bmc1_ucm_layered_model none
% 151.55/151.91 % --bmc1_ucm_max_lemma_size 10
% 151.55/151.91
% 151.55/151.91 % ------ AIG Options
% 151.55/151.91
% 151.55/151.91 % --aig_mode false
% 151.55/151.91
% 151.55/151.91 % ------ Instantiation Options
% 151.55/151.91
% 151.55/151.91 % --instantiation_flag true
% 151.55/151.91 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 151.55/151.91 % --inst_solver_per_active 750
% 151.55/151.91 % --inst_solver_calls_frac 0.5
% 151.55/151.91 % --inst_passive_queue_type priority_queues
% 151.55/151.91 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 151.55/151.91 % --inst_passive_queues_freq [25;2]
% 151.55/151.91 % --inst_dismatching true
% 151.55/151.91 % --inst_eager_unprocessed_to_passive true
% 151.55/151.91 % --inst_prop_sim_given true
% 151.55/151.91 % --inst_prop_sim_new false
% 151.55/151.91 % --inst_orphan_elimination true
% 151.55/151.91 % --inst_learning_loop_flag true
% 151.55/151.91 % --inst_learning_start 3000
% 151.55/151.91 % --inst_learning_factor 2
% 151.55/151.91 % --inst_start_prop_sim_after_learn 3
% 151.55/151.91 % --inst_sel_renew solver
% 151.55/151.91 % --inst_lit_activity_flag true
% 151.55/151.91 % --inst_out_proof true
% 151.55/151.91
% 151.55/151.91 % ------ Resolution Options
% 151.55/151.91
% 151.55/151.91 % --resolution_flag true
% 151.55/151.91 % --res_lit_sel kbo_max
% 151.55/151.91 % --res_to_prop_solver none
% 151.55/151.91 % --res_prop_simpl_new false
% 151.55/151.91 % --res_prop_simpl_given false
% 151.55/151.91 % --res_passive_queue_type priority_queues
% 151.55/151.91 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 151.55/151.91 % --res_passive_queues_freq [15;5]
% 151.55/151.91 % --res_forward_subs full
% 151.55/151.91 % --res_backward_subs full
% 151.55/151.91 % --res_forward_subs_resolution true
% 151.55/151.91 % --res_backward_subs_resolution true
% 151.55/151.91 % --res_orphan_elimination false
% 151.55/151.91 % --res_time_limit 1000.
% 151.55/151.91 % --res_out_proof true
% 151.55/151.91 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_509f88.s
% 151.55/151.91 % --modulo true
% 151.55/151.91
% 151.55/151.91 % ------ Combination Options
% 151.55/151.91
% 151.55/151.91 % --comb_res_mult 1000
% 151.55/151.91 % --comb_inst_mult 300
% 151.55/151.91 % ------
% 151.55/151.91
% 151.55/151.91 % ------ Parsing...% successful
% 151.55/151.91
% 151.55/151.91 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 151.55/151.91
% 151.55/151.91 % ------ Proving...
% 151.55/151.91 % ------ Problem Properties
% 151.55/151.91
% 151.55/151.91 %
% 151.55/151.91 % EPR false
% 151.55/151.91 % Horn false
% 151.55/151.91 % Has equality true
% 151.55/151.91
% 151.55/151.91 % % ------ Input Options Time Limit: Unbounded
% 151.55/151.91
% 151.55/151.91
% 151.55/151.91 % warning: Clause {~(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0));v_thesis____} has no selected literals
% 151.55/151.91 cnf(c_773,negated_conjecture,
% 151.55/151.91 ( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
% 151.55/151.91 | v_thesis____ ),
% 151.55/151.91 file('/export/starexec/sandbox/tmp/iprover_modulo_da4f08.p', c_0_8) ).
% 151.55/151.91
% 151.55/151.91 % warning: Clause {~(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0));v_thesis____} has no selected literals
% 151.55/151.91 cnf(c_773,negated_conjecture,
% 151.55/151.91 ( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
% 151.55/151.91 | v_thesis____ ),
% 151.55/151.91 file('/export/starexec/sandbox/tmp/iprover_modulo_da4f08.p', c_0_8) ).
% 151.55/151.91
% 151.55/151.91 Compiling...
% 151.55/151.91 Loading plugin: done.
% 151.55/151.91 Compiling...
% 151.55/151.91 Loading plugin: done.
% 151.55/151.91 Compiling...
% 151.55/151.91 Loading plugin: done.
% 151.55/151.91 Compiling...
% 151.55/151.91 Loading plugin: done.
% 151.55/151.91 Compiling...
% 151.55/151.91 Loading plugin: done.
% 151.55/151.91 Compiling...
% 151.55/151.91 Loading plugin: done.
% 151.55/151.91 Compiling...
% 151.55/151.91 Loading plugin: done.
% 151.55/151.91 Compiling...
% 151.55/151.91 Loading plugin: done.
% 151.55/151.91 Compiling...
% 151.55/151.91 Loading plugin: done.
% 152.53/152.72 Compiling...
% 152.53/152.72 Loading plugin: done.
% 152.53/152.72 Compiling...
% 152.53/152.72 Loading plugin: done.
% 152.53/152.72 Compiling...
% 152.53/152.72 Loading plugin: done.
% 152.53/152.72 % warning: Clause {~(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0));v_thesis____} has no selected literals
% 152.53/152.72 cnf(c_773,negated_conjecture,
% 152.53/152.72 ( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
% 152.53/152.72 | v_thesis____ ),
% 152.53/152.72 file('/export/starexec/sandbox/tmp/iprover_modulo_da4f08.p', c_0_8) ).
% 152.53/152.72
% 152.53/152.72 % warning: Clause {~(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0));v_thesis____} has no selected literals
% 152.53/152.72 cnf(c_773,negated_conjecture,
% 152.53/152.72 ( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
% 152.53/152.72 | v_thesis____ ),
% 152.53/152.72 file('/export/starexec/sandbox/tmp/iprover_modulo_da4f08.p', c_0_8) ).
% 152.53/152.72
% 152.53/152.72 % % ------ Current options:
% 152.53/152.72
% 152.53/152.72 % ------ Input Options
% 152.53/152.72
% 152.53/152.72 % --out_options all
% 152.53/152.72 % --tptp_safe_out true
% 152.53/152.72 % --problem_path ""
% 152.53/152.72 % --include_path ""
% 152.53/152.72 % --clausifier .//eprover
% 152.53/152.72 % --clausifier_options --tstp-format
% 152.53/152.72 % --stdin false
% 152.53/152.72 % --dbg_backtrace false
% 152.53/152.72 % --dbg_dump_prop_clauses false
% 152.53/152.72 % --dbg_dump_prop_clauses_file -
% 152.53/152.72 % --dbg_out_stat false
% 152.53/152.72
% 152.53/152.72 % ------ General Options
% 152.53/152.72
% 152.53/152.72 % --fof false
% 152.53/152.72 % --time_out_real 150.
% 152.53/152.72 % --time_out_prep_mult 0.2
% 152.53/152.72 % --time_out_virtual -1.
% 152.53/152.72 % --schedule none
% 152.53/152.72 % --ground_splitting input
% 152.53/152.72 % --splitting_nvd 16
% 152.53/152.72 % --non_eq_to_eq false
% 152.53/152.72 % --prep_gs_sim true
% 152.53/152.72 % --prep_unflatten false
% 152.53/152.72 % --prep_res_sim true
% 152.53/152.72 % --prep_upred true
% 152.53/152.72 % --res_sim_input true
% 152.53/152.72 % --clause_weak_htbl true
% 152.53/152.72 % --gc_record_bc_elim false
% 152.53/152.72 % --symbol_type_check false
% 152.53/152.72 % --clausify_out false
% 152.53/152.72 % --large_theory_mode false
% 152.53/152.72 % --prep_sem_filter none
% 152.53/152.72 % --prep_sem_filter_out false
% 152.53/152.72 % --preprocessed_out false
% 152.53/152.72 % --sub_typing false
% 152.53/152.72 % --brand_transform false
% 152.53/152.72 % --pure_diseq_elim true
% 152.53/152.72 % --min_unsat_core false
% 152.53/152.72 % --pred_elim true
% 152.53/152.72 % --add_important_lit false
% 152.53/152.72 % --soft_assumptions false
% 152.53/152.72 % --reset_solvers false
% 152.53/152.72 % --bc_imp_inh []
% 152.53/152.72 % --conj_cone_tolerance 1.5
% 152.53/152.72 % --prolific_symb_bound 500
% 152.53/152.72 % --lt_threshold 2000
% 152.53/152.72
% 152.53/152.72 % ------ SAT Options
% 152.53/152.72
% 152.53/152.72 % --sat_mode false
% 152.53/152.72 % --sat_fm_restart_options ""
% 152.53/152.72 % --sat_gr_def false
% 152.53/152.72 % --sat_epr_types true
% 152.53/152.72 % --sat_non_cyclic_types false
% 152.53/152.72 % --sat_finite_models false
% 152.53/152.72 % --sat_fm_lemmas false
% 152.53/152.72 % --sat_fm_prep false
% 152.53/152.72 % --sat_fm_uc_incr true
% 152.53/152.72 % --sat_out_model small
% 152.53/152.72 % --sat_out_clauses false
% 152.53/152.72
% 152.53/152.72 % ------ QBF Options
% 152.53/152.72
% 152.53/152.72 % --qbf_mode false
% 152.53/152.72 % --qbf_elim_univ true
% 152.53/152.72 % --qbf_sk_in true
% 152.53/152.72 % --qbf_pred_elim true
% 152.53/152.72 % --qbf_split 32
% 152.53/152.72
% 152.53/152.72 % ------ BMC1 Options
% 152.53/152.72
% 152.53/152.72 % --bmc1_incremental false
% 152.53/152.72 % --bmc1_axioms reachable_all
% 152.53/152.72 % --bmc1_min_bound 0
% 152.53/152.72 % --bmc1_max_bound -1
% 152.53/152.72 % --bmc1_max_bound_default -1
% 152.53/152.72 % --bmc1_symbol_reachability true
% 152.53/152.72 % --bmc1_property_lemmas false
% 152.53/152.72 % --bmc1_k_induction false
% 152.53/152.72 % --bmc1_non_equiv_states false
% 158.22/158.47 % --bmc1_deadlock false
% 158.22/158.47 % --bmc1_ucm false
% 158.22/158.47 % --bmc1_add_unsat_core none
% 158.22/158.47 % --bmc1_unsat_core_children false
% 158.22/158.47 % --bmc1_unsat_core_extrapolate_axioms false
% 158.22/158.47 % --bmc1_out_stat full
% 158.22/158.47 % --bmc1_ground_init false
% 158.22/158.47 % --bmc1_pre_inst_next_state false
% 158.22/158.47 % --bmc1_pre_inst_state false
% 158.22/158.47 % --bmc1_pre_inst_reach_state false
% 158.22/158.47 % --bmc1_out_unsat_core false
% 158.22/158.47 % --bmc1_aig_witness_out false
% 158.22/158.47 % --bmc1_verbose false
% 158.22/158.47 % --bmc1_dump_clauses_tptp false
% 158.22/158.47 % --bmc1_dump_unsat_core_tptp false
% 158.22/158.47 % --bmc1_dump_file -
% 158.22/158.47 % --bmc1_ucm_expand_uc_limit 128
% 158.22/158.47 % --bmc1_ucm_n_expand_iterations 6
% 158.22/158.47 % --bmc1_ucm_extend_mode 1
% 158.22/158.47 % --bmc1_ucm_init_mode 2
% 158.22/158.47 % --bmc1_ucm_cone_mode none
% 158.22/158.47 % --bmc1_ucm_reduced_relation_type 0
% 158.22/158.47 % --bmc1_ucm_relax_model 4
% 158.22/158.47 % --bmc1_ucm_full_tr_after_sat true
% 158.22/158.47 % --bmc1_ucm_expand_neg_assumptions false
% 158.22/158.47 % --bmc1_ucm_layered_model none
% 158.22/158.47 % --bmc1_ucm_max_lemma_size 10
% 158.22/158.47
% 158.22/158.47 % ------ AIG Options
% 158.22/158.47
% 158.22/158.47 % --aig_mode false
% 158.22/158.47
% 158.22/158.47 % ------ Instantiation Options
% 158.22/158.47
% 158.22/158.47 % --instantiation_flag true
% 158.22/158.47 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 158.22/158.47 % --inst_solver_per_active 750
% 158.22/158.47 % --inst_solver_calls_frac 0.5
% 158.22/158.47 % --inst_passive_queue_type priority_queues
% 158.22/158.47 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 158.22/158.47 % --inst_passive_queues_freq [25;2]
% 158.22/158.47 % --inst_dismatching true
% 158.22/158.47 % --inst_eager_unprocessed_to_passive true
% 158.22/158.47 % --inst_prop_sim_given true
% 158.22/158.47 % --inst_prop_sim_new false
% 158.22/158.47 % --inst_orphan_elimination true
% 158.22/158.47 % --inst_learning_loop_flag true
% 158.22/158.47 % --inst_learning_start 3000
% 158.22/158.47 % --inst_learning_factor 2
% 158.22/158.47 % --inst_start_prop_sim_after_learn 3
% 158.22/158.47 % --inst_sel_renew solver
% 158.22/158.47 % --inst_lit_activity_flag true
% 158.22/158.47 % --inst_out_proof true
% 158.22/158.47
% 158.22/158.47 % ------ Resolution Options
% 158.22/158.47
% 158.22/158.47 % --resolution_flag true
% 158.22/158.47 % --res_lit_sel kbo_max
% 158.22/158.47 % --res_to_prop_solver none
% 158.22/158.47 % --res_prop_simpl_new false
% 158.22/158.47 % --res_prop_simpl_given false
% 158.22/158.47 % --res_passive_queue_type priority_queues
% 158.22/158.47 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 158.22/158.47 % --res_passive_queues_freq [15;5]
% 158.22/158.47 % --res_forward_subs full
% 158.22/158.47 % --res_backward_subs full
% 158.22/158.47 % --res_forward_subs_resolution true
% 158.22/158.47 % --res_backward_subs_resolution true
% 158.22/158.47 % --res_orphan_elimination false
% 158.22/158.47 % --res_time_limit 1000.
% 158.22/158.47 % --res_out_proof true
% 158.22/158.47 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_509f88.s
% 158.22/158.47 % --modulo true
% 158.22/158.47
% 158.22/158.47 % ------ Combination Options
% 158.22/158.47
% 158.22/158.47 % --comb_res_mult 1000
% 158.22/158.47 % --comb_inst_mult 300
% 158.22/158.47 % ------
% 158.22/158.47
% 158.22/158.47
% 158.22/158.47
% 158.22/158.47 % ------ Proving...
% 158.22/158.47 %
% 158.22/158.47
% 158.22/158.47
% 158.22/158.47 % ------ Statistics
% 158.22/158.47
% 158.22/158.47 % ------ General
% 158.22/158.47
% 158.22/158.47 % num_of_input_clauses: 775
% 158.22/158.47 % num_of_input_neg_conjectures: 2
% 158.22/158.47 % num_of_splits: 0
% 158.22/158.47 % num_of_split_atoms: 0
% 158.22/158.47 % num_of_sem_filtered_clauses: 0
% 158.22/158.47 % num_of_subtypes: 0
% 158.22/158.47 % monotx_restored_types: 0
% 158.22/158.47 % sat_num_of_epr_types: 0
% 158.22/158.47 % sat_num_of_non_cyclic_types: 0
% 158.22/158.47 % sat_guarded_non_collapsed_types: 0
% 158.22/158.47 % is_epr: 0
% 158.22/158.47 % is_horn: 0
% 158.22/158.47 % has_eq: 1
% 158.22/158.47 % num_pure_diseq_elim: 0
% 158.22/158.47 % simp_replaced_by: 0
% 158.22/158.47 % res_preprocessed: 2
% 158.22/158.47 % prep_upred: 0
% 158.22/158.47 % prep_unflattend: 0
% 158.22/158.47 % pred_elim_cands: 0
% 158.22/158.47 % pred_elim: 0
% 158.22/158.47 % pred_elim_cl: 0
% 158.22/158.47 % pred_elim_cycles: 0
% 158.22/158.47 % forced_gc_time: 0
% 158.22/158.47 % gc_basic_clause_elim: 0
% 158.22/158.47 % parsing_time: 0.021
% 158.22/158.47 % sem_filter_time: 0.
% 158.22/158.47 % pred_elim_time: 0.
% 158.22/158.47 % out_proof_time: 0.
% 158.22/158.47 % monotx_time: 0.
% 158.22/158.47 % subtype_inf_time: 0.
% 158.22/158.47 % unif_index_cands_time: 0.002
% 158.22/158.47 % unif_index_add_time: 0.003
% 158.22/158.47 % total_time: 7.789
% 158.22/158.47 % num_of_symbols: 110
% 158.22/158.47 % num_of_terms: 8569
% 158.22/158.47
% 158.22/158.47 % ------ Propositional Solver
% 158.22/158.47
% 158.22/158.47 % prop_solver_calls: 3
% 158.22/158.47 % prop_fast_solver_calls: 3
% 158.22/158.47 % prop_num_of_clauses: 1409
% 158.22/158.47 % prop_preprocess_simplified: 4496
% 158.22/158.47 % prop_fo_subsumed: 0
% 158.22/158.47 % prop_solver_time: 0.
% 158.22/158.47 % prop_fast_solver_time: 0.
% 158.22/158.47 % prop_unsat_core_time: 0.
% 158.22/158.47
% 158.22/158.47 % ------ QBF
% 158.22/158.47
% 158.22/158.47 % qbf_q_res: 0
% 158.22/158.47 % qbf_num_tautologies: 0
% 158.22/158.47 % qbf_prep_cycles: 0
% 158.22/158.47
% 158.22/158.47 % ------ BMC1
% 158.22/158.47
% 158.22/158.47 % bmc1_current_bound: -1
% 158.22/158.47 % bmc1_last_solved_bound: -1
% 158.22/158.47 % bmc1_unsat_core_size: -1
% 158.22/158.47 % bmc1_unsat_core_parents_size: -1
% 158.22/158.47 % bmc1_merge_next_fun: 0
% 158.22/158.47 % bmc1_unsat_core_clauses_time: 0.
% 158.22/158.47
% 158.22/158.47 % ------ Instantiation
% 158.22/158.47
% 158.22/158.47 % inst_num_of_clauses: 1064
% 158.22/158.47 % inst_num_in_passive: 692
% 158.22/158.47 % inst_num_in_active: 352
% 158.22/158.47 % inst_num_in_unprocessed: 18
% 158.22/158.47 % inst_num_of_loops: 354
% 158.22/158.47 % inst_num_of_learning_restarts: 0
% 158.22/158.47 % inst_num_moves_active_passive: 0
% 158.22/158.47 % inst_lit_activity: 55
% 158.22/158.47 % inst_lit_activity_moves: 0
% 158.22/158.47 % inst_num_tautologies: 0
% 158.22/158.47 % inst_num_prop_implied: 0
% 158.22/158.47 % inst_num_existing_simplified: 0
% 158.22/158.47 % inst_num_eq_res_simplified: 0
% 158.22/158.47 % inst_num_child_elim: 0
% 158.22/158.47 % inst_num_of_dismatching_blockings: 44
% 158.22/158.47 % inst_num_of_non_proper_insts: 426
% 158.22/158.47 % inst_num_of_duplicates: 592
% 158.22/158.47 % inst_inst_num_from_inst_to_res: 0
% 158.22/158.47 % inst_dismatching_checking_time: 0.
% 158.22/158.47
% 158.22/158.47 % ------ Resolution
% 158.22/158.47
% 158.22/158.47 % res_num_of_clauses: 1875
% 158.22/158.47 % res_num_in_passive: 80
% 158.22/158.47 % res_num_in_active: 1382
% 158.22/158.47 % res_num_of_loops: 2000
% 158.22/158.47 % res_forward_subset_subsumed: 443
% 158.22/158.47 % res_backward_subset_subsumed: 0
% 158.22/158.47 % res_forward_subsumed: 944
% 158.22/158.47 % res_backward_subsumed: 0
% 158.22/158.47 % res_forward_subsumption_resolution: 0
% 158.22/158.47 % res_backward_subsumption_resolution: 1
% 158.22/158.47 % res_clause_to_clause_subsumption: 253599
% 158.22/158.47 % res_orphan_elimination: 0
% 158.22/158.47 % res_tautology_del: 0
% 158.22/158.47 % res_num_eq_res_simplified: 0
% 158.22/158.47 % res_num_sel_changes: 0
% 158.22/158.47 % res_moves_from_active_to_pass: 0
% 158.22/158.47
% 158.22/158.47 % Status Unsatisfiable
% 158.22/158.47 % SZS status Unsatisfiable
% 158.22/158.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------