TSTP Solution File: LCL835-1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : LCL835-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n023.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 11:40:30 EDT 2022
% Result : Unsatisfiable 152.90s 153.47s
% Output : CNFRefutation 153.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 498
% Syntax : Number of formulae : 3457 ( 984 unt; 0 def)
% Number of atoms : 7188 (2655 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 7292 (3561 ~;3731 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-6 aty)
% Number of functors : 62 ( 62 usr; 23 con; 0-5 aty)
% Number of variables : 11780 (1566 sgn4959 !; 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,
! [X19,X49,X60,X82] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X19),X49)))
| ~ c_Type_Otyping(X60,X19,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
| ~ c_Type_Otyping(c_Type_Oshift(X60,X49,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X82) ),
file('<stdin>',cls_SI1_0) ).
fof(c_0_1,axiom,
! [X19,X46,X33,X49] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB)),X19),X49) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X19),X49),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X19,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X49,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X46,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_subst__map_0) ).
fof(c_0_2,axiom,
! [X48,X46,X49,X60,X62,X63,X61] :
( X62 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X61,X62,X60,X48),X61,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X62)
| ~ c_Type_Otypings(X60,X46,X63)
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X48,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
file('<stdin>',cls_var__app__types_0) ).
fof(c_0_3,axiom,
! [X19,X46,X49,X60,X63,X61] :
( c_Type_Otypings(X60,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X19,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X49,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X46,tc_Lambda_OdB,tc_Lambda_OdB),X63)
| ~ c_Type_Otypings(c_Type_Oshift(X60,X49,X61,tc_Type_Otype),X46,X63)
| ~ c_Type_Otyping(X60,X19,X61) ),
file('<stdin>',cls_substs__lemma_0) ).
fof(c_0_4,axiom,
! [X48,X46,X49,X60,X62,X63,X61] :
( c_Type_Otypings(X60,X48,c_Type_Osko__Type__Xvar__app__types__1__1(X61,X62,X60,X48))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X62)
| ~ c_Type_Otypings(X60,X46,X63)
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X48,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
file('<stdin>',cls_var__app__types_1) ).
fof(c_0_5,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,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)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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_CHAINED_0) ).
fof(c_0_6,axiom,
! [X77,X5,X12] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X5,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X77,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X5,X77,tc_Lambda_OdB) ),
file('<stdin>',cls_apps__preserves__betas_0) ).
fof(c_0_7,axiom,
! [X77,X28,X12] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X77,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X28)) ),
file('<stdin>',cls_apps__preserves__beta2_0) ).
fof(c_0_8,axiom,
! [X77,X28,X12] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X77,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X28)) ),
file('<stdin>',cls_apps__preserves__beta_0) ).
fof(c_0_9,axiom,
! [X77,X28,X12] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12)),X28),X77,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X28),c_HOL_Ozero__class_Ozero(tc_nat)),X77,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('<stdin>',cls_IT_OBeta_0) ).
fof(c_0_10,axiom,
! [X46,X33,X49] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB)),X49) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X33),X49),c_List_Omap(c_COMBC(c_Lambda_Olift,X49,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X46,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_lift__map_0) ).
fof(c_0_11,axiom,
! [X56,X57,X40,X41,X43,X44,X59,X58,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),hAPP(hAPP(X44,X57),X56)) = hAPP(hAPP(X44,X57),hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),X56))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
fof(c_0_12,axiom,
! [X56,X57,X40,X41,X43,X44,X59,X58,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),hAPP(hAPP(X44,X57),X56)) = hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X57)),hAPP(hAPP(X44,X59),X56))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
fof(c_0_13,axiom,
! [X56,X57,X40,X41,X43,X44,X59,X58,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),hAPP(hAPP(X44,X57),X56)) = hAPP(hAPP(X44,X58),hAPP(hAPP(X44,X59),hAPP(hAPP(X44,X57),X56)))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
fof(c_0_14,axiom,
! [X40,X41,X43,X44,X10,X7,X8,X45,X9,X4] :
( hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X8)),hAPP(hAPP(X45,X7),X10)) = hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X7)),hAPP(hAPP(X45,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_15,axiom,
! [X40,X41,X43,X44,X11,X8,X45,X9,X4] :
( hAPP(hAPP(X45,hAPP(hAPP(X44,X9),X11)),hAPP(hAPP(X44,X8),X11)) = hAPP(hAPP(X44,hAPP(hAPP(X45,X9),X8)),X11)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
fof(c_0_16,axiom,
! [X40,X41,X43,X44,X7,X8,X45,X9,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X45,X9),X8)),X7) = hAPP(hAPP(X45,hAPP(hAPP(X44,X9),X7)),hAPP(hAPP(X44,X8),X7))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
fof(c_0_17,axiom,
! [X18,X16,X40,X41,X42,X43,X44,X45,X4] :
( hAPP(hAPP(X43,hAPP(hAPP(X44,X16),X18)),X42) = hAPP(hAPP(X44,hAPP(hAPP(X43,X16),X42)),hAPP(hAPP(X43,X18),X42))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Opwr__mul_0) ).
fof(c_0_18,axiom,
! [X16,X40,X41,X42,X43,X53,X44,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X43,X16),X53)),hAPP(hAPP(X43,X16),X42)) = hAPP(hAPP(X43,X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X53),X42))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Omul__pwr_0) ).
fof(c_0_19,axiom,
! [X40,X41,X43,X44,X11,X45,X9,X4] :
( hAPP(hAPP(X45,hAPP(hAPP(X44,X9),X11)),X11) = hAPP(hAPP(X44,hAPP(hAPP(X45,X9),X40)),X11)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
fof(c_0_20,axiom,
! [X57,X40,X41,X43,X44,X59,X58,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),X57) = hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X57)),X59)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
fof(c_0_21,axiom,
! [X40,X41,X43,X44,X7,X8,X45,X9,X4] :
( hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X8)),X7) = hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X7)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_22,axiom,
! [X17,X18,X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X16),hAPP(hAPP(X45,X18),X17)) = hAPP(hAPP(X45,hAPP(hAPP(X44,X16),X18)),hAPP(hAPP(X44,X16),X17))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Omul__d_0) ).
fof(c_0_23,axiom,
! [X40,X41,X43,X44,X11,X45,X9,X4] :
( hAPP(hAPP(X45,X11),hAPP(hAPP(X44,X9),X11)) = hAPP(hAPP(X44,hAPP(hAPP(X45,X9),X40)),X11)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
fof(c_0_24,axiom,
! [X57,X40,X41,X43,X44,X59,X58,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),X57) = hAPP(hAPP(X44,X58),hAPP(hAPP(X44,X59),X57))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
fof(c_0_25,axiom,
! [X56,X57,X40,X41,X43,X44,X58,X45,X4] :
( hAPP(hAPP(X44,X58),hAPP(hAPP(X44,X57),X56)) = hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X57)),X56)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
fof(c_0_26,axiom,
! [X40,X41,X43,X44,X7,X8,X45,X9,X4] :
( hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X8)),X7) = hAPP(hAPP(X45,X9),hAPP(hAPP(X45,X8),X7))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_27,axiom,
! [X40,X41,X43,X44,X10,X7,X45,X9,X4] :
( hAPP(hAPP(X45,X9),hAPP(hAPP(X45,X7),X10)) = hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X7)),X10)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_28,axiom,
! [X17,X18,X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X45,X16),hAPP(hAPP(X45,X18),X17)) = hAPP(hAPP(X45,hAPP(hAPP(X45,X16),X18)),X17)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Oadd__a_0) ).
fof(c_0_29,axiom,
! [X17,X18,X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X16),hAPP(hAPP(X44,X18),X17)) = hAPP(hAPP(X44,hAPP(hAPP(X44,X16),X18)),X17)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Omul__a_0) ).
fof(c_0_30,axiom,
! [X16,X40,X41,X42,X43,X44,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X43,X16),X42)),X16) = hAPP(hAPP(X43,X16),c_Suc(X42))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I28_J_0) ).
fof(c_0_31,axiom,
! [X40,X41,X43,X44,X11,X45,X4] :
( hAPP(hAPP(X45,X11),X11) = hAPP(hAPP(X44,hAPP(hAPP(X45,X40),X40)),X11)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
fof(c_0_32,axiom,
! [X56,X57,X40,X41,X43,X44,X58,X45,X4] :
( hAPP(hAPP(X44,X58),hAPP(hAPP(X44,X57),X56)) = hAPP(hAPP(X44,X57),hAPP(hAPP(X44,X58),X56))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
fof(c_0_33,axiom,
! [X40,X41,X43,X44,X10,X7,X45,X9,X4] :
( hAPP(hAPP(X45,X9),hAPP(hAPP(X45,X7),X10)) = hAPP(hAPP(X45,X7),hAPP(hAPP(X45,X9),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_34,axiom,
! [X16,X40,X41,X43,X6,X44,X45,X4] :
( hAPP(hAPP(X43,X16),c_Suc(X6)) = hAPP(hAPP(X44,X16),hAPP(hAPP(X43,X16),X6))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Opwr__Suc_0) ).
fof(c_0_35,axiom,
! [X16,X40,X41,X42,X43,X44,X45,X4] :
( hAPP(hAPP(X43,X16),c_Suc(X42)) = hAPP(hAPP(X44,X16),hAPP(hAPP(X43,X16),X42))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I35_J_0) ).
fof(c_0_36,axiom,
! [X16,X40,X41,X42,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X16),hAPP(hAPP(X43,X16),X42)) = hAPP(hAPP(X43,X16),c_Suc(X42))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I27_J_0) ).
fof(c_0_37,axiom,
! [X40,X41,X43,X44,X8,X45,X9,X4] :
( hAPP(hAPP(X44,X9),X8) = hAPP(hAPP(X44,X8),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
fof(c_0_38,axiom,
! [X40,X41,X43,X44,X7,X45,X9,X4] :
( hAPP(hAPP(X45,X9),X7) = hAPP(hAPP(X45,X7),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_39,axiom,
! [X18,X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X45,X16),X18) = hAPP(hAPP(X45,X18),X16)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Oadd__c_0) ).
fof(c_0_40,axiom,
! [X18,X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X16),X18) = hAPP(hAPP(X44,X18),X16)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Omul__c_0) ).
fof(c_0_41,axiom,
! [X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X43,X16),c_HOL_Ozero__class_Ozero(tc_nat)) = X40
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Opwr__0_0) ).
fof(c_0_42,axiom,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X45,X41),X9) = X9
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_43,axiom,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X45,X9),X41) = X9
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_44,axiom,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X44,X41),X9) = X41
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
fof(c_0_45,axiom,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X44,X9),X41) = X41
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
fof(c_0_46,axiom,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X44,X40),X9) = X9
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
fof(c_0_47,axiom,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X44,X9),X40) = X9
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
fof(c_0_48,axiom,
! [X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X45,X41),X16) = X16
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Oadd__0_0) ).
fof(c_0_49,axiom,
! [X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X41),X16) = X41
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Omul__0_0) ).
fof(c_0_50,axiom,
! [X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X40),X16) = X16
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
file('<stdin>',cls_gb__semiring_Omul__1_0) ).
fof(c_0_51,axiom,
! [X21,X22,X23,X72,X73,X4] : c_Lambda_OdB_OdB__rec(X23,X22,X21,hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72),X4) = hAPP(hAPP(hAPP(hAPP(X22,X73),X72),c_Lambda_OdB_OdB__rec(X23,X22,X21,X73,X4)),c_Lambda_OdB_OdB__rec(X23,X22,X21,X72,X4)),
file('<stdin>',cls_dB_Orecs_I2_J_0) ).
fof(c_0_52,axiom,
! [X21,X22,X23,X72,X73,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72),t_a)))
| hBOOL(hAPP(X26,hAPP(hAPP(X22,X73),X72))) ),
file('<stdin>',cls_dB_Osplit_1) ).
fof(c_0_53,axiom,
! [X74,X35,X21,X22,X23,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,hAPP(hAPP(c_Lambda_OdB_OApp,X35),X74),t_a)))
| hBOOL(hAPP(X26,hAPP(hAPP(X22,X35),X74))) ),
file('<stdin>',cls_dB_Osplit__asm_1) ).
fof(c_0_54,axiom,
! [X46,X49,X60,X62,X61] :
( X61 = X62
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X62)
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
file('<stdin>',cls_var__app__type__eq_0) ).
fof(c_0_55,axiom,
! [X71,X21,X22,X23,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OVar(X71),t_a)))
| hBOOL(hAPP(X26,hAPP(X23,X71))) ),
file('<stdin>',cls_dB_Osplit__asm_0) ).
fof(c_0_56,axiom,
! [X20,X21,X22,X23,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OVar(X20),t_a)))
| hBOOL(hAPP(X26,hAPP(X23,X20))) ),
file('<stdin>',cls_dB_Osplit_0) ).
fof(c_0_57,axiom,
! [X31,X21,X22,X23,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OAbs(X31),t_a)))
| hBOOL(hAPP(X26,hAPP(X21,X31))) ),
file('<stdin>',cls_dB_Osplit__asm_2) ).
fof(c_0_58,axiom,
! [X21,X22,X23,X50,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OAbs(X50),t_a)))
| hBOOL(hAPP(X26,hAPP(X21,X50))) ),
file('<stdin>',cls_dB_Osplit_2) ).
fof(c_0_59,axiom,
! [X77,X28,X12] :
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X28),c_HOL_Ozero__class_Ozero(tc_nat)),X77,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X28,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(X12)),X28),X77,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('<stdin>',cls_double__induction__lemma_0) ).
fof(c_0_60,axiom,
! [X46,X49,X60,X61] :
( c_Type_Otyping(X60,c_Lambda_OdB_OVar(X49),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X61,X60,X49,X46),X61,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
file('<stdin>',cls_var__app__typesE_0) ).
fof(c_0_61,axiom,
! [X46,X33,X60,X61] :
( c_Type_Otyping(X60,X33,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X61,X60,X33,X46),X61,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
file('<stdin>',cls_list__app__typeD_0) ).
fof(c_0_62,axiom,
! [X46,X33,X60,X61] :
( c_Type_Otyping(X60,X33,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X61,X60,X33,X46),X61,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
file('<stdin>',cls_list__app__typeE_0) ).
fof(c_0_63,axiom,
! [X46,X33,X60,X63,X61] :
( c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB),X61)
| ~ c_Type_Otypings(X60,X46,X63)
| ~ c_Type_Otyping(X60,X33,c_List_Ofoldr(c_Type_Otype_OFun,X63,X61,tc_Type_Otype,tc_Type_Otype)) ),
file('<stdin>',cls_list__app__typeI_0) ).
fof(c_0_64,axiom,
! [X46,X49,X60,X62,X63] :
( c_Type_Otypings(c_Type_Oshift(X60,X49,X62,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X49,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X46,tc_Lambda_OdB,tc_Lambda_OdB),X63)
| ~ c_Type_Otypings(X60,X46,X63) ),
file('<stdin>',cls_lift__types_0) ).
fof(c_0_65,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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_66,axiom,
! [X46] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X46,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X46,tc_Lambda_OdB) ),
file('<stdin>',cls_lifts__IT_0) ).
fof(c_0_67,axiom,
! [X5,X6] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X5,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X5,tc_Lambda_OdB) ),
file('<stdin>',cls_IT_OVar_0) ).
fof(c_0_68,axiom,
! [X1,X2,X29,X9,X13,X4] : c_List_Ofoldl(X29,X9,c_List_Oappend(X2,X1,X13),X4,X13) = c_List_Ofoldl(X29,c_List_Ofoldl(X29,X9,X2,X4,X13),X1,X4,X13),
file('<stdin>',cls_foldl__append_0) ).
fof(c_0_69,axiom,
! [X1,X2,X29,X9,X13,X4] : c_List_Ofoldr(X29,c_List_Oappend(X2,X1,X13),X9,X13,X4) = c_List_Ofoldr(X29,X2,c_List_Ofoldr(X29,X1,X9,X13,X4),X13,X4),
file('<stdin>',cls_foldr__append_0) ).
fof(c_0_70,axiom,
! [X46,X49,X60,X61] :
( c_Type_Otypings(X60,X46,c_Type_Osko__Type__Xvar__app__typesE__1__1(X61,X60,X49,X46))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
file('<stdin>',cls_var__app__typesE_1) ).
fof(c_0_71,axiom,
! [X46,X33,X60,X61] :
( c_Type_Otypings(X60,X46,c_Type_Osko__Type__Xlist__app__typeE__1__1(X61,X60,X33,X46))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
file('<stdin>',cls_list__app__typeE_1) ).
fof(c_0_72,axiom,
! [X46,X33,X60,X61] :
( c_Type_Otypings(X60,X46,c_Type_Osko__Type__Xlist__app__typeD__1__1(X61,X60,X33,X46))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
file('<stdin>',cls_list__app__typeD_1) ).
fof(c_0_73,axiom,
! [X77,X28,X5,X12] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),X5,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X28),X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X5 = X77 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_1) ).
fof(c_0_74,axiom,
! [X77,X28,X5,X12] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),X5,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X28),X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X12 = X28 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_0) ).
fof(c_0_75,axiom,
! [X77,X5,X6,X11] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X5,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X5 = X77 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_1) ).
fof(c_0_76,axiom,
! [X77,X5,X6,X11] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X5,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X11 = X6 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_0) ).
fof(c_0_77,axiom,
! [X30,X18,X16,X4] :
( ~ class_OrderedGroup_Osemigroup__add(X4)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X18),X30,X4,X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),X18,X30,X4,X4)) ),
file('<stdin>',cls_foldl__assoc_0) ).
fof(c_0_78,axiom,
! [X46,X77,X12,X6] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),X77,tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Var__apps__neq__Abs__apps_0) ).
fof(c_0_79,axiom,
! [X46,X28,X12] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X46,tc_Lambda_OdB,tc_Lambda_OdB)
| X12 = X28 ),
file('<stdin>',cls_apps__eq__tail__conv_0) ).
fof(c_0_80,axiom,
! [X2,X16,X29,X9,X13,X4] : c_List_Ofoldr(X29,c_List_Olist_OCons(X16,X2,X13),X9,X13,X4) = hAPP(hAPP(X29,X16),c_List_Ofoldr(X29,X2,X9,X13,X4)),
file('<stdin>',cls_foldr_Osimps_I2_J_0) ).
fof(c_0_81,axiom,
! [X30,X18,X16,X65,X4] :
( c_List_Ofoldl(X65,hAPP(hAPP(X65,X16),X18),X30,X4,X4) = hAPP(hAPP(X65,X16),c_List_Ofoldl(X65,X18,X30,X4,X4))
| ~ c_OrderedGroup_Osemigroup__add(X65,X4) ),
file('<stdin>',cls_semigroup__add_Ofoldl__assoc_0) ).
fof(c_0_82,axiom,
! [X30,X64,X16,X65,X4] :
( hAPP(hAPP(X65,X16),c_List_Ofoldl(X65,X64,X30,X4,X4)) = c_List_Ofoldl(X65,X16,X30,X4,X4)
| ~ c_OrderedGroup_Omonoid__add(X64,X65,X4) ),
file('<stdin>',cls_monoid__add_Ofoldl__absorb0_0) ).
fof(c_0_83,axiom,
! [X30,X16,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4),X30,X4,X4)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),X16,X30,X4,X4) ),
file('<stdin>',cls_foldl__absorb0_0) ).
fof(c_0_84,axiom,
! [X2,X9,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),X9,X2,X4,X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X4),X2,c_HOL_Ozero__class_Ozero(X4),X4,X4)) ),
file('<stdin>',cls_foldl__foldr1__lemma_0) ).
fof(c_0_85,axiom,
! [X21,X22,X23,X50,X4] : c_Lambda_OdB_OdB__rec(X23,X22,X21,c_Lambda_OdB_OAbs(X50),X4) = hAPP(hAPP(X21,X50),c_Lambda_OdB_OdB__rec(X23,X22,X21,X50,X4)),
file('<stdin>',cls_dB_Orecs_I3_J_0) ).
fof(c_0_86,axiom,
! [X46,X33,X28,X12] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X12),X28) != c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB)
| X12 = c_List_Ofoldl(c_Lambda_OdB_OApp,X33,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X12,X28,X33,X46),tc_Lambda_OdB,tc_Lambda_OdB)
| X46 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_App__eq__foldl__conv_2) ).
fof(c_0_87,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_CHAINED_0_01) ).
fof(c_0_88,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_89,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_90,axiom,
! [X2,X16,X29,X9,X13,X4] : c_List_Ofoldl(X29,X9,c_List_Olist_OCons(X16,X2,X13),X4,X13) = c_List_Ofoldl(X29,hAPP(hAPP(X29,X9),X16),X2,X4,X13),
file('<stdin>',cls_foldl__Cons_0) ).
fof(c_0_91,axiom,
! [X24,X25,X26,X27,X13,X4] : hAPP(c_COMBC(X26,X25,X13,X27,X4),X24) = hAPP(hAPP(X26,X24),X25),
file('<stdin>',cls_COMBC__def_0) ).
fof(c_0_92,axiom,
! [X2,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4),X2,X4,X4) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X4),X2,c_HOL_Ozero__class_Ozero(X4),X4,X4) ),
file('<stdin>',cls_foldl__foldr1_0) ).
fof(c_0_93,axiom,
! [X2,X9,X4] :
( ~ class_OrderedGroup_Oab__semigroup__add(X4)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X4),X2,X9,X4,X4) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),X9,X2,X4,X4) ),
file('<stdin>',cls_foldr__conv__foldl_0) ).
fof(c_0_94,axiom,
! [X19,X33,X60,X61] :
( c_Type_Otyping(X60,X33,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X61,X60,X33,X19)),X61))
| ~ c_Type_Otyping(X60,hAPP(hAPP(c_Lambda_OdB_OApp,X33),X19),X61) ),
file('<stdin>',cls_typing__elims_I2_J_0) ).
fof(c_0_95,axiom,
! [X33,X28,X12] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X12),X28) != c_List_Ofoldl(c_Lambda_OdB_OApp,X33,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X12),X28) = X33 ),
file('<stdin>',cls_App__eq__foldl__conv_0) ).
fof(c_0_96,axiom,
! [X33,X77,X28,X6] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X28)),X33) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X77,tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Abs__App__neq__Var__apps_0) ).
fof(c_0_97,axiom,
! [X77,X28,X12] :
( c_Lambda_OdB_OAbs(X12) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X12) = X28 ),
file('<stdin>',cls_Abs__eq__apps__conv_0) ).
fof(c_0_98,axiom,
! [X77,X28,X11] :
( c_Lambda_OdB_OVar(X11) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X11) = X28 ),
file('<stdin>',cls_Var__eq__apps__conv_0) ).
fof(c_0_99,axiom,
! [X77,X28,X12] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X12)
| X28 = c_Lambda_OdB_OAbs(X12) ),
file('<stdin>',cls_apps__eq__Abs__conv_0) ).
fof(c_0_100,axiom,
! [X77,X28,X11] :
( c_Lambda_OdB_OVar(X11) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X77 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Var__eq__apps__conv_1) ).
fof(c_0_101,axiom,
! [X77,X28,X12] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X12)
| X77 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_apps__eq__Abs__conv_1) ).
fof(c_0_102,axiom,
! [X77,X28,X12] :
( c_Lambda_OdB_OAbs(X12) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X77 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Abs__eq__apps__conv_1) ).
fof(c_0_103,axiom,
! [X18,X16,X12,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X18),X16))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X12,X4,X4),X4),X16),X18)) ),
file('<stdin>',cls_rtranclp__converseD_0) ).
fof(c_0_104,axiom,
! [X1,X18,X2,X16,X12,X4] :
( hBOOL(hAPP(hAPP(X12,X18),X16))
| c_ListOrder_Ostep1(X12,X1,X2,X4)
| ~ c_ListOrder_Ostep1(X12,c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4),X4) ),
file('<stdin>',cls_Snoc__step1__SnocD_1) ).
fof(c_0_105,axiom,
! [X1,X18,X2,X16,X12,X4] :
( X1 = X2
| c_ListOrder_Ostep1(X12,X1,X2,X4)
| ~ c_ListOrder_Ostep1(X12,c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4),X4) ),
file('<stdin>',cls_Snoc__step1__SnocD_0) ).
fof(c_0_106,axiom,
! [X1,X18,X2,X16,X12,X4] :
( hBOOL(hAPP(hAPP(X12,X18),X16))
| X18 = X16
| ~ c_ListOrder_Ostep1(X12,c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4),X4) ),
file('<stdin>',cls_Snoc__step1__SnocD_3) ).
fof(c_0_107,axiom,
! [X49,X60,X62,X61,X4] : c_Type_Oshift(c_Type_Oshift(X60,X49,X62,X4),c_HOL_Ozero__class_Ozero(tc_nat),X61,X4) = c_Type_Oshift(c_Type_Oshift(X60,c_HOL_Ozero__class_Ozero(tc_nat),X61,X4),c_Suc(X49),X62,X4),
file('<stdin>',cls_shift__commute_0) ).
fof(c_0_108,axiom,
! [X1,X18,X2,X16,X12,X4] :
( X1 = X2
| X18 = X16
| ~ c_ListOrder_Ostep1(X12,c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4),X4) ),
file('<stdin>',cls_Snoc__step1__SnocD_2) ).
fof(c_0_109,axiom,
! [X19,X33,X49,X60,X79,X80,X81] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X81),X80)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X19),X49)))
| ~ c_Type_Otyping(X60,X19,X81)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
| ~ c_Type_Otyping(c_Type_Oshift(X60,X49,X81,tc_Type_Otype),X33,X79)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_MI1_0) ).
fof(c_0_110,axiom,
! [X19,X33,X49,X60,X79,X80,X81] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X81),X80)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X19),X49)))
| ~ c_Type_Otyping(X60,X19,X80)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
| ~ c_Type_Otyping(c_Type_Oshift(X60,X49,X80,tc_Type_Otype),X33,X79)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_MI2_0) ).
fof(c_0_111,axiom,
! [X33,X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X12),X49)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X28),X49)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X28)) ),
file('<stdin>',cls_subst__preserves__beta2_H_0) ).
fof(c_0_112,axiom,
! [X33,X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X33),X49)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X33),X49)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X28)) ),
file('<stdin>',cls_subst__preserves__beta_H_0) ).
fof(c_0_113,axiom,
! [X1,X2,X29,X13,X4] : c_List_Omap(X29,c_List_Oappend(X2,X1,X13),X13,X4) = c_List_Oappend(c_List_Omap(X29,X2,X13,X4),c_List_Omap(X29,X1,X13,X4),X4),
file('<stdin>',cls_map__append_0) ).
fof(c_0_114,axiom,
! [X18,X16,X12,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X12,X4,X4),X4),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X18),X16)) ),
file('<stdin>',cls_rtranclp__converseI_0) ).
fof(c_0_115,axiom,
! [X19,X49,X60,X82] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X19),X49)))
| ~ c_Type_Otyping(X60,X19,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
| ~ c_Type_Otyping(c_Type_Oshift(X60,X49,v_T____,tc_Type_Otype),v_a____,X82) ),
file('<stdin>',cls_SI2_0) ).
fof(c_0_116,axiom,
! [X21,X22,X23,X72,X73,X4] : c_Lambda_OdB_OdB__case(X23,X22,X21,hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72),X4) = hAPP(hAPP(X22,X73),X72),
file('<stdin>',cls_dB_Osimps_I11_J_0) ).
fof(c_0_117,axiom,
! [X28,X12] : hAPP(hAPP(c_Lambda_OdB_OApp,X12),X28) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X12),X28),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_App__eq__foldl__conv_4) ).
fof(c_0_118,axiom,
! [X33,X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X12),X49)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X28),X49)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X28)) ),
file('<stdin>',cls_subst__preserves__beta2_0) ).
fof(c_0_119,axiom,
! [X2,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(X2,X4) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4),X2,X4,X4) ),
file('<stdin>',cls_listsum_0) ).
fof(c_0_120,axiom,
! [X2,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(X2,X4) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X4),X2,c_HOL_Ozero__class_Ozero(X4),X4,X4) ),
file('<stdin>',cls_listsum__foldr_0) ).
fof(c_0_121,axiom,
! [X20,X21,X22,X23,X4] : c_Lambda_OdB_OdB__rec(X23,X22,X21,c_Lambda_OdB_OVar(X20),X4) = hAPP(X23,X20),
file('<stdin>',cls_dB_Orecs_I1_J_0) ).
fof(c_0_122,axiom,
! [X21,X22,X23,X50,X4] : c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OAbs(X50),X4) = hAPP(X21,X50),
file('<stdin>',cls_dB_Osimps_I12_J_0) ).
fof(c_0_123,axiom,
! [X20,X21,X22,X23,X4] : c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OVar(X20),X4) = hAPP(X23,X20),
file('<stdin>',cls_dB_Osimps_I10_J_0) ).
fof(c_0_124,axiom,
! [X33,X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X33),X49)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X33),X49)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X28)) ),
file('<stdin>',cls_subst__preserves__beta_0) ).
fof(c_0_125,axiom,
! [X12] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X12),
file('<stdin>',cls_apps__eq__Abs__conv_2) ).
fof(c_0_126,axiom,
! [X33] : X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X33),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X33),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_ex__head__tail_0) ).
fof(c_0_127,axiom,
! [X12] : c_Lambda_OdB_OAbs(X12) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Abs__eq__apps__conv_2) ).
fof(c_0_128,axiom,
! [X11] : c_Lambda_OdB_OVar(X11) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('<stdin>',cls_Var__eq__apps__conv_2) ).
fof(c_0_129,axiom,
! [X29,X9,X13,X4] : c_List_Ofoldl(X29,X9,c_List_Olist_ONil(X13),X4,X13) = X9,
file('<stdin>',cls_foldl__Nil_0) ).
fof(c_0_130,axiom,
! [X29,X9,X13,X4] : c_List_Ofoldr(X29,c_List_Olist_ONil(X13),X9,X13,X4) = X9,
file('<stdin>',cls_foldr_Osimps_I1_J_0) ).
fof(c_0_131,axiom,
! [X19,X33,X49,X83,X62,X61] :
( ~ c_Type_Otyping(X83,X19,X62)
| ~ c_Type_Otyping(c_Type_Oshift(X83,X49,X62,tc_Type_Otype),X33,X61)
| c_Type_Otyping(X83,hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X19),X49),X61) ),
file('<stdin>',cls_subst__lemma_0) ).
fof(c_0_132,axiom,
! [X32,X33,X34,X28] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X32)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X33),X32))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X34)) ),
file('<stdin>',cls_rtrancl__beta__App_0) ).
fof(c_0_133,axiom,
! [X1,X18,X2,X16,X12,X4] :
( c_ListOrder_Ostep1(X12,X1,X2,X4)
| hBOOL(hAPP(hAPP(X12,X18),X16))
| ~ c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X18,X1,X4),c_List_Olist_OCons(X16,X2,X4),X4) ),
file('<stdin>',cls_Cons__step1__Cons_1) ).
fof(c_0_134,axiom,
! [X33,X78,X62,X61] :
( c_Type_Otyping(X78,c_Lambda_OdB_OAbs(X33),hAPP(hAPP(c_Type_Otype_OFun,X61),X62))
| ~ c_Type_Otyping(c_Type_Oshift(X78,c_HOL_Ozero__class_Ozero(tc_nat),X61,tc_Type_Otype),X33,X62) ),
file('<stdin>',cls_Abs_0) ).
fof(c_0_135,axiom,
! [X1,X18,X2,X16,X12,X4] :
( c_ListOrder_Ostep1(X12,X1,X2,X4)
| X2 = X1
| ~ c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X18,X1,X4),c_List_Olist_OCons(X16,X2,X4),X4) ),
file('<stdin>',cls_Cons__step1__Cons_3) ).
fof(c_0_136,axiom,
! [X33,X60,X61] :
( c_Type_Otyping(c_Type_Oshift(X60,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X61,X60,X33),tc_Type_Otype),X33,c_Type_Osko__Type__Xtyping__elims__3__2(X61,X60,X33))
| ~ c_Type_Otyping(X60,c_Lambda_OdB_OAbs(X33),X61) ),
file('<stdin>',cls_typing__elims_I3_J_1) ).
fof(c_0_137,axiom,
! [X2,X16,X29,X13,X4] : c_List_Omap(X29,c_List_Olist_OCons(X16,X2,X13),X13,X4) = c_List_Olist_OCons(hAPP(X29,X16),c_List_Omap(X29,X2,X13,X4),X4),
file('<stdin>',cls_map_Osimps_I2_J_0) ).
fof(c_0_138,axiom,
! [X35,X31,X29,X13,X4] : c_List_Olist_OCons(hAPP(X29,X31),c_List_Omap(X29,X35,X13,X4),X4) = c_List_Omap(X29,c_List_Olist_OCons(X31,X35,X13),X13,X4),
file('<stdin>',cls_Cons__eq__map__conv_3) ).
fof(c_0_139,axiom,
! [X31,X16,X29,X13,X4] : c_List_Omap(X29,c_List_Olist_OCons(X16,X31,X13),X13,X4) = c_List_Olist_OCons(hAPP(X29,X16),c_List_Omap(X29,X31,X13,X4),X4),
file('<stdin>',cls_map__eq__Cons__conv_3) ).
fof(c_0_140,axiom,
! [X19,X33,X28,X36] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X33),X19)),X28),X36) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X28),X36)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X28),X36)),
file('<stdin>',cls_subst__App_0) ).
fof(c_0_141,axiom,
! [X12,X8,X9,X13,X4] :
( hBOOL(hAPP(hAPP(X12,X8),X9))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X12,X4,X13),X9),X8)) ),
file('<stdin>',cls_conversepD_0) ).
fof(c_0_142,axiom,
! [X12,X14,X15,X13,X4] :
( hBOOL(hAPP(hAPP(X12,X14),X15))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X12,X4,X13),X15),X14)) ),
file('<stdin>',cls_conversep_Ocases_0) ).
fof(c_0_143,axiom,
! [X1,X2,X16,X12,X4] :
( c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X16,X1,X4),c_List_Olist_OCons(X16,X2,X4),X4)
| ~ c_ListOrder_Ostep1(X12,X1,X2,X4) ),
file('<stdin>',cls_Cons__step1__Cons_5) ).
fof(c_0_144,axiom,
! [X16,X47,X48,X12,X4] :
( c_ListOrder_Ostep1(X12,c_List_Oappend(X16,X47,X4),c_List_Oappend(X16,X48,X4),X4)
| ~ c_ListOrder_Ostep1(X12,X47,X48,X4) ),
file('<stdin>',cls_append__step1I_1) ).
fof(c_0_145,axiom,
! [X1,X2,X16,X12,X4] :
( ~ c_ListOrder_Ostep1(X12,X1,X2,X4)
| c_ListOrder_Ostep1(X12,c_List_Oappend(X1,X16,X4),c_List_Oappend(X2,X16,X4),X4) ),
file('<stdin>',cls_append__step1I_0) ).
fof(c_0_146,axiom,
! [X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X12),X49)),hAPP(hAPP(c_Lambda_Olift,X28),X49)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X28)) ),
file('<stdin>',cls_lift__preserves__beta_H_0) ).
fof(c_0_147,axiom,
! [X33,X34,X28] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X33)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X34)) ),
file('<stdin>',cls_rtrancl__beta__AppL_0) ).
fof(c_0_148,axiom,
! [X32,X33,X28] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33)),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X32)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X33),X32)) ),
file('<stdin>',cls_rtrancl__beta__AppR_0) ).
fof(c_0_149,axiom,
! [X33,X28] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X28)),X33)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X33),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('<stdin>',cls_beta_0) ).
fof(c_0_150,axiom,
! [X1,X18,X2,X16,X12,X4] :
( X16 = X18
| hBOOL(hAPP(hAPP(X12,X18),X16))
| ~ c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X18,X1,X4),c_List_Olist_OCons(X16,X2,X4),X4) ),
file('<stdin>',cls_Cons__step1__Cons_0) ).
fof(c_0_151,axiom,
! [X17,X18,X16,X12,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X16),X17))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X18),X17))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X16),X18)) ),
file('<stdin>',cls_rtranclp__trans_0) ).
fof(c_0_152,axiom,
! [X19,X33,X60,X61] :
( c_Type_Otyping(X60,X19,c_Type_Osko__Type__Xtyping__elims__2__1(X61,X60,X33,X19))
| ~ c_Type_Otyping(X60,hAPP(hAPP(c_Lambda_OdB_OApp,X33),X19),X61) ),
file('<stdin>',cls_typing__elims_I2_J_1) ).
fof(c_0_153,axiom,
! [X1,X18,X2,X16,X12,X4] :
( X16 = X18
| X2 = X1
| ~ c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X18,X1,X4),c_List_Olist_OCons(X16,X2,X4),X4) ),
file('<stdin>',cls_Cons__step1__Cons_2) ).
fof(c_0_154,axiom,
! [X10,X7,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X10)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X10)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_155,axiom,
! [X33,X60,X61] :
( c_Type_Otyping(c_Type_Oshift(X60,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X60,X33),tc_Type_Otype),X33,c_Type_Osko__Type__Xabs__typeE__1__2(X60,X33))
| ~ c_Type_Otyping(X60,c_Lambda_OdB_OAbs(X33),X61) ),
file('<stdin>',cls_abs__typeE_0) ).
fof(c_0_156,axiom,
! [X33,X49,X60,X62,X61] :
( c_Type_Otyping(c_Type_Oshift(X60,X49,X62,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X33),X49),X61)
| ~ c_Type_Otyping(X60,X33,X61) ),
file('<stdin>',cls_lift__type_0) ).
fof(c_0_157,axiom,
! [X2,X16,X6,X4] : c_List_Oappend(c_List_Oreplicate(X6,X16,X4),c_List_Olist_OCons(X16,X2,X4),X4) = c_List_Olist_OCons(X16,c_List_Oappend(c_List_Oreplicate(X6,X16,X4),X2,X4),X4),
file('<stdin>',cls_replicate__app__Cons__same_0) ).
fof(c_0_158,axiom,
! [X12,X8,X9,X13,X4] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X12,X4,X13),X9),X8))
| ~ hBOOL(hAPP(hAPP(X12,X8),X9)) ),
file('<stdin>',cls_conversep__iff_1) ).
fof(c_0_159,axiom,
! [X12,X8,X9,X13,X4] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X12,X4,X13),X8),X9))
| ~ hBOOL(hAPP(hAPP(X12,X9),X8)) ),
file('<stdin>',cls_conversep_Ointros_0) ).
fof(c_0_160,axiom,
! [X19,X33,X28] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X19)),hAPP(hAPP(c_Lambda_OdB_OApp,X33),X19)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X33)) ),
file('<stdin>',cls_appL_0) ).
fof(c_0_161,axiom,
! [X19,X33,X28] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X19),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X19),X33)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X33)) ),
file('<stdin>',cls_appR_0) ).
fof(c_0_162,axiom,
! [X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X12),X49)),hAPP(hAPP(c_Lambda_Olift,X28),X49)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X28)) ),
file('<stdin>',cls_lift__preserves__beta_0) ).
fof(c_0_163,axiom,
! [X12,X7,X8,X9,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X9),X7))
| ~ hBOOL(hAPP(hAPP(X12,X8),X7))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X9),X8)) ),
file('<stdin>',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
fof(c_0_164,axiom,
! [X12,X7,X8,X9,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X9),X7))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X8),X7))
| ~ hBOOL(hAPP(hAPP(X12,X9),X8)) ),
file('<stdin>',cls_converse__rtranclp__into__rtranclp_0) ).
fof(c_0_165,axiom,
! [X51,X49,X60,X61,X4] :
( hAPP(c_Type_Oshift(X60,X49,X61,X4),X51) = hAPP(X60,X51)
| ~ c_HOL_Oord__class_Oless(X51,X49,tc_nat) ),
file('<stdin>',cls_shift__gt_0) ).
fof(c_0_166,axiom,
! [X18,X31,X16,X12,X4] :
( ~ hBOOL(hAPP(hAPP(X12,X18),X31))
| c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X18,X16,X4),c_List_Olist_OCons(X31,X16,X4),X4) ),
file('<stdin>',cls_Cons__step1__Cons_4) ).
fof(c_0_167,axiom,
! [X1,X18,X2,X16,X4] :
( c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4)
| X16 = X18 ),
file('<stdin>',cls_append1__eq__conv_1) ).
fof(c_0_168,axiom,
! [X1,X18,X2,X16,X4] :
( c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4)
| X2 = X1 ),
file('<stdin>',cls_append1__eq__conv_0) ).
fof(c_0_169,axiom,
! [X16,X6,X36,X4] : c_List_Oappend(c_List_Oreplicate(X6,X16,X4),c_List_Oreplicate(X36,X16,X4),X4) = c_List_Oappend(c_List_Oreplicate(X36,X16,X4),c_List_Oreplicate(X6,X16,X4),X4),
file('<stdin>',cls_append__replicate__commute_0) ).
fof(c_0_170,axiom,
! [X17,X18,X16,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Orderings_Oord__class_Omax(X16,X18,X4)),X17) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X17),X4) ),
file('<stdin>',cls_max__add__distrib__left_0) ).
fof(c_0_171,axiom,
! [X7,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8)),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)),X8) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_172,axiom,
! [X16,X60,X61,X4] : hAPP(c_Type_Oshift(X60,X16,X61,X4),X16) = X61,
file('<stdin>',cls_shift__eq_0) ).
fof(c_0_173,axiom,
! [X19,X33,X28,X36] : c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X33),X19),X28,X36) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X33,X28,X36)),c_Lambda_Osubstn(X19,X28,X36)),
file('<stdin>',cls_substn_Osimps_I2_J_0) ).
fof(c_0_174,axiom,
! [X33,X28,X6,X36] : c_Lambda_Oliftn(X6,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33),X36) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X6,X28,X36)),c_Lambda_Oliftn(X6,X33,X36)),
file('<stdin>',cls_liftn_Osimps_I2_J_0) ).
fof(c_0_175,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X8),X4) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_176,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7),X4) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_177,axiom,
! [X12,X51,X49] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),c_Lambda_OdB_OVar(X49)),X51)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X12)) ),
file('<stdin>',cls_subst__Var__IT_0) ).
fof(c_0_178,axiom,
! [X33,X60,X61] :
( X61 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X61,X60,X33)),c_Type_Osko__Type__Xtyping__elims__3__2(X61,X60,X33))
| ~ c_Type_Otyping(X60,c_Lambda_OdB_OAbs(X33),X61) ),
file('<stdin>',cls_typing__elims_I3_J_0) ).
fof(c_0_179,axiom,
! [X34,X28] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X28)),c_Lambda_OdB_OAbs(X34)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X34)) ),
file('<stdin>',cls_rtrancl__beta__Abs_0) ).
fof(c_0_180,axiom,
! [X16,X49,X4] : c_List_Oappend(c_List_Oreplicate(X49,X16,X4),c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4) = c_List_Olist_OCons(X16,c_List_Oreplicate(X49,X16,X4),X4),
file('<stdin>',cls_replicate__append__same_0) ).
fof(c_0_181,axiom,
! [X10,X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X10),X4)
| ~ c_HOL_Oord__class_Oless(X7,X10,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_182,axiom,
! [X16,X6,X29,X13,X4] : c_List_Omap(X29,c_List_Oreplicate(X6,X16,X13),X13,X4) = c_List_Oreplicate(X6,hAPP(X29,X16),X4),
file('<stdin>',cls_map__replicate_0) ).
fof(c_0_183,axiom,
! [X12,X8,X9,X4] :
( c_Wellfounded_Oaccp(X12,X8,X4)
| ~ c_Wellfounded_Oaccp(X12,X9,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X8),X9)) ),
file('<stdin>',cls_accp__downwards__aux_0) ).
fof(c_0_184,axiom,
! [X12,X8,X9,X4] :
( c_Wellfounded_Oaccp(X12,X8,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X8),X9))
| ~ c_Wellfounded_Oaccp(X12,X9,X4) ),
file('<stdin>',cls_accp__downwards_0) ).
fof(c_0_185,axiom,
! [X33,X28,X36] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33)),X36) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X28),X36)),hAPP(hAPP(c_Lambda_Olift,X33),X36)),
file('<stdin>',cls_lift_Osimps_I2_J_0) ).
fof(c_0_186,axiom,
! [X6,X11,X36] :
( c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X6),tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_0) ).
fof(c_0_187,axiom,
! [X17,X18,X16,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X18)),X17) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_188,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8)),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7)) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_189,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Oab__semigroup__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8)),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7)) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_190,axiom,
! [X10,X7,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X10)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)),X10) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_191,axiom,
! [X7,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8)),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_192,axiom,
! [X16,X6,X11,X4] : c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X11),X16,X4) = c_List_Oappend(c_List_Oreplicate(X6,X16,X4),c_List_Oreplicate(X11,X16,X4),X4),
file('<stdin>',cls_replicate__add_0) ).
fof(c_0_193,axiom,
! [X33,X28,X78,X62,X61] :
( c_Type_Otyping(X78,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33),X62)
| ~ c_Type_Otyping(X78,X33,X61)
| ~ c_Type_Otyping(X78,X28,hAPP(hAPP(c_Type_Otype_OFun,X61),X62)) ),
file('<stdin>',cls_App_0) ).
fof(c_0_194,axiom,
! [X52,X36,X51,X49] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X51),X52),tc_nat)
| ~ c_HOL_Oord__class_Oless(X36,X52,tc_nat)
| ~ c_HOL_Oord__class_Oless(X49,X51,tc_nat) ),
file('<stdin>',cls_add__less__mono_0) ).
fof(c_0_195,axiom,
! [X2,X29,X13,X4] :
( c_List_Omap(X29,X2,X13,X4) != c_List_Olist_ONil(X4)
| X2 = c_List_Olist_ONil(X13) ),
file('<stdin>',cls_map__is__Nil__conv_0) ).
fof(c_0_196,axiom,
! [X2,X29,X13,X4] :
( c_List_Olist_ONil(X4) != c_List_Omap(X29,X2,X13,X4)
| X2 = c_List_Olist_ONil(X13) ),
file('<stdin>',cls_Nil__is__map__conv_0) ).
fof(c_0_197,axiom,
! [X2,X12,X4] : ~ c_ListOrder_Ostep1(X12,X2,c_List_Olist_ONil(X4),X4),
file('<stdin>',cls_not__step1__Nil_0) ).
fof(c_0_198,axiom,
! [X2,X12,X4] : ~ c_ListOrder_Ostep1(X12,c_List_Olist_ONil(X4),X2,X4),
file('<stdin>',cls_not__Nil__step1_0) ).
fof(c_0_199,axiom,
! [X32,X33,X60,X61] :
( c_Type_Otyping(X60,X32,X61)
| ~ c_Type_Otyping(X60,X33,X61)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X33),X32)) ),
file('<stdin>',cls_subject__reduction_H_0) ).
fof(c_0_200,axiom,
! [X17,X18,X16,X19,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X17)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X19)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X17) = X19 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_201,axiom,
! [X33,X28,X36] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X33),X36)),X28),X36) = X33,
file('<stdin>',cls_subst__lift_0) ).
fof(c_0_202,axiom,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X17,X18,X4)
| c_HOL_Oord__class_Oless(X17,X16,X4)
| ~ c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omax(X16,X18,X4),X4) ),
file('<stdin>',cls_less__max__iff__disj_0) ).
fof(c_0_203,axiom,
! [X33,X28,X6] : c_Lambda_Osubstn(X33,X28,X6) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),c_Lambda_Oliftn(X6,X28,c_HOL_Ozero__class_Ozero(tc_nat))),X6),
file('<stdin>',cls_substn__subst__n_0) ).
fof(c_0_204,axiom,
! [X6,X11,X36] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X36)),
file('<stdin>',cls_nat__add__assoc_0) ).
fof(c_0_205,axiom,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_206,axiom,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_207,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X8),X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_208,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X8),X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_209,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7),X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_210,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7),X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_211,axiom,
! [X7,X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X8,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7),X4)
| ~ c_HOL_Oord__class_Oless(X8,X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_212,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6),tc_nat) ),
file('<stdin>',cls_add__gr__0_0) ).
fof(c_0_213,axiom,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X16,X18,X4),X17,X4)
| ~ c_HOL_Oord__class_Oless(X18,X17,X4)
| ~ c_HOL_Oord__class_Oless(X16,X17,X4) ),
file('<stdin>',cls_max__less__iff__conj_2) ).
fof(c_0_214,axiom,
! [X65,X7,X8,X9,X4] :
( hAPP(hAPP(X65,hAPP(hAPP(X65,X9),X8)),X7) = hAPP(hAPP(X65,X9),hAPP(hAPP(X65,X8),X7))
| ~ c_OrderedGroup_Osemigroup__add(X65,X4) ),
file('<stdin>',cls_semigroup__add_Oadd__assoc_0) ).
fof(c_0_215,axiom,
! [X1,X2,X3,X4] :
( c_List_Olistsp(X3,c_List_Oappend(X2,X1,X4),X4)
| ~ c_List_Olistsp(X3,X1,X4)
| ~ c_List_Olistsp(X3,X2,X4) ),
file('<stdin>',cls_append__in__listsp__conv_2) ).
fof(c_0_216,axiom,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(X16,c_Orderings_Oord__class_Omax(X18,X17,X4),X4) = c_Orderings_Oord__class_Omax(X18,c_Orderings_Oord__class_Omax(X16,X17,X4),X4) ),
file('<stdin>',cls_min__max_Osup__left__commute_0) ).
fof(c_0_217,axiom,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X16,X18,X4),X17,X4) = c_Orderings_Oord__class_Omax(X16,c_Orderings_Oord__class_Omax(X18,X17,X4),X4) ),
file('<stdin>',cls_min__max_Osup__assoc_0) ).
fof(c_0_218,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X9,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),X4) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_219,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_220,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_221,axiom,
! [X2,X16,X46,X4] : c_List_Oappend(X2,c_List_Oappend(X16,X46,X4),X4) = c_List_Oappend(c_List_Oappend(X2,X16,X4),X46,X4),
file('<stdin>',cls_append__eq__append__conv2_5) ).
fof(c_0_222,axiom,
! [X30,X1,X16,X4] : c_List_Oappend(c_List_Oappend(X30,X16,X4),X1,X4) = c_List_Oappend(X30,c_List_Oappend(X16,X1,X4),X4),
file('<stdin>',cls_append__eq__append__conv2_4) ).
fof(c_0_223,axiom,
! [X37,X2,X48,X4] : c_List_Oappend(X2,c_List_Oappend(X37,X48,X4),X4) = c_List_Oappend(c_List_Oappend(X2,X37,X4),X48,X4),
file('<stdin>',cls_append__eq__appendI_0) ).
fof(c_0_224,axiom,
! [X30,X1,X2,X4] : c_List_Oappend(c_List_Oappend(X2,X1,X4),X30,X4) = c_List_Oappend(X2,c_List_Oappend(X1,X30,X4),X4),
file('<stdin>',cls_append__assoc_0) ).
fof(c_0_225,axiom,
! [X30,X37,X16,X4] : c_List_Olist_OCons(X16,c_List_Oappend(X37,X30,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X16,X37,X4),X30,X4),
file('<stdin>',cls_Cons__eq__appendI_0) ).
fof(c_0_226,axiom,
! [X30,X31,X16,X4] : c_List_Olist_OCons(X16,c_List_Oappend(X31,X30,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X16,X31,X4),X30,X4),
file('<stdin>',cls_Cons__eq__append__conv_5) ).
fof(c_0_227,axiom,
! [X1,X2,X16,X4] : c_List_Oappend(c_List_Olist_OCons(X16,X2,X4),X1,X4) = c_List_Olist_OCons(X16,c_List_Oappend(X2,X1,X4),X4),
file('<stdin>',cls_append__Cons_0) ).
fof(c_0_228,axiom,
! [X30,X31,X16,X4] : c_List_Oappend(c_List_Olist_OCons(X16,X31,X4),X30,X4) = c_List_Olist_OCons(X16,c_List_Oappend(X31,X30,X4),X4),
file('<stdin>',cls_append__eq__Cons__conv_5) ).
fof(c_0_229,axiom,
! [X6,X11,X36] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
file('<stdin>',cls_nat__add__left__cancel__less_1) ).
fof(c_0_230,axiom,
! [X36,X51,X49] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X51),X36),tc_nat)
| ~ c_HOL_Oord__class_Oless(X49,X51,tc_nat) ),
file('<stdin>',cls_add__less__mono1_0) ).
fof(c_0_231,axiom,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X18,X17,X4)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X16,X18,X4),X17,X4) ),
file('<stdin>',cls_max__less__iff__conj_1) ).
fof(c_0_232,axiom,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X16,X17,X4)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X16,X18,X4),X17,X4) ),
file('<stdin>',cls_max__less__iff__conj_0) ).
fof(c_0_233,axiom,
! [X17,X18,X16,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X17)) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_234,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_235,axiom,
! [X10,X7,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X10)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X10)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_236,axiom,
! [X18,X16,X12,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X16),X18))
| ~ hBOOL(hAPP(hAPP(X12,X16),X18)) ),
file('<stdin>',cls_r__into__rtranclp_0) ).
fof(c_0_237,axiom,
! [X33,X6,X36] : c_Lambda_Oliftn(c_Suc(X6),X33,X36) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X6,X33,X36)),X36),
file('<stdin>',cls_liftn__lift_0) ).
fof(c_0_238,axiom,
! [X1,X2,X3,X4] :
( c_List_Olistsp(X3,X1,X4)
| ~ c_List_Olistsp(X3,c_List_Oappend(X2,X1,X4),X4) ),
file('<stdin>',cls_append__in__listsp__conv_1) ).
fof(c_0_239,axiom,
! [X1,X2,X3,X4] :
( c_List_Olistsp(X3,X2,X4)
| ~ c_List_Olistsp(X3,c_List_Oappend(X2,X1,X4),X4) ),
file('<stdin>',cls_append__in__listsp__conv_0) ).
fof(c_0_240,axiom,
! [X6,X11,X52,X36] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X52) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X6)
| ~ c_HOL_Oord__class_Oless(X36,X52,tc_nat)
| c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
file('<stdin>',cls_less__add__eq__less_0) ).
fof(c_0_241,axiom,
! [X36,X51,X49] :
( c_HOL_Oord__class_Oless(X49,X36,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X51),X36,tc_nat) ),
file('<stdin>',cls_add__lessD1_0) ).
fof(c_0_242,axiom,
! [X17,X18,X16] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X17)),
file('<stdin>',cls_nat__add__left__commute_0) ).
fof(c_0_243,axiom,
! [X6,X9,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X9,X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
file('<stdin>',cls_zero__less__power_0) ).
fof(c_0_244,axiom,
! [X12,X8,X9,X4] :
( c_Wellfounded_Oaccp(X12,X9,X4)
| ~ hBOOL(hAPP(hAPP(X12,X9),X8))
| ~ c_Wellfounded_Oaccp(X12,X8,X4) ),
file('<stdin>',cls_accp__downward_0) ).
fof(c_0_245,axiom,
! [X18,X12,X9,X4] :
( c_Wellfounded_Oaccp(X12,X18,X4)
| ~ hBOOL(hAPP(hAPP(X12,X18),X9))
| ~ c_Wellfounded_Oaccp(X12,X9,X4) ),
file('<stdin>',cls_accp_Ocases_0) ).
fof(c_0_246,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_247,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_248,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_249,axiom,
! [X12] :
( hBOOL(hAPP(c_InductTermi_OIT,X12))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X12,tc_Lambda_OdB) ),
file('<stdin>',cls_termi__implies__IT_0) ).
fof(c_0_250,axiom,
! [X32,X33,X60,X61] :
( c_Type_Otyping(X60,X32,X61)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X33),X32))
| ~ c_Type_Otyping(X60,X33,X61) ),
file('<stdin>',cls_subject__reduction_0) ).
fof(c_0_251,axiom,
! [X1,X2,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(c_List_Oappend(X2,X1,X4),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_List_Olistsum(X2,X4)),c_List_Olistsum(X1,X4)) ),
file('<stdin>',cls_listsum__append_0) ).
fof(c_0_252,axiom,
! [X29,X13,X4] : c_List_Olist_ONil(X4) = c_List_Omap(X29,c_List_Olist_ONil(X13),X13,X4),
file('<stdin>',cls_Nil__is__map__conv_1) ).
fof(c_0_253,axiom,
! [X29,X13,X4] : c_List_Omap(X29,c_List_Olist_ONil(X13),X13,X4) = c_List_Olist_ONil(X4),
file('<stdin>',cls_map__is__Nil__conv_1) ).
fof(c_0_254,axiom,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omax(X16,X18,X4),X4)
| ~ c_HOL_Oord__class_Oless(X17,X18,X4) ),
file('<stdin>',cls_less__max__iff__disj_2) ).
fof(c_0_255,axiom,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omax(X16,X18,X4),X4)
| ~ c_HOL_Oord__class_Oless(X17,X16,X4) ),
file('<stdin>',cls_less__max__iff__disj_1) ).
fof(c_0_256,axiom,
! [X16,X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X16,c_Orderings_Oord__class_Omax(X9,X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X16,X8,X4) ),
file('<stdin>',cls_min__max_Oless__supI2_0) ).
fof(c_0_257,axiom,
! [X16,X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X16,c_Orderings_Oord__class_Omax(X9,X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X16,X9,X4) ),
file('<stdin>',cls_min__max_Oless__supI1_0) ).
fof(c_0_258,axiom,
! [X6,X11,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Nat_Osemiring__1__class_Oof__nat(X11,X4)),c_Nat_Osemiring__1__class_Oof__nat(X6,X4)) ),
file('<stdin>',cls_of__nat__add_0) ).
fof(c_0_259,axiom,
! [X16,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X16)),tc_nat),
file('<stdin>',cls_less__iff__Suc__add_1) ).
fof(c_0_260,axiom,
! [X11,X49] : c_HOL_Oord__class_Oless(X49,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X49)),tc_nat),
file('<stdin>',cls_less__add__Suc2_0) ).
fof(c_0_261,axiom,
! [X11,X49] : c_HOL_Oord__class_Oless(X49,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X11)),tc_nat),
file('<stdin>',cls_less__add__Suc1_0) ).
fof(c_0_262,axiom,
! [X33,X49] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X33),c_Lambda_OdB_OVar(X49))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_app__Var__IT_0) ).
fof(c_0_263,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
file('<stdin>',cls_add__gr__0_1) ).
fof(c_0_264,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
file('<stdin>',cls_add__gr__0_2) ).
fof(c_0_265,axiom,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X16,X17,X4)
| ~ c_HOL_Oord__class_Oless(X18,X17,X4)
| ~ c_HOL_Oord__class_Oless(X16,X18,X4) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_266,axiom,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X17,X16,X4)
| ~ c_HOL_Oord__class_Oless(X17,X18,X4)
| ~ c_HOL_Oord__class_Oless(X18,X16,X4) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_267,axiom,
! [X33,X28] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X28)),c_Lambda_OdB_OAbs(X33)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X33)) ),
file('<stdin>',cls_abs_0) ).
fof(c_0_268,axiom,
! [X6,X11,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X11,X4),c_Nat_Osemiring__1__class_Oof__nat(X6,X4),X4) ),
file('<stdin>',cls_of__nat__less__iff_0) ).
fof(c_0_269,axiom,
! [X36,X51,X49] :
( c_HOL_Oord__class_Oless(c_Suc(X49),X36,tc_nat)
| ~ c_HOL_Oord__class_Oless(X51,X36,tc_nat)
| ~ c_HOL_Oord__class_Oless(X49,X51,tc_nat) ),
file('<stdin>',cls_less__trans__Suc_0) ).
fof(c_0_270,axiom,
! [X11,X51,X49] :
( c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X51),tc_nat)
| ~ c_HOL_Oord__class_Oless(X49,X51,tc_nat) ),
file('<stdin>',cls_trans__less__add2_0) ).
fof(c_0_271,axiom,
! [X11,X51,X49] :
( c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X51),X11),tc_nat)
| ~ c_HOL_Oord__class_Oless(X49,X51,tc_nat) ),
file('<stdin>',cls_trans__less__add1_0) ).
fof(c_0_272,axiom,
! [X17,X18,X16] :
( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X17,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I2_J_0) ).
fof(c_0_273,axiom,
! [X17,X18,X16] :
( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X18,tc_nat) ),
file('<stdin>',cls_termination__basic__simps_I1_J_0) ).
fof(c_0_274,axiom,
! [X51,X49] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X51),X49),X49,tc_nat),
file('<stdin>',cls_not__add__less2_0) ).
fof(c_0_275,axiom,
! [X51,X49] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X51),X49,tc_nat),
file('<stdin>',cls_not__add__less1_0) ).
fof(c_0_276,axiom,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(X16,c_Orderings_Oord__class_Omax(X16,X18,X4),X4) = c_Orderings_Oord__class_Omax(X16,X18,X4) ),
file('<stdin>',cls_min__max_Osup__left__idem_0) ).
fof(c_0_277,axiom,
! [X2,X16,X4] : c_List_Oappend(c_List_Olist_ONil(X4),c_List_Olist_OCons(X16,X2,X4),X4) = c_List_Olist_OCons(X16,X2,X4),
file('<stdin>',cls_append__eq__Cons__conv_4) ).
fof(c_0_278,axiom,
! [X2,X16,X4] : c_List_Olist_OCons(X16,X2,X4) = c_List_Oappend(c_List_Olist_ONil(X4),c_List_Olist_OCons(X16,X2,X4),X4),
file('<stdin>',cls_Cons__eq__append__conv_4) ).
fof(c_0_279,axiom,
! [X16,X6,X4] : c_List_Oreplicate(c_Suc(X6),X16,X4) = c_List_Olist_OCons(X16,c_List_Oreplicate(X6,X16,X4),X4),
file('<stdin>',cls_replicate__Suc_0) ).
fof(c_0_280,axiom,
! [X33,X49] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X33),X49)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_lift__IT_0) ).
fof(c_0_281,axiom,
! [X6,X36,X49] :
( c_Lambda_Oliftn(X6,c_Lambda_OdB_OVar(X49),X36) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X6))
| c_HOL_Oord__class_Oless(X49,X36,tc_nat) ),
file('<stdin>',cls_liftn_Osimps_I1_J_1) ).
fof(c_0_282,axiom,
! [X2,X16,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(c_List_Olist_OCons(X16,X2,X4),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),c_List_Olistsum(X2,X4)) ),
file('<stdin>',cls_listsum_Osimps_I2_J_0) ).
fof(c_0_283,axiom,
! [X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Nat_Osemiring__1__class_Oof__nat(X6,X4),X4) ),
file('<stdin>',cls_of__nat__0__less__iff_0) ).
fof(c_0_284,axiom,
! [X19,X51,X49] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X51)),X19),X49) = c_Lambda_OdB_OVar(X51)
| ~ c_HOL_Oord__class_Oless(X51,X49,tc_nat) ),
file('<stdin>',cls_subst__lt_0) ).
fof(c_0_285,axiom,
! [X6,X11,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X11,X4),c_Nat_Osemiring__1__class_Oof__nat(X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
file('<stdin>',cls_of__nat__less__iff_1) ).
fof(c_0_286,axiom,
! [X33] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X33,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT__implies__termi_0) ).
fof(c_0_287,axiom,
! [X6,X11,X26] :
( hBOOL(hAPP(hAPP(X26,X6),X11))
| c_HOL_Oord__class_Oless(X6,X11,tc_nat)
| X11 = X6
| c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
file('<stdin>',cls_nat__less__cases_0) ).
fof(c_0_288,axiom,
! [X16,X12,X4] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X16),X16)),
file('<stdin>',cls_Nitpick_Ortranclp__def_1) ).
fof(c_0_289,axiom,
! [X12,X9,X4] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X9),X9)),
file('<stdin>',cls_rtranclp_Ortrancl__refl_0) ).
fof(c_0_290,axiom,
! [X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Nat_Osemiring__1__class_Oof__nat(X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
file('<stdin>',cls_of__nat__0__less__iff_1) ).
fof(c_0_291,axiom,
! [X17,X18,X16,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X17)
| X18 = X17 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_292,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_293,axiom,
! [X18,X16,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X18,X16,X4)
| ~ c_HOL_Oord__class_Oless(X16,X18,X4) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_294,axiom,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X16,X18,X4)
| ~ c_HOL_Oord__class_Oless(X18,X16,X4) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_295,axiom,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_296,axiom,
! [X18,X16,X6,X11,X4] :
( c_List_Oreplicate(X11,X16,X4) != c_List_Oreplicate(X6,X18,X4)
| X16 = X18
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_replicate__eq__replicate_1) ).
fof(c_0_297,axiom,
! [X6,X11] :
( ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X11),tc_nat) ),
file('<stdin>',cls_not__less__eq_1) ).
fof(c_0_298,axiom,
! [X38,X70,X39,X9,X4] :
( c_List_Olist_OCons(X9,X70,X4) != c_List_Olist_OCons(X39,X38,X4)
| X70 = X38 ),
file('<stdin>',cls_list_Oinject_1) ).
fof(c_0_299,axiom,
! [X38,X70,X39,X9,X4] :
( c_List_Olist_OCons(X9,X70,X4) != c_List_Olist_OCons(X39,X38,X4)
| X9 = X39 ),
file('<stdin>',cls_list_Oinject_0) ).
fof(c_0_300,axiom,
! [X30,X1,X2,X4] :
( c_List_Oappend(X2,X1,X4) != c_List_Oappend(X2,X30,X4)
| X1 = X30 ),
file('<stdin>',cls_same__append__eq_0) ).
fof(c_0_301,axiom,
! [X30,X1,X2,X4] :
( c_List_Oappend(X1,X2,X4) != c_List_Oappend(X30,X2,X4)
| X1 = X30 ),
file('<stdin>',cls_append__same__eq_0) ).
fof(c_0_302,axiom,
! [X18,X16,X6,X11,X4] :
( c_List_Oreplicate(X11,X16,X4) != c_List_Oreplicate(X6,X18,X4)
| X11 = X6 ),
file('<stdin>',cls_replicate__eq__replicate_0) ).
fof(c_0_303,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X9)
| X8 = X7 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_304,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)
| X8 = X7 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_305,axiom,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)
| X8 = X7 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_306,axiom,
! [X6,X11] : c_Orderings_Oord__class_Omax(c_Suc(X11),c_Suc(X6),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X11,X6,tc_nat)),
file('<stdin>',cls_max__Suc__Suc_0) ).
fof(c_0_307,axiom,
! [X16,X28] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X16),X28,X16) = c_Lambda_Oliftn(X16,X28,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_substn_Osimps_I1_J_1) ).
fof(c_0_308,axiom,
! [X86,X87,X4] :
( X87 = X86
| ~ hBOOL(hAPP(hAPP(c_fequal(X4),X87),X86)) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_309,axiom,
! [X28,X36,X49] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X49)),X28),X36) = c_Lambda_OdB_OVar(X49)
| X49 = X36
| c_HOL_Oord__class_Oless(X36,X49,tc_nat) ),
file('<stdin>',cls_subst__Var_2) ).
fof(c_0_310,axiom,
! [X16,X28] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X28),X16) = X28 ),
file('<stdin>',cls_subst__Var_1) ).
fof(c_0_311,axiom,
! [X12,X13,X4] : c_Predicate_Oconversep(c_Predicate_Oconversep(X12,X4,X13),X13,X4) = X12,
file('<stdin>',cls_conversep__conversep_0) ).
fof(c_0_312,axiom,
! [X33,X49] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X49)),X33)),
file('<stdin>',cls_beta__cases_I1_J_0) ).
fof(c_0_313,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X11),c_Suc(X6),tc_nat) ),
file('<stdin>',cls_Suc__less__eq_0) ).
fof(c_0_314,axiom,
! [X6,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X11)),X6) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)),
file('<stdin>',cls_add__Suc_0) ).
fof(c_0_315,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(c_Suc(X11),c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
file('<stdin>',cls_Suc__mono_0) ).
fof(c_0_316,axiom,
! [X16,X6] :
( c_HOL_Oord__class_Oless(c_Suc(X16),c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X6,tc_nat) ),
file('<stdin>',cls_less__Suc__eq__0__disj_3) ).
fof(c_0_317,axiom,
! [X6,X11] :
( X6 = X11
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X11),tc_nat)
| c_HOL_Oord__class_Oless(X6,X11,tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_0) ).
fof(c_0_318,axiom,
! [X6,X11] :
( X11 = X6
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X11),tc_nat)
| c_HOL_Oord__class_Oless(X6,X11,tc_nat) ),
file('<stdin>',cls_less__antisym_0) ).
fof(c_0_319,axiom,
! [X6,X11] :
( X11 = X6
| c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(X6),tc_nat) ),
file('<stdin>',cls_less__SucE_0) ).
fof(c_0_320,axiom,
! [X6,X36,X49] :
( c_Lambda_Oliftn(X6,c_Lambda_OdB_OVar(X49),X36) = c_Lambda_OdB_OVar(X49)
| ~ c_HOL_Oord__class_Oless(X49,X36,tc_nat) ),
file('<stdin>',cls_liftn_Osimps_I1_J_0) ).
fof(c_0_321,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(c_Suc(X11),X6,tc_nat)
| c_Suc(X11) = X6
| ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
file('<stdin>',cls_Suc__lessI_0) ).
fof(c_0_322,axiom,
! [X6,X11,X36] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X6)
| X11 = X6 ),
file('<stdin>',cls_nat__add__left__cancel_0) ).
fof(c_0_323,axiom,
! [X6,X11,X36] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X36) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X36)
| X11 = X6 ),
file('<stdin>',cls_nat__add__right__cancel_0) ).
fof(c_0_324,axiom,
! [X17,X18,X16] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X17)
| X18 = X17 ),
file('<stdin>',cls_natgb_Oadd__cancel_0) ).
fof(c_0_325,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X11),X6,tc_nat) ),
file('<stdin>',cls_Suc__lessD_0) ).
fof(c_0_326,axiom,
! [X33,X28] : c_Lambda_Osubstn(X33,X28,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X28),c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_substn__subst__0_0) ).
fof(c_0_327,axiom,
! [X6,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_Suc(X6)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)),
file('<stdin>',cls_add__Suc__right_0) ).
fof(c_0_328,axiom,
! [X11,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X11,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
file('<stdin>',cls_of__nat__less__0__iff_0) ).
fof(c_0_329,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(X11,c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
file('<stdin>',cls_less__SucI_0) ).
fof(c_0_330,axiom,
! [X36,X49] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X49)),X36) = c_Lambda_OdB_OVar(X49)
| ~ c_HOL_Oord__class_Oless(X49,X36,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_0) ).
fof(c_0_331,axiom,
! [X64,X65,X9,X4] :
( hAPP(hAPP(X65,X64),X9) = X9
| ~ c_OrderedGroup_Omonoid__add(X64,X65,X4) ),
file('<stdin>',cls_monoid__add_Oadd__0__left_0) ).
fof(c_0_332,axiom,
! [X64,X65,X9,X4] :
( hAPP(hAPP(X65,X9),X64) = X9
| ~ c_OrderedGroup_Omonoid__add(X64,X65,X4) ),
file('<stdin>',cls_monoid__add_Oadd__0__right_0) ).
fof(c_0_333,axiom,
! [X6,X9,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X9,X6,X4) != c_HOL_Ozero__class_Ozero(X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_power__eq__0__iff_0) ).
fof(c_0_334,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X9,c_HOL_Ozero__class_Ozero(tc_nat),X4) != c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_power__eq__0__iff_1) ).
fof(c_0_335,axiom,
! [X28,X36,X49] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X49),X28,X36) = c_Lambda_OdB_OVar(X49)
| X49 = X36
| c_HOL_Oord__class_Oless(X36,X49,tc_nat) ),
file('<stdin>',cls_substn_Osimps_I1_J_2) ).
fof(c_0_336,axiom,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| X16 = X18
| c_HOL_Oord__class_Oless(X16,X18,X4)
| c_HOL_Oord__class_Oless(X18,X16,X4) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_337,axiom,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X18,X16,X4)
| X16 = X18
| c_HOL_Oord__class_Oless(X16,X18,X4) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_338,axiom,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X18,X16,X4)
| c_HOL_Oord__class_Oless(X16,X18,X4)
| X16 = X18 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_339,axiom,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| X16 = X18
| c_HOL_Oord__class_Oless(X18,X16,X4)
| c_HOL_Oord__class_Oless(X16,X18,X4) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_340,axiom,
! [X18,X16,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X18,X16,X4)
| c_HOL_Oord__class_Oless(X16,X18,X4)
| X16 = X18 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_341,axiom,
! [X75,X72,X76,X73] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72) != hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75)
| X72 = X75 ),
file('<stdin>',cls_dB_Osimps_I2_J_1) ).
fof(c_0_342,axiom,
! [X75,X72,X76,X73] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72) != hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75)
| X73 = X76 ),
file('<stdin>',cls_dB_Osimps_I2_J_0) ).
fof(c_0_343,axiom,
! [X66,X67,X68,X69] :
( hAPP(hAPP(c_Type_Otype_OFun,X69),X67) != hAPP(hAPP(c_Type_Otype_OFun,X68),X66)
| X69 = X68 ),
file('<stdin>',cls_type_Osimps_I2_J_0) ).
fof(c_0_344,axiom,
! [X66,X67,X68,X69] :
( hAPP(hAPP(c_Type_Otype_OFun,X69),X67) != hAPP(hAPP(c_Type_Otype_OFun,X68),X66)
| X67 = X66 ),
file('<stdin>',cls_type_Osimps_I2_J_1) ).
fof(c_0_345,axiom,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(X16,X18,X4) = c_Orderings_Oord__class_Omax(X18,X16,X4) ),
file('<stdin>',cls_min__max_Osup__commute_0) ).
fof(c_0_346,axiom,
! [X18,X16,X4] : c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X16,X4) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X18,X4),
file('<stdin>',cls_replicate__eq__replicate_2) ).
fof(c_0_347,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(X6,c_Suc(X11),tc_nat)
| c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
file('<stdin>',cls_not__less__eq_0) ).
fof(c_0_348,axiom,
! [X16] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,c_Suc(X16),tc_nat) ),
file('<stdin>',cls_not__less__less__Suc__eq_1) ).
fof(c_0_349,axiom,
! [X18,X16,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X18) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X16) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_350,axiom,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X9) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_351,axiom,
! [X7,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X9) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_352,axiom,
! [X19,X36] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X36)),X19),X36) = X19,
file('<stdin>',cls_subst__eq_0) ).
fof(c_0_353,axiom,
! [X49,X60,X61] :
( hAPP(X60,X49) = X61
| ~ c_Type_Otyping(X60,c_Lambda_OdB_OVar(X49),X61) ),
file('<stdin>',cls_typing__elims_I1_J_0) ).
fof(c_0_354,axiom,
! [X6,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X11)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_Suc(X6)),
file('<stdin>',cls_add__Suc__shift_0) ).
fof(c_0_355,axiom,
! [X18,X16] :
( c_HOL_Oord__class_Oless(X18,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,X18,tc_nat)
| X16 = X18 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_356,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(X6,X11,tc_nat)
| c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| X11 = X6 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_357,axiom,
! [X6] :
( X6 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('<stdin>',cls_less__Suc0_0) ).
fof(c_0_358,axiom,
! [X16,X4] : hBOOL(hAPP(hAPP(c_fequal(X4),X16),X16)),
file('<stdin>',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(c_0_359,axiom,
! [X6,X9,X4] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X4)
| c_Power_Opower__class_Opower(X9,X6,X4) != c_HOL_Ozero__class_Ozero(X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_field__power__not__zero_0) ).
fof(c_0_360,axiom,
! [X16,X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X16 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X9)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_361,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9) != c_HOL_Ozero__class_Ozero(X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_362,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_1) ).
fof(c_0_363,axiom,
! [X6,X11] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_1) ).
fof(c_0_364,axiom,
! [X1,X2,X4] :
( c_List_Oappend(X2,X1,X4) != c_List_Olist_ONil(X4)
| X1 = c_List_Olist_ONil(X4) ),
file('<stdin>',cls_append__is__Nil__conv_1) ).
fof(c_0_365,axiom,
! [X1,X2,X4] :
( c_List_Oappend(X2,X1,X4) != c_List_Olist_ONil(X4)
| X2 = c_List_Olist_ONil(X4) ),
file('<stdin>',cls_append__is__Nil__conv_0) ).
fof(c_0_366,axiom,
! [X1,X2,X4] :
( c_List_Olist_ONil(X4) != c_List_Oappend(X2,X1,X4)
| X1 = c_List_Olist_ONil(X4) ),
file('<stdin>',cls_Nil__is__append__conv_1) ).
fof(c_0_367,axiom,
! [X1,X2,X4] :
( c_List_Olist_ONil(X4) != c_List_Oappend(X2,X1,X4)
| X2 = c_List_Olist_ONil(X4) ),
file('<stdin>',cls_Nil__is__append__conv_0) ).
fof(c_0_368,axiom,
! [X6,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),X6,X4) = c_HOL_Ozero__class_Ozero(X4)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__eq__0__iff_2) ).
fof(c_0_369,axiom,
! [X16,X6,X4] :
( c_List_Olist_ONil(X4) != c_List_Oreplicate(X6,X16,X4)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_empty__replicate_0) ).
fof(c_0_370,axiom,
! [X16,X6,X4] :
( c_List_Oreplicate(X6,X16,X4) != c_List_Olist_ONil(X4)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_replicate__empty_0) ).
fof(c_0_371,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_add__is__1_0) ).
fof(c_0_372,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_3) ).
fof(c_0_373,axiom,
! [X6,X11] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_one__is__add_0) ).
fof(c_0_374,axiom,
! [X6,X11] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_3) ).
fof(c_0_375,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_376,axiom,
! [X16,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X16,X16,X4) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_377,axiom,
! [X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X16,X16,X4) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_378,axiom,
! [X16,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X16,X16,X4) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_379,axiom,
! [X1,X2,X4] :
( X1 != c_List_Oappend(X2,X1,X4)
| X2 = c_List_Olist_ONil(X4) ),
file('<stdin>',cls_self__append__conv2_0) ).
fof(c_0_380,axiom,
! [X1,X2,X4] :
( c_List_Oappend(X2,X1,X4) != X1
| X2 = c_List_Olist_ONil(X4) ),
file('<stdin>',cls_append__self__conv2_0) ).
fof(c_0_381,axiom,
! [X1,X2,X4] :
( X2 != c_List_Oappend(X2,X1,X4)
| X1 = c_List_Olist_ONil(X4) ),
file('<stdin>',cls_self__append__conv_0) ).
fof(c_0_382,axiom,
! [X1,X2,X4] :
( c_List_Oappend(X2,X1,X4) != X2
| X1 = c_List_Olist_ONil(X4) ),
file('<stdin>',cls_append__self__conv_0) ).
fof(c_0_383,axiom,
! [X38,X39,X4] : c_List_Olist_ONil(X4) != c_List_Olist_OCons(X39,X38,X4),
file('<stdin>',cls_list_Osimps_I2_J_0) ).
fof(c_0_384,axiom,
! [X6,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X11),
file('<stdin>',cls_nat__add__commute_0) ).
fof(c_0_385,axiom,
! [X38,X39,X4] : c_List_Olist_OCons(X39,X38,X4) != c_List_Olist_ONil(X4),
file('<stdin>',cls_list_Osimps_I3_J_0) ).
fof(c_0_386,axiom,
! [X31,X16,X4] : c_List_Olist_OCons(X16,X31,X4) != c_List_Olist_ONil(X4),
file('<stdin>',cls_neq__Nil__conv_1) ).
fof(c_0_387,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__1_2) ).
fof(c_0_388,axiom,
! [X6,X11] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_one__is__add_2) ).
fof(c_0_389,axiom,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_not__less0_0) ).
fof(c_0_390,axiom,
! [X11] : ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('<stdin>',cls_gr__implies__not0_0) ).
fof(c_0_391,axiom,
! [X2,X16,X4] : X2 != c_List_Olist_OCons(X16,X2,X4),
file('<stdin>',cls_not__Cons__self_0) ).
fof(c_0_392,axiom,
! [X16,X33,X4] : c_List_Olist_OCons(X16,X33,X4) != X33,
file('<stdin>',cls_not__Cons__self2_0) ).
fof(c_0_393,axiom,
! [X16,X78] : c_Type_Otyping(X78,c_Lambda_OdB_OVar(X16),hAPP(X78,X16)),
file('<stdin>',cls_typing_OVar_0) ).
fof(c_0_394,axiom,
! [X6,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Suc(X6),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_power__0__Suc_0) ).
fof(c_0_395,axiom,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,X6,tc_nat),
file('<stdin>',cls_less__not__refl_0) ).
fof(c_0_396,axiom,
! [X16] : ~ c_HOL_Oord__class_Oless(X16,X16,tc_nat),
file('<stdin>',cls_nat__less__le_1) ).
fof(c_0_397,axiom,
! [X6,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),X6,X4) = c_HOL_Ozero__class_Ozero(X4)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_power__0__left_1) ).
fof(c_0_398,axiom,
! [X12] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X12)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X12)) ),
file('<stdin>',cls_Lambda_0) ).
fof(c_0_399,axiom,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_400,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_401,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_402,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_0) ).
fof(c_0_403,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__is__0_1) ).
fof(c_0_404,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != X11
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_add__eq__self__zero_0) ).
fof(c_0_405,axiom,
! [X16,X9] :
( X16 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X9)
| X9 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).
fof(c_0_406,axiom,
! [X16,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X16 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),c_HOL_Ozero__class_Ozero(X4)) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_407,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),X9) = X9 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_408,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),X9) = X9 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_409,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),X9) = X9 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_410,axiom,
! [X16,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),X16) = X16 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_411,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_412,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_413,axiom,
! [X4] : c_List_Oappend(c_List_Olist_ONil(X4),c_List_Olist_ONil(X4),X4) = c_List_Olist_ONil(X4),
file('<stdin>',cls_append__is__Nil__conv_2) ).
fof(c_0_414,axiom,
! [X4] : c_List_Olist_ONil(X4) = c_List_Oappend(c_List_Olist_ONil(X4),c_List_Olist_ONil(X4),X4),
file('<stdin>',cls_Nil__is__append__conv_2) ).
fof(c_0_415,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_416,axiom,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),c_HOL_Ozero__class_Ozero(X4)) = X9 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_417,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),c_HOL_Ozero__class_Ozero(X4)) = X9 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_418,axiom,
! [X9,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),c_HOL_Ozero__class_Ozero(X4)) = X9 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_419,axiom,
! [X4] : c_Predicate_Oconversep(c_fequal(X4),X4,X4) = c_fequal(X4),
file('<stdin>',cls_conversep__eq_0) ).
fof(c_0_420,axiom,
! [X20,X75,X76] : hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75) != c_Lambda_OdB_OVar(X20),
file('<stdin>',cls_dB_Osimps_I5_J_0) ).
fof(c_0_421,axiom,
! [X20,X75,X76] : c_Lambda_OdB_OVar(X20) != hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75),
file('<stdin>',cls_dB_Osimps_I4_J_0) ).
fof(c_0_422,axiom,
! [X55,X72,X73] : c_Lambda_OdB_OAbs(X55) != hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72),
file('<stdin>',cls_dB_Osimps_I9_J_0) ).
fof(c_0_423,axiom,
! [X55,X72,X73] : hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72) != c_Lambda_OdB_OAbs(X55),
file('<stdin>',cls_dB_Osimps_I8_J_0) ).
fof(c_0_424,axiom,
! [X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(X16,X16,X4) = X16 ),
file('<stdin>',cls_min__max_Osup__idem_0) ).
fof(c_0_425,axiom,
! [X16] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X16),tc_nat),
file('<stdin>',cls_gr0__conv__Suc_1) ).
fof(c_0_426,axiom,
! [X6] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X6),tc_nat),
file('<stdin>',cls_zero__less__Suc_0) ).
fof(c_0_427,axiom,
! [X16,X4] : c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X16,X4) = c_List_Olist_ONil(X4),
file('<stdin>',cls_replicate__empty_1) ).
fof(c_0_428,axiom,
! [X16,X4] : c_List_Olist_ONil(X4) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X16,X4),
file('<stdin>',cls_empty__replicate_1) ).
fof(c_0_429,axiom,
! [X1,X4] : X1 = c_List_Oappend(c_List_Olist_ONil(X4),X1,X4),
file('<stdin>',cls_self__append__conv2_1) ).
fof(c_0_430,axiom,
! [X1,X4] : c_List_Oappend(c_List_Olist_ONil(X4),X1,X4) = X1,
file('<stdin>',cls_append__Nil_0) ).
fof(c_0_431,axiom,
! [X2,X4] : X2 = c_List_Oappend(X2,c_List_Olist_ONil(X4),X4),
file('<stdin>',cls_self__append__conv_1) ).
fof(c_0_432,axiom,
! [X16,X4] : X16 = c_List_Oappend(c_List_Olist_ONil(X4),X16,X4),
file('<stdin>',cls_eq__Nil__appendI_0) ).
fof(c_0_433,axiom,
! [X2,X4] : c_List_Oappend(X2,c_List_Olist_ONil(X4),X4) = X2,
file('<stdin>',cls_append__Nil2_0) ).
fof(c_0_434,axiom,
! [X3,X4] : c_List_Olistsp(X3,c_List_Olist_ONil(X4),X4),
file('<stdin>',cls_listsp_ONil_0) ).
fof(c_0_435,axiom,
! [X6] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_gr0I_0) ).
fof(c_0_436,axiom,
! [X16] : c_HOL_Oord__class_Oless(X16,c_Suc(X16),tc_nat),
file('<stdin>',cls_less__Suc__eq_2) ).
fof(c_0_437,axiom,
! [X6] : c_HOL_Oord__class_Oless(X6,c_Suc(X6),tc_nat),
file('<stdin>',cls_lessI_0) ).
fof(c_0_438,axiom,
! [X33,X36] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X33,X36) = X33,
file('<stdin>',cls_liftn__0_0) ).
fof(c_0_439,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_440,axiom,
! [X6] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) = X6,
file('<stdin>',cls_max__0L_0) ).
fof(c_0_441,axiom,
! [X6] : c_Orderings_Oord__class_Omax(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6,
file('<stdin>',cls_max__0R_0) ).
fof(c_0_442,axiom,
! [X12,X4] : c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X12,X4),X4) = c_Transitive__Closure_Ortranclp(X12,X4),
file('<stdin>',cls_rtranclp__idemp_0) ).
fof(c_0_443,axiom,
! [X6,X11,X4] :
( ~ class_Nat_Osemiring__char__0(X4)
| c_Nat_Osemiring__1__class_Oof__nat(X11,X4) != c_Nat_Osemiring__1__class_Oof__nat(X6,X4)
| X11 = X6 ),
file('<stdin>',cls_of__nat__eq__iff_0) ).
fof(c_0_444,axiom,
! [X6] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X6) = X6,
file('<stdin>',cls_plus__nat_Oadd__0_0) ).
fof(c_0_445,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('<stdin>',cls_uT_0) ).
fof(c_0_446,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
file('<stdin>',cls_Beta_I7_J_0) ).
fof(c_0_447,axiom,
! [X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Ozero__class_Ozero(tc_nat)) = X11,
file('<stdin>',cls_Nat_Oadd__0__right_0) ).
fof(c_0_448,axiom,
! [X16] : X16 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Ozero__class_Ozero(tc_nat)),
file('<stdin>',cls_natgb_Oadd__r0__iff_1) ).
fof(c_0_449,axiom,
! [X6] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X6))),
file('<stdin>',cls_Var__IT_0) ).
fof(c_0_450,axiom,
! [X84,X85] :
( class_Orderings_Oorder(tc_fun(X84,X85))
| ~ class_Orderings_Oorder(X85) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_451,axiom,
! [X84,X85] :
( class_Orderings_Opreorder(tc_fun(X84,X85))
| ~ class_Orderings_Opreorder(X85) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_452,axiom,
! [X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(c_List_Olist_ONil(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_listsum_Osimps_I1_J_0) ).
fof(c_0_453,axiom,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4) ),
file('<stdin>',cls_of__nat__0_0) ).
fof(c_0_454,axiom,
! [X4] :
( ~ class_OrderedGroup_Osemigroup__add(X4)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X4),X4) ),
file('<stdin>',cls_semigroup__add__class_Oaxioms_0) ).
fof(c_0_455,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
file('<stdin>',cls_Beta_I3_J_0) ).
fof(c_0_456,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('<stdin>',cls_uIT_0) ).
fof(c_0_457,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
file('<stdin>',cls_Beta_I6_J_0) ).
fof(c_0_458,axiom,
! [X54,X20] :
( c_Lambda_OdB_OVar(X20) != c_Lambda_OdB_OVar(X54)
| X20 = X54 ),
file('<stdin>',cls_dB_Osimps_I1_J_0) ).
fof(c_0_459,axiom,
! [X55,X50] :
( c_Lambda_OdB_OAbs(X50) != c_Lambda_OdB_OAbs(X55)
| X50 = X55 ),
file('<stdin>',cls_dB_Osimps_I3_J_0) ).
fof(c_0_460,axiom,
! [X54,X20] :
( c_Suc(X20) != c_Suc(X54)
| X20 = X54 ),
file('<stdin>',cls_nat_Oinject_0) ).
fof(c_0_461,axiom,
! [X18,X16] :
( c_Suc(X16) != c_Suc(X18)
| X16 = X18 ),
file('<stdin>',cls_Suc__inject_0) ).
fof(c_0_462,axiom,
! [X20,X55] : c_Lambda_OdB_OAbs(X55) != c_Lambda_OdB_OVar(X20),
file('<stdin>',cls_dB_Osimps_I7_J_0) ).
fof(c_0_463,axiom,
! [X20,X55] : c_Lambda_OdB_OVar(X20) != c_Lambda_OdB_OAbs(X55),
file('<stdin>',cls_dB_Osimps_I6_J_0) ).
fof(c_0_464,axiom,
! [X54] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X54),
file('<stdin>',cls_nat_Osimps_I2_J_0) ).
fof(c_0_465,axiom,
! [X11] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X11),
file('<stdin>',cls_Zero__neq__Suc_0) ).
fof(c_0_466,axiom,
! [X54] : c_Suc(X54) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_nat_Osimps_I3_J_0) ).
fof(c_0_467,axiom,
! [X11] : c_Suc(X11) != c_HOL_Ozero__class_Ozero(tc_nat),
file('<stdin>',cls_Suc__neq__Zero_0) ).
fof(c_0_468,axiom,
! [X6] : X6 != c_Suc(X6),
file('<stdin>',cls_n__not__Suc__n_0) ).
fof(c_0_469,axiom,
! [X6] : c_Suc(X6) != X6,
file('<stdin>',cls_Suc__n__not__n_0) ).
fof(c_0_470,axiom,
class_Orderings_Oorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Oorder) ).
fof(c_0_471,axiom,
class_Orderings_Opreorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Opreorder) ).
fof(c_0_472,axiom,
class_Power_Opower(tc_nat),
file('<stdin>',clsarity_nat__Power_Opower) ).
fof(c_0_473,axiom,
class_Orderings_Oorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Oorder) ).
fof(c_0_474,axiom,
class_Orderings_Olinorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Olinorder) ).
fof(c_0_475,axiom,
class_Orderings_Opreorder(tc_nat),
file('<stdin>',clsarity_nat__Orderings_Opreorder) ).
fof(c_0_476,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('<stdin>',clsarity_nat__Nat_Osemiring__char__0) ).
fof(c_0_477,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(c_0_478,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(c_0_479,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(c_0_480,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(c_0_481,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(c_0_482,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(c_0_483,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(c_0_484,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(c_0_485,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(c_0_486,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(c_0_487,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('<stdin>',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(c_0_488,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(c_0_489,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(c_0_490,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(c_0_491,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_492,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('<stdin>',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(c_0_493,plain,
! [X19,X49,X60,X82] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X19),X49)))
| ~ c_Type_Otyping(X60,X19,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
| ~ c_Type_Otyping(c_Type_Oshift(X60,X49,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X82) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_494,axiom,
! [X19,X46,X33,X49] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB)),X19),X49) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X19),X49),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X19,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X49,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X46,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_1 ).
fof(c_0_495,plain,
! [X48,X46,X49,X60,X62,X63,X61] :
( X62 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X61,X62,X60,X48),X61,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X62)
| ~ c_Type_Otypings(X60,X46,X63)
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X48,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_496,plain,
! [X19,X46,X49,X60,X63,X61] :
( c_Type_Otypings(X60,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X19,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X49,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X46,tc_Lambda_OdB,tc_Lambda_OdB),X63)
| ~ c_Type_Otypings(c_Type_Oshift(X60,X49,X61,tc_Type_Otype),X46,X63)
| ~ c_Type_Otyping(X60,X19,X61) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_497,plain,
! [X48,X46,X49,X60,X62,X63,X61] :
( c_Type_Otypings(X60,X48,c_Type_Osko__Type__Xvar__app__types__1__1(X61,X62,X60,X48))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X62)
| ~ c_Type_Otypings(X60,X46,X63)
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X48,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_498,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,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)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_5 ).
fof(c_0_499,plain,
! [X77,X5,X12] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X5,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X77,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X5,X77,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_500,plain,
! [X77,X28,X12] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X77,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_501,plain,
! [X77,X28,X12] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X77,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_502,plain,
! [X77,X28,X12] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12)),X28),X77,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X28))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X28),c_HOL_Ozero__class_Ozero(tc_nat)),X77,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_503,axiom,
! [X46,X33,X49] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB)),X49) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X33),X49),c_List_Omap(c_COMBC(c_Lambda_Olift,X49,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X46,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_10 ).
fof(c_0_504,plain,
! [X56,X57,X40,X41,X43,X44,X59,X58,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),hAPP(hAPP(X44,X57),X56)) = hAPP(hAPP(X44,X57),hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),X56))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_505,plain,
! [X56,X57,X40,X41,X43,X44,X59,X58,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),hAPP(hAPP(X44,X57),X56)) = hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X57)),hAPP(hAPP(X44,X59),X56))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_506,plain,
! [X56,X57,X40,X41,X43,X44,X59,X58,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),hAPP(hAPP(X44,X57),X56)) = hAPP(hAPP(X44,X58),hAPP(hAPP(X44,X59),hAPP(hAPP(X44,X57),X56)))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_507,plain,
! [X40,X41,X43,X44,X10,X7,X8,X45,X9,X4] :
( hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X8)),hAPP(hAPP(X45,X7),X10)) = hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X7)),hAPP(hAPP(X45,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_508,plain,
! [X40,X41,X43,X44,X11,X8,X45,X9,X4] :
( hAPP(hAPP(X45,hAPP(hAPP(X44,X9),X11)),hAPP(hAPP(X44,X8),X11)) = hAPP(hAPP(X44,hAPP(hAPP(X45,X9),X8)),X11)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_509,plain,
! [X40,X41,X43,X44,X7,X8,X45,X9,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X45,X9),X8)),X7) = hAPP(hAPP(X45,hAPP(hAPP(X44,X9),X7)),hAPP(hAPP(X44,X8),X7))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_510,plain,
! [X18,X16,X40,X41,X42,X43,X44,X45,X4] :
( hAPP(hAPP(X43,hAPP(hAPP(X44,X16),X18)),X42) = hAPP(hAPP(X44,hAPP(hAPP(X43,X16),X42)),hAPP(hAPP(X43,X18),X42))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_511,plain,
! [X16,X40,X41,X42,X43,X53,X44,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X43,X16),X53)),hAPP(hAPP(X43,X16),X42)) = hAPP(hAPP(X43,X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X53),X42))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_512,plain,
! [X40,X41,X43,X44,X11,X45,X9,X4] :
( hAPP(hAPP(X45,hAPP(hAPP(X44,X9),X11)),X11) = hAPP(hAPP(X44,hAPP(hAPP(X45,X9),X40)),X11)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_513,plain,
! [X57,X40,X41,X43,X44,X59,X58,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),X57) = hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X57)),X59)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_514,plain,
! [X40,X41,X43,X44,X7,X8,X45,X9,X4] :
( hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X8)),X7) = hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X7)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_515,plain,
! [X17,X18,X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X16),hAPP(hAPP(X45,X18),X17)) = hAPP(hAPP(X45,hAPP(hAPP(X44,X16),X18)),hAPP(hAPP(X44,X16),X17))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_516,plain,
! [X40,X41,X43,X44,X11,X45,X9,X4] :
( hAPP(hAPP(X45,X11),hAPP(hAPP(X44,X9),X11)) = hAPP(hAPP(X44,hAPP(hAPP(X45,X9),X40)),X11)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_517,plain,
! [X57,X40,X41,X43,X44,X59,X58,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X59)),X57) = hAPP(hAPP(X44,X58),hAPP(hAPP(X44,X59),X57))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_518,plain,
! [X56,X57,X40,X41,X43,X44,X58,X45,X4] :
( hAPP(hAPP(X44,X58),hAPP(hAPP(X44,X57),X56)) = hAPP(hAPP(X44,hAPP(hAPP(X44,X58),X57)),X56)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_519,plain,
! [X40,X41,X43,X44,X7,X8,X45,X9,X4] :
( hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X8)),X7) = hAPP(hAPP(X45,X9),hAPP(hAPP(X45,X8),X7))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_520,plain,
! [X40,X41,X43,X44,X10,X7,X45,X9,X4] :
( hAPP(hAPP(X45,X9),hAPP(hAPP(X45,X7),X10)) = hAPP(hAPP(X45,hAPP(hAPP(X45,X9),X7)),X10)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_521,plain,
! [X17,X18,X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X45,X16),hAPP(hAPP(X45,X18),X17)) = hAPP(hAPP(X45,hAPP(hAPP(X45,X16),X18)),X17)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_522,plain,
! [X17,X18,X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X16),hAPP(hAPP(X44,X18),X17)) = hAPP(hAPP(X44,hAPP(hAPP(X44,X16),X18)),X17)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_523,plain,
! [X16,X40,X41,X42,X43,X44,X45,X4] :
( hAPP(hAPP(X44,hAPP(hAPP(X43,X16),X42)),X16) = hAPP(hAPP(X43,X16),c_Suc(X42))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_524,plain,
! [X40,X41,X43,X44,X11,X45,X4] :
( hAPP(hAPP(X45,X11),X11) = hAPP(hAPP(X44,hAPP(hAPP(X45,X40),X40)),X11)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_525,plain,
! [X56,X57,X40,X41,X43,X44,X58,X45,X4] :
( hAPP(hAPP(X44,X58),hAPP(hAPP(X44,X57),X56)) = hAPP(hAPP(X44,X57),hAPP(hAPP(X44,X58),X56))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_526,plain,
! [X40,X41,X43,X44,X10,X7,X45,X9,X4] :
( hAPP(hAPP(X45,X9),hAPP(hAPP(X45,X7),X10)) = hAPP(hAPP(X45,X7),hAPP(hAPP(X45,X9),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_527,plain,
! [X16,X40,X41,X43,X6,X44,X45,X4] :
( hAPP(hAPP(X43,X16),c_Suc(X6)) = hAPP(hAPP(X44,X16),hAPP(hAPP(X43,X16),X6))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_528,plain,
! [X16,X40,X41,X42,X43,X44,X45,X4] :
( hAPP(hAPP(X43,X16),c_Suc(X42)) = hAPP(hAPP(X44,X16),hAPP(hAPP(X43,X16),X42))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_529,plain,
! [X16,X40,X41,X42,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X16),hAPP(hAPP(X43,X16),X42)) = hAPP(hAPP(X43,X16),c_Suc(X42))
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_530,plain,
! [X40,X41,X43,X44,X8,X45,X9,X4] :
( hAPP(hAPP(X44,X9),X8) = hAPP(hAPP(X44,X8),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_531,plain,
! [X40,X41,X43,X44,X7,X45,X9,X4] :
( hAPP(hAPP(X45,X9),X7) = hAPP(hAPP(X45,X7),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_532,plain,
! [X18,X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X45,X16),X18) = hAPP(hAPP(X45,X18),X16)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_533,plain,
! [X18,X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X16),X18) = hAPP(hAPP(X44,X18),X16)
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_534,plain,
! [X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X43,X16),c_HOL_Ozero__class_Ozero(tc_nat)) = X40
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_535,plain,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X45,X41),X9) = X9
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_536,plain,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X45,X9),X41) = X9
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_537,plain,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X44,X41),X9) = X41
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_538,plain,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X44,X9),X41) = X41
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_539,plain,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X44,X40),X9) = X9
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_540,plain,
! [X40,X41,X43,X44,X45,X9,X4] :
( hAPP(hAPP(X44,X9),X40) = X9
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_541,plain,
! [X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X45,X41),X16) = X16
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_542,plain,
! [X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X41),X16) = X41
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_543,plain,
! [X16,X40,X41,X43,X44,X45,X4] :
( hAPP(hAPP(X44,X40),X16) = X16
| ~ c_Groebner__Basis_Ogb__semiring(X45,X44,X43,X41,X40,X4) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_544,axiom,
! [X21,X22,X23,X72,X73,X4] : c_Lambda_OdB_OdB__rec(X23,X22,X21,hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72),X4) = hAPP(hAPP(hAPP(hAPP(X22,X73),X72),c_Lambda_OdB_OdB__rec(X23,X22,X21,X73,X4)),c_Lambda_OdB_OdB__rec(X23,X22,X21,X72,X4)),
c_0_51 ).
fof(c_0_545,plain,
! [X21,X22,X23,X72,X73,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72),t_a)))
| hBOOL(hAPP(X26,hAPP(hAPP(X22,X73),X72))) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_546,plain,
! [X74,X35,X21,X22,X23,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,hAPP(hAPP(c_Lambda_OdB_OApp,X35),X74),t_a)))
| hBOOL(hAPP(X26,hAPP(hAPP(X22,X35),X74))) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_547,plain,
! [X46,X49,X60,X62,X61] :
( X61 = X62
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X62)
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_548,plain,
! [X71,X21,X22,X23,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OVar(X71),t_a)))
| hBOOL(hAPP(X26,hAPP(X23,X71))) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_549,plain,
! [X20,X21,X22,X23,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OVar(X20),t_a)))
| hBOOL(hAPP(X26,hAPP(X23,X20))) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_550,plain,
! [X31,X21,X22,X23,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OAbs(X31),t_a)))
| hBOOL(hAPP(X26,hAPP(X21,X31))) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_551,plain,
! [X21,X22,X23,X50,X26] :
( ~ hBOOL(hAPP(X26,c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OAbs(X50),t_a)))
| hBOOL(hAPP(X26,hAPP(X21,X50))) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_552,plain,
! [X77,X28,X12] :
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X28),c_HOL_Ozero__class_Ozero(tc_nat)),X77,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X28,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(X12)),X28),X77,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_553,plain,
! [X46,X49,X60,X61] :
( c_Type_Otyping(X60,c_Lambda_OdB_OVar(X49),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X61,X60,X49,X46),X61,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_554,plain,
! [X46,X33,X60,X61] :
( c_Type_Otyping(X60,X33,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X61,X60,X33,X46),X61,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_555,plain,
! [X46,X33,X60,X61] :
( c_Type_Otyping(X60,X33,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X61,X60,X33,X46),X61,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_556,plain,
! [X46,X33,X60,X63,X61] :
( c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB),X61)
| ~ c_Type_Otypings(X60,X46,X63)
| ~ c_Type_Otyping(X60,X33,c_List_Ofoldr(c_Type_Otype_OFun,X63,X61,tc_Type_Otype,tc_Type_Otype)) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_557,plain,
! [X46,X49,X60,X62,X63] :
( c_Type_Otypings(c_Type_Oshift(X60,X49,X62,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X49,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X46,tc_Lambda_OdB,tc_Lambda_OdB),X63)
| ~ c_Type_Otypings(X60,X46,X63) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_558,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_65 ).
fof(c_0_559,plain,
! [X46] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X46,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X46,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_560,plain,
! [X5,X6] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X5,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X5,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_561,axiom,
! [X1,X2,X29,X9,X13,X4] : c_List_Ofoldl(X29,X9,c_List_Oappend(X2,X1,X13),X4,X13) = c_List_Ofoldl(X29,c_List_Ofoldl(X29,X9,X2,X4,X13),X1,X4,X13),
c_0_68 ).
fof(c_0_562,axiom,
! [X1,X2,X29,X9,X13,X4] : c_List_Ofoldr(X29,c_List_Oappend(X2,X1,X13),X9,X13,X4) = c_List_Ofoldr(X29,X2,c_List_Ofoldr(X29,X1,X9,X13,X4),X13,X4),
c_0_69 ).
fof(c_0_563,plain,
! [X46,X49,X60,X61] :
( c_Type_Otypings(X60,X46,c_Type_Osko__Type__Xvar__app__typesE__1__1(X61,X60,X49,X46))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X49),X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_564,plain,
! [X46,X33,X60,X61] :
( c_Type_Otypings(X60,X46,c_Type_Osko__Type__Xlist__app__typeE__1__1(X61,X60,X33,X46))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_565,plain,
! [X46,X33,X60,X61] :
( c_Type_Otypings(X60,X46,c_Type_Osko__Type__Xlist__app__typeD__1__1(X61,X60,X33,X46))
| ~ c_Type_Otyping(X60,c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB),X61) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_566,axiom,
! [X77,X28,X5,X12] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),X5,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X28),X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X5 = X77 ),
c_0_73 ).
fof(c_0_567,axiom,
! [X77,X28,X5,X12] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),X5,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X28),X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X12 = X28 ),
c_0_74 ).
fof(c_0_568,axiom,
! [X77,X5,X6,X11] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X5,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X5 = X77 ),
c_0_75 ).
fof(c_0_569,axiom,
! [X77,X5,X6,X11] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X5,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X11 = X6 ),
c_0_76 ).
fof(c_0_570,plain,
! [X30,X18,X16,X4] :
( ~ class_OrderedGroup_Osemigroup__add(X4)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X18),X30,X4,X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),X18,X30,X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_571,axiom,
! [X46,X77,X12,X6] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),X77,tc_Lambda_OdB,tc_Lambda_OdB),
c_0_78 ).
fof(c_0_572,axiom,
! [X46,X28,X12] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X46,tc_Lambda_OdB,tc_Lambda_OdB)
| X12 = X28 ),
c_0_79 ).
fof(c_0_573,axiom,
! [X2,X16,X29,X9,X13,X4] : c_List_Ofoldr(X29,c_List_Olist_OCons(X16,X2,X13),X9,X13,X4) = hAPP(hAPP(X29,X16),c_List_Ofoldr(X29,X2,X9,X13,X4)),
c_0_80 ).
fof(c_0_574,plain,
! [X30,X18,X16,X65,X4] :
( c_List_Ofoldl(X65,hAPP(hAPP(X65,X16),X18),X30,X4,X4) = hAPP(hAPP(X65,X16),c_List_Ofoldl(X65,X18,X30,X4,X4))
| ~ c_OrderedGroup_Osemigroup__add(X65,X4) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_575,plain,
! [X30,X64,X16,X65,X4] :
( hAPP(hAPP(X65,X16),c_List_Ofoldl(X65,X64,X30,X4,X4)) = c_List_Ofoldl(X65,X16,X30,X4,X4)
| ~ c_OrderedGroup_Omonoid__add(X64,X65,X4) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_576,plain,
! [X30,X16,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4),X30,X4,X4)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),X16,X30,X4,X4) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_577,plain,
! [X2,X9,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),X9,X2,X4,X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X4),X2,c_HOL_Ozero__class_Ozero(X4),X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_578,axiom,
! [X21,X22,X23,X50,X4] : c_Lambda_OdB_OdB__rec(X23,X22,X21,c_Lambda_OdB_OAbs(X50),X4) = hAPP(hAPP(X21,X50),c_Lambda_OdB_OdB__rec(X23,X22,X21,X50,X4)),
c_0_85 ).
fof(c_0_579,axiom,
! [X46,X33,X28,X12] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X12),X28) != c_List_Ofoldl(c_Lambda_OdB_OApp,X33,X46,tc_Lambda_OdB,tc_Lambda_OdB)
| X12 = c_List_Ofoldl(c_Lambda_OdB_OApp,X33,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X12,X28,X33,X46),tc_Lambda_OdB,tc_Lambda_OdB)
| X46 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_86 ).
fof(c_0_580,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_87 ).
fof(c_0_581,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_88 ).
fof(c_0_582,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_89 ).
fof(c_0_583,axiom,
! [X2,X16,X29,X9,X13,X4] : c_List_Ofoldl(X29,X9,c_List_Olist_OCons(X16,X2,X13),X4,X13) = c_List_Ofoldl(X29,hAPP(hAPP(X29,X9),X16),X2,X4,X13),
c_0_90 ).
fof(c_0_584,axiom,
! [X24,X25,X26,X27,X13,X4] : hAPP(c_COMBC(X26,X25,X13,X27,X4),X24) = hAPP(hAPP(X26,X24),X25),
c_0_91 ).
fof(c_0_585,plain,
! [X2,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4),X2,X4,X4) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X4),X2,c_HOL_Ozero__class_Ozero(X4),X4,X4) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_586,plain,
! [X2,X9,X4] :
( ~ class_OrderedGroup_Oab__semigroup__add(X4)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X4),X2,X9,X4,X4) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),X9,X2,X4,X4) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_587,plain,
! [X19,X33,X60,X61] :
( c_Type_Otyping(X60,X33,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X61,X60,X33,X19)),X61))
| ~ c_Type_Otyping(X60,hAPP(hAPP(c_Lambda_OdB_OApp,X33),X19),X61) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_588,axiom,
! [X33,X28,X12] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X12),X28) != c_List_Ofoldl(c_Lambda_OdB_OApp,X33,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X12),X28) = X33 ),
c_0_95 ).
fof(c_0_589,axiom,
! [X33,X77,X28,X6] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X28)),X33) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X6),X77,tc_Lambda_OdB,tc_Lambda_OdB),
c_0_96 ).
fof(c_0_590,axiom,
! [X77,X28,X12] :
( c_Lambda_OdB_OAbs(X12) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X12) = X28 ),
c_0_97 ).
fof(c_0_591,axiom,
! [X77,X28,X11] :
( c_Lambda_OdB_OVar(X11) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X11) = X28 ),
c_0_98 ).
fof(c_0_592,axiom,
! [X77,X28,X12] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X12)
| X28 = c_Lambda_OdB_OAbs(X12) ),
c_0_99 ).
fof(c_0_593,axiom,
! [X77,X28,X11] :
( c_Lambda_OdB_OVar(X11) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X77 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_100 ).
fof(c_0_594,axiom,
! [X77,X28,X12] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X12)
| X77 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_101 ).
fof(c_0_595,axiom,
! [X77,X28,X12] :
( c_Lambda_OdB_OAbs(X12) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X77,tc_Lambda_OdB,tc_Lambda_OdB)
| X77 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_102 ).
fof(c_0_596,plain,
! [X18,X16,X12,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X18),X16))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X12,X4,X4),X4),X16),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_597,plain,
! [X1,X18,X2,X16,X12,X4] :
( hBOOL(hAPP(hAPP(X12,X18),X16))
| c_ListOrder_Ostep1(X12,X1,X2,X4)
| ~ c_ListOrder_Ostep1(X12,c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_598,plain,
! [X1,X18,X2,X16,X12,X4] :
( X1 = X2
| c_ListOrder_Ostep1(X12,X1,X2,X4)
| ~ c_ListOrder_Ostep1(X12,c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_599,plain,
! [X1,X18,X2,X16,X12,X4] :
( hBOOL(hAPP(hAPP(X12,X18),X16))
| X18 = X16
| ~ c_ListOrder_Ostep1(X12,c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_600,axiom,
! [X49,X60,X62,X61,X4] : c_Type_Oshift(c_Type_Oshift(X60,X49,X62,X4),c_HOL_Ozero__class_Ozero(tc_nat),X61,X4) = c_Type_Oshift(c_Type_Oshift(X60,c_HOL_Ozero__class_Ozero(tc_nat),X61,X4),c_Suc(X49),X62,X4),
c_0_107 ).
fof(c_0_601,plain,
! [X1,X18,X2,X16,X12,X4] :
( X1 = X2
| X18 = X16
| ~ c_ListOrder_Ostep1(X12,c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_602,plain,
! [X19,X33,X49,X60,X79,X80,X81] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X81),X80)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X19),X49)))
| ~ c_Type_Otyping(X60,X19,X81)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
| ~ c_Type_Otyping(c_Type_Oshift(X60,X49,X81,tc_Type_Otype),X33,X79)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_603,plain,
! [X19,X33,X49,X60,X79,X80,X81] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X81),X80)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X19),X49)))
| ~ c_Type_Otyping(X60,X19,X80)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
| ~ c_Type_Otyping(c_Type_Oshift(X60,X49,X80,tc_Type_Otype),X33,X79)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_604,plain,
! [X33,X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X12),X49)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X28),X49)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_605,plain,
! [X33,X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X33),X49)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X33),X49)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_606,axiom,
! [X1,X2,X29,X13,X4] : c_List_Omap(X29,c_List_Oappend(X2,X1,X13),X13,X4) = c_List_Oappend(c_List_Omap(X29,X2,X13,X4),c_List_Omap(X29,X1,X13,X4),X4),
c_0_113 ).
fof(c_0_607,plain,
! [X18,X16,X12,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X12,X4,X4),X4),X16),X18))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X18),X16)) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_608,plain,
! [X19,X49,X60,X82] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X19),X49)))
| ~ c_Type_Otyping(X60,X19,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
| ~ c_Type_Otyping(c_Type_Oshift(X60,X49,v_T____,tc_Type_Otype),v_a____,X82) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_609,axiom,
! [X21,X22,X23,X72,X73,X4] : c_Lambda_OdB_OdB__case(X23,X22,X21,hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72),X4) = hAPP(hAPP(X22,X73),X72),
c_0_116 ).
fof(c_0_610,axiom,
! [X28,X12] : hAPP(hAPP(c_Lambda_OdB_OApp,X12),X28) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X12),X28),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_117 ).
fof(c_0_611,plain,
! [X33,X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X12),X49)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X28),X49)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_612,plain,
! [X2,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(X2,X4) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4),X2,X4,X4) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_613,plain,
! [X2,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(X2,X4) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X4),X2,c_HOL_Ozero__class_Ozero(X4),X4,X4) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_614,axiom,
! [X20,X21,X22,X23,X4] : c_Lambda_OdB_OdB__rec(X23,X22,X21,c_Lambda_OdB_OVar(X20),X4) = hAPP(X23,X20),
c_0_121 ).
fof(c_0_615,axiom,
! [X21,X22,X23,X50,X4] : c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OAbs(X50),X4) = hAPP(X21,X50),
c_0_122 ).
fof(c_0_616,axiom,
! [X20,X21,X22,X23,X4] : c_Lambda_OdB_OdB__case(X23,X22,X21,c_Lambda_OdB_OVar(X20),X4) = hAPP(X23,X20),
c_0_123 ).
fof(c_0_617,plain,
! [X33,X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X33),X49)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X33),X49)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_618,axiom,
! [X12] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X12),
c_0_125 ).
fof(c_0_619,axiom,
! [X33] : X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X33),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X33),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_126 ).
fof(c_0_620,axiom,
! [X12] : c_Lambda_OdB_OAbs(X12) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_127 ).
fof(c_0_621,axiom,
! [X11] : c_Lambda_OdB_OVar(X11) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
c_0_128 ).
fof(c_0_622,axiom,
! [X29,X9,X13,X4] : c_List_Ofoldl(X29,X9,c_List_Olist_ONil(X13),X4,X13) = X9,
c_0_129 ).
fof(c_0_623,axiom,
! [X29,X9,X13,X4] : c_List_Ofoldr(X29,c_List_Olist_ONil(X13),X9,X13,X4) = X9,
c_0_130 ).
fof(c_0_624,plain,
! [X19,X33,X49,X83,X62,X61] :
( ~ c_Type_Otyping(X83,X19,X62)
| ~ c_Type_Otyping(c_Type_Oshift(X83,X49,X62,tc_Type_Otype),X33,X61)
| c_Type_Otyping(X83,hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X19),X49),X61) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_625,plain,
! [X32,X33,X34,X28] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X32)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X33),X32))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X34)) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_626,plain,
! [X1,X18,X2,X16,X12,X4] :
( c_ListOrder_Ostep1(X12,X1,X2,X4)
| hBOOL(hAPP(hAPP(X12,X18),X16))
| ~ c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X18,X1,X4),c_List_Olist_OCons(X16,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_627,plain,
! [X33,X78,X62,X61] :
( c_Type_Otyping(X78,c_Lambda_OdB_OAbs(X33),hAPP(hAPP(c_Type_Otype_OFun,X61),X62))
| ~ c_Type_Otyping(c_Type_Oshift(X78,c_HOL_Ozero__class_Ozero(tc_nat),X61,tc_Type_Otype),X33,X62) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_628,plain,
! [X1,X18,X2,X16,X12,X4] :
( c_ListOrder_Ostep1(X12,X1,X2,X4)
| X2 = X1
| ~ c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X18,X1,X4),c_List_Olist_OCons(X16,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_629,plain,
! [X33,X60,X61] :
( c_Type_Otyping(c_Type_Oshift(X60,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X61,X60,X33),tc_Type_Otype),X33,c_Type_Osko__Type__Xtyping__elims__3__2(X61,X60,X33))
| ~ c_Type_Otyping(X60,c_Lambda_OdB_OAbs(X33),X61) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_630,axiom,
! [X2,X16,X29,X13,X4] : c_List_Omap(X29,c_List_Olist_OCons(X16,X2,X13),X13,X4) = c_List_Olist_OCons(hAPP(X29,X16),c_List_Omap(X29,X2,X13,X4),X4),
c_0_137 ).
fof(c_0_631,axiom,
! [X35,X31,X29,X13,X4] : c_List_Olist_OCons(hAPP(X29,X31),c_List_Omap(X29,X35,X13,X4),X4) = c_List_Omap(X29,c_List_Olist_OCons(X31,X35,X13),X13,X4),
c_0_138 ).
fof(c_0_632,axiom,
! [X31,X16,X29,X13,X4] : c_List_Omap(X29,c_List_Olist_OCons(X16,X31,X13),X13,X4) = c_List_Olist_OCons(hAPP(X29,X16),c_List_Omap(X29,X31,X13,X4),X4),
c_0_139 ).
fof(c_0_633,axiom,
! [X19,X33,X28,X36] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X33),X19)),X28),X36) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X28),X36)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X19),X28),X36)),
c_0_140 ).
fof(c_0_634,plain,
! [X12,X8,X9,X13,X4] :
( hBOOL(hAPP(hAPP(X12,X8),X9))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X12,X4,X13),X9),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_635,plain,
! [X12,X14,X15,X13,X4] :
( hBOOL(hAPP(hAPP(X12,X14),X15))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X12,X4,X13),X15),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_636,plain,
! [X1,X2,X16,X12,X4] :
( c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X16,X1,X4),c_List_Olist_OCons(X16,X2,X4),X4)
| ~ c_ListOrder_Ostep1(X12,X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_637,plain,
! [X16,X47,X48,X12,X4] :
( c_ListOrder_Ostep1(X12,c_List_Oappend(X16,X47,X4),c_List_Oappend(X16,X48,X4),X4)
| ~ c_ListOrder_Ostep1(X12,X47,X48,X4) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_638,plain,
! [X1,X2,X16,X12,X4] :
( ~ c_ListOrder_Ostep1(X12,X1,X2,X4)
| c_ListOrder_Ostep1(X12,c_List_Oappend(X1,X16,X4),c_List_Oappend(X2,X16,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_639,plain,
! [X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X12),X49)),hAPP(hAPP(c_Lambda_Olift,X28),X49)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_640,plain,
! [X33,X34,X28] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X33)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X34)) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_641,plain,
! [X32,X33,X28] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33)),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X32)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X33),X32)) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_642,axiom,
! [X33,X28] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X28)),X33)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X33),c_HOL_Ozero__class_Ozero(tc_nat)))),
c_0_149 ).
fof(c_0_643,plain,
! [X1,X18,X2,X16,X12,X4] :
( X16 = X18
| hBOOL(hAPP(hAPP(X12,X18),X16))
| ~ c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X18,X1,X4),c_List_Olist_OCons(X16,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_644,plain,
! [X17,X18,X16,X12,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X16),X17))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X18),X17))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X16),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_645,plain,
! [X19,X33,X60,X61] :
( c_Type_Otyping(X60,X19,c_Type_Osko__Type__Xtyping__elims__2__1(X61,X60,X33,X19))
| ~ c_Type_Otyping(X60,hAPP(hAPP(c_Lambda_OdB_OApp,X33),X19),X61) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_646,plain,
! [X1,X18,X2,X16,X12,X4] :
( X16 = X18
| X2 = X1
| ~ c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X18,X1,X4),c_List_Olist_OCons(X16,X2,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_647,plain,
! [X10,X7,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X10)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_648,plain,
! [X33,X60,X61] :
( c_Type_Otyping(c_Type_Oshift(X60,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X60,X33),tc_Type_Otype),X33,c_Type_Osko__Type__Xabs__typeE__1__2(X60,X33))
| ~ c_Type_Otyping(X60,c_Lambda_OdB_OAbs(X33),X61) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_649,plain,
! [X33,X49,X60,X62,X61] :
( c_Type_Otyping(c_Type_Oshift(X60,X49,X62,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X33),X49),X61)
| ~ c_Type_Otyping(X60,X33,X61) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_650,axiom,
! [X2,X16,X6,X4] : c_List_Oappend(c_List_Oreplicate(X6,X16,X4),c_List_Olist_OCons(X16,X2,X4),X4) = c_List_Olist_OCons(X16,c_List_Oappend(c_List_Oreplicate(X6,X16,X4),X2,X4),X4),
c_0_157 ).
fof(c_0_651,plain,
! [X12,X8,X9,X13,X4] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X12,X4,X13),X9),X8))
| ~ hBOOL(hAPP(hAPP(X12,X8),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_652,plain,
! [X12,X8,X9,X13,X4] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X12,X4,X13),X8),X9))
| ~ hBOOL(hAPP(hAPP(X12,X9),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_653,plain,
! [X19,X33,X28] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X19)),hAPP(hAPP(c_Lambda_OdB_OApp,X33),X19)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X33)) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_654,plain,
! [X19,X33,X28] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X19),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X19),X33)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X33)) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_655,plain,
! [X28,X12,X49] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X12),X49)),hAPP(hAPP(c_Lambda_Olift,X28),X49)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X28)) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_656,plain,
! [X12,X7,X8,X9,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X9),X7))
| ~ hBOOL(hAPP(hAPP(X12,X8),X7))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X9),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_657,plain,
! [X12,X7,X8,X9,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X9),X7))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X8),X7))
| ~ hBOOL(hAPP(hAPP(X12,X9),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_658,plain,
! [X51,X49,X60,X61,X4] :
( hAPP(c_Type_Oshift(X60,X49,X61,X4),X51) = hAPP(X60,X51)
| ~ c_HOL_Oord__class_Oless(X51,X49,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_659,plain,
! [X18,X31,X16,X12,X4] :
( ~ hBOOL(hAPP(hAPP(X12,X18),X31))
| c_ListOrder_Ostep1(X12,c_List_Olist_OCons(X18,X16,X4),c_List_Olist_OCons(X31,X16,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_660,axiom,
! [X1,X18,X2,X16,X4] :
( c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4)
| X16 = X18 ),
c_0_167 ).
fof(c_0_661,axiom,
! [X1,X18,X2,X16,X4] :
( c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X1,c_List_Olist_OCons(X18,c_List_Olist_ONil(X4),X4),X4)
| X2 = X1 ),
c_0_168 ).
fof(c_0_662,axiom,
! [X16,X6,X36,X4] : c_List_Oappend(c_List_Oreplicate(X6,X16,X4),c_List_Oreplicate(X36,X16,X4),X4) = c_List_Oappend(c_List_Oreplicate(X36,X16,X4),c_List_Oreplicate(X6,X16,X4),X4),
c_0_169 ).
fof(c_0_663,plain,
! [X17,X18,X16,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Orderings_Oord__class_Omax(X16,X18,X4)),X17) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X17),X4) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_664,plain,
! [X7,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8)),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)),X8) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_665,axiom,
! [X16,X60,X61,X4] : hAPP(c_Type_Oshift(X60,X16,X61,X4),X16) = X61,
c_0_172 ).
fof(c_0_666,axiom,
! [X19,X33,X28,X36] : c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X33),X19),X28,X36) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X33,X28,X36)),c_Lambda_Osubstn(X19,X28,X36)),
c_0_173 ).
fof(c_0_667,axiom,
! [X33,X28,X6,X36] : c_Lambda_Oliftn(X6,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33),X36) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X6,X28,X36)),c_Lambda_Oliftn(X6,X33,X36)),
c_0_174 ).
fof(c_0_668,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X8),X4) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_669,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7),X4) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_670,plain,
! [X12,X51,X49] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),c_Lambda_OdB_OVar(X49)),X51)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X12)) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_671,plain,
! [X33,X60,X61] :
( X61 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X61,X60,X33)),c_Type_Osko__Type__Xtyping__elims__3__2(X61,X60,X33))
| ~ c_Type_Otyping(X60,c_Lambda_OdB_OAbs(X33),X61) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_672,plain,
! [X34,X28] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X28)),c_Lambda_OdB_OAbs(X34)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X34)) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_673,axiom,
! [X16,X49,X4] : c_List_Oappend(c_List_Oreplicate(X49,X16,X4),c_List_Olist_OCons(X16,c_List_Olist_ONil(X4),X4),X4) = c_List_Olist_OCons(X16,c_List_Oreplicate(X49,X16,X4),X4),
c_0_180 ).
fof(c_0_674,plain,
! [X10,X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X10),X4)
| ~ c_HOL_Oord__class_Oless(X7,X10,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_675,axiom,
! [X16,X6,X29,X13,X4] : c_List_Omap(X29,c_List_Oreplicate(X6,X16,X13),X13,X4) = c_List_Oreplicate(X6,hAPP(X29,X16),X4),
c_0_182 ).
fof(c_0_676,plain,
! [X12,X8,X9,X4] :
( c_Wellfounded_Oaccp(X12,X8,X4)
| ~ c_Wellfounded_Oaccp(X12,X9,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X8),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_677,plain,
! [X12,X8,X9,X4] :
( c_Wellfounded_Oaccp(X12,X8,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X8),X9))
| ~ c_Wellfounded_Oaccp(X12,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_678,axiom,
! [X33,X28,X36] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33)),X36) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X28),X36)),hAPP(hAPP(c_Lambda_Olift,X33),X36)),
c_0_185 ).
fof(c_0_679,plain,
! [X6,X11,X36] :
( c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X6),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_680,plain,
! [X17,X18,X16,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X18)),X17) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_681,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8)),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_682,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Oab__semigroup__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8)),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_683,plain,
! [X10,X7,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X10)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)),X10) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_684,plain,
! [X7,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8)),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_685,axiom,
! [X16,X6,X11,X4] : c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X11),X16,X4) = c_List_Oappend(c_List_Oreplicate(X6,X16,X4),c_List_Oreplicate(X11,X16,X4),X4),
c_0_192 ).
fof(c_0_686,plain,
! [X33,X28,X78,X62,X61] :
( c_Type_Otyping(X78,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X33),X62)
| ~ c_Type_Otyping(X78,X33,X61)
| ~ c_Type_Otyping(X78,X28,hAPP(hAPP(c_Type_Otype_OFun,X61),X62)) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_687,plain,
! [X52,X36,X51,X49] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X51),X52),tc_nat)
| ~ c_HOL_Oord__class_Oless(X36,X52,tc_nat)
| ~ c_HOL_Oord__class_Oless(X49,X51,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_688,axiom,
! [X2,X29,X13,X4] :
( c_List_Omap(X29,X2,X13,X4) != c_List_Olist_ONil(X4)
| X2 = c_List_Olist_ONil(X13) ),
c_0_195 ).
fof(c_0_689,axiom,
! [X2,X29,X13,X4] :
( c_List_Olist_ONil(X4) != c_List_Omap(X29,X2,X13,X4)
| X2 = c_List_Olist_ONil(X13) ),
c_0_196 ).
fof(c_0_690,plain,
! [X2,X12,X4] : ~ c_ListOrder_Ostep1(X12,X2,c_List_Olist_ONil(X4),X4),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_691,plain,
! [X2,X12,X4] : ~ c_ListOrder_Ostep1(X12,c_List_Olist_ONil(X4),X2,X4),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_692,plain,
! [X32,X33,X60,X61] :
( c_Type_Otyping(X60,X32,X61)
| ~ c_Type_Otyping(X60,X33,X61)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X33),X32)) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_693,plain,
! [X17,X18,X16,X19,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X17)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X19)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X17) = X19 ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_694,axiom,
! [X33,X28,X36] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X33),X36)),X28),X36) = X33,
c_0_201 ).
fof(c_0_695,plain,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X17,X18,X4)
| c_HOL_Oord__class_Oless(X17,X16,X4)
| ~ c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omax(X16,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_696,axiom,
! [X33,X28,X6] : c_Lambda_Osubstn(X33,X28,X6) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),c_Lambda_Oliftn(X6,X28,c_HOL_Ozero__class_Ozero(tc_nat))),X6),
c_0_203 ).
fof(c_0_697,axiom,
! [X6,X11,X36] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X36)),
c_0_204 ).
fof(c_0_698,plain,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X8,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_699,plain,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_700,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X8),X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_701,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X8),X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_702,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7),X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_703,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7),X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_704,plain,
! [X7,X8,X9,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X8,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7),X4)
| ~ c_HOL_Oord__class_Oless(X8,X7,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_705,plain,
! [X6,X11] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_706,plain,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X16,X18,X4),X17,X4)
| ~ c_HOL_Oord__class_Oless(X18,X17,X4)
| ~ c_HOL_Oord__class_Oless(X16,X17,X4) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_707,plain,
! [X65,X7,X8,X9,X4] :
( hAPP(hAPP(X65,hAPP(hAPP(X65,X9),X8)),X7) = hAPP(hAPP(X65,X9),hAPP(hAPP(X65,X8),X7))
| ~ c_OrderedGroup_Osemigroup__add(X65,X4) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_708,plain,
! [X1,X2,X3,X4] :
( c_List_Olistsp(X3,c_List_Oappend(X2,X1,X4),X4)
| ~ c_List_Olistsp(X3,X1,X4)
| ~ c_List_Olistsp(X3,X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_709,plain,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(X16,c_Orderings_Oord__class_Omax(X18,X17,X4),X4) = c_Orderings_Oord__class_Omax(X18,c_Orderings_Oord__class_Omax(X16,X17,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_710,plain,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X16,X18,X4),X17,X4) = c_Orderings_Oord__class_Omax(X16,c_Orderings_Oord__class_Omax(X18,X17,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_711,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X9,X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),X4) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_712,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_713,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_714,axiom,
! [X2,X16,X46,X4] : c_List_Oappend(X2,c_List_Oappend(X16,X46,X4),X4) = c_List_Oappend(c_List_Oappend(X2,X16,X4),X46,X4),
c_0_221 ).
fof(c_0_715,axiom,
! [X30,X1,X16,X4] : c_List_Oappend(c_List_Oappend(X30,X16,X4),X1,X4) = c_List_Oappend(X30,c_List_Oappend(X16,X1,X4),X4),
c_0_222 ).
fof(c_0_716,axiom,
! [X37,X2,X48,X4] : c_List_Oappend(X2,c_List_Oappend(X37,X48,X4),X4) = c_List_Oappend(c_List_Oappend(X2,X37,X4),X48,X4),
c_0_223 ).
fof(c_0_717,axiom,
! [X30,X1,X2,X4] : c_List_Oappend(c_List_Oappend(X2,X1,X4),X30,X4) = c_List_Oappend(X2,c_List_Oappend(X1,X30,X4),X4),
c_0_224 ).
fof(c_0_718,axiom,
! [X30,X37,X16,X4] : c_List_Olist_OCons(X16,c_List_Oappend(X37,X30,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X16,X37,X4),X30,X4),
c_0_225 ).
fof(c_0_719,axiom,
! [X30,X31,X16,X4] : c_List_Olist_OCons(X16,c_List_Oappend(X31,X30,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X16,X31,X4),X30,X4),
c_0_226 ).
fof(c_0_720,axiom,
! [X1,X2,X16,X4] : c_List_Oappend(c_List_Olist_OCons(X16,X2,X4),X1,X4) = c_List_Olist_OCons(X16,c_List_Oappend(X2,X1,X4),X4),
c_0_227 ).
fof(c_0_721,axiom,
! [X30,X31,X16,X4] : c_List_Oappend(c_List_Olist_OCons(X16,X31,X4),X30,X4) = c_List_Olist_OCons(X16,c_List_Oappend(X31,X30,X4),X4),
c_0_228 ).
fof(c_0_722,plain,
! [X6,X11,X36] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_723,plain,
! [X36,X51,X49] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X36),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X51),X36),tc_nat)
| ~ c_HOL_Oord__class_Oless(X49,X51,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_724,plain,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X18,X17,X4)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X16,X18,X4),X17,X4) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_725,plain,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X16,X17,X4)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X16,X18,X4),X17,X4) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_726,plain,
! [X17,X18,X16,X4] :
( ~ class_OrderedGroup_Oab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X17)) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_727,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_728,plain,
! [X10,X7,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X10)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_729,plain,
! [X18,X16,X12,X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X16),X18))
| ~ hBOOL(hAPP(hAPP(X12,X16),X18)) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_730,axiom,
! [X33,X6,X36] : c_Lambda_Oliftn(c_Suc(X6),X33,X36) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X6,X33,X36)),X36),
c_0_237 ).
fof(c_0_731,plain,
! [X1,X2,X3,X4] :
( c_List_Olistsp(X3,X1,X4)
| ~ c_List_Olistsp(X3,c_List_Oappend(X2,X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_732,plain,
! [X1,X2,X3,X4] :
( c_List_Olistsp(X3,X2,X4)
| ~ c_List_Olistsp(X3,c_List_Oappend(X2,X1,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_733,plain,
! [X6,X11,X52,X36] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X52) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X6)
| ~ c_HOL_Oord__class_Oless(X36,X52,tc_nat)
| c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_734,plain,
! [X36,X51,X49] :
( c_HOL_Oord__class_Oless(X49,X36,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X51),X36,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_735,axiom,
! [X17,X18,X16] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X17)),
c_0_242 ).
fof(c_0_736,plain,
! [X6,X9,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Power_Opower__class_Opower(X9,X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_737,plain,
! [X12,X8,X9,X4] :
( c_Wellfounded_Oaccp(X12,X9,X4)
| ~ hBOOL(hAPP(hAPP(X12,X9),X8))
| ~ c_Wellfounded_Oaccp(X12,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_738,plain,
! [X18,X12,X9,X4] :
( c_Wellfounded_Oaccp(X12,X18,X4)
| ~ hBOOL(hAPP(hAPP(X12,X18),X9))
| ~ c_Wellfounded_Oaccp(X12,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_739,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_740,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_741,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9),c_HOL_Ozero__class_Ozero(X4),X4)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_742,plain,
! [X12] :
( hBOOL(hAPP(c_InductTermi_OIT,X12))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X12,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_743,plain,
! [X32,X33,X60,X61] :
( c_Type_Otyping(X60,X32,X61)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X33),X32))
| ~ c_Type_Otyping(X60,X33,X61) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_744,plain,
! [X1,X2,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(c_List_Oappend(X2,X1,X4),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_List_Olistsum(X2,X4)),c_List_Olistsum(X1,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_745,axiom,
! [X29,X13,X4] : c_List_Olist_ONil(X4) = c_List_Omap(X29,c_List_Olist_ONil(X13),X13,X4),
c_0_252 ).
fof(c_0_746,axiom,
! [X29,X13,X4] : c_List_Omap(X29,c_List_Olist_ONil(X13),X13,X4) = c_List_Olist_ONil(X4),
c_0_253 ).
fof(c_0_747,plain,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omax(X16,X18,X4),X4)
| ~ c_HOL_Oord__class_Oless(X17,X18,X4) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_748,plain,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omax(X16,X18,X4),X4)
| ~ c_HOL_Oord__class_Oless(X17,X16,X4) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_749,plain,
! [X16,X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X16,c_Orderings_Oord__class_Omax(X9,X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X16,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_750,plain,
! [X16,X8,X9,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X16,c_Orderings_Oord__class_Omax(X9,X8,X4),X4)
| ~ c_HOL_Oord__class_Oless(X16,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_751,plain,
! [X6,X11,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Nat_Osemiring__1__class_Oof__nat(X11,X4)),c_Nat_Osemiring__1__class_Oof__nat(X6,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_752,axiom,
! [X16,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X16)),tc_nat),
c_0_259 ).
fof(c_0_753,axiom,
! [X11,X49] : c_HOL_Oord__class_Oless(X49,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X49)),tc_nat),
c_0_260 ).
fof(c_0_754,axiom,
! [X11,X49] : c_HOL_Oord__class_Oless(X49,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X11)),tc_nat),
c_0_261 ).
fof(c_0_755,plain,
! [X33,X49] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X33),c_Lambda_OdB_OVar(X49))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_756,plain,
! [X6,X11] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_757,plain,
! [X6,X11] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_758,plain,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_HOL_Oord__class_Oless(X16,X17,X4)
| ~ c_HOL_Oord__class_Oless(X18,X17,X4)
| ~ c_HOL_Oord__class_Oless(X16,X18,X4) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_759,plain,
! [X17,X18,X16,X4] :
( ~ class_Orderings_Oorder(X4)
| c_HOL_Oord__class_Oless(X17,X16,X4)
| ~ c_HOL_Oord__class_Oless(X17,X18,X4)
| ~ c_HOL_Oord__class_Oless(X18,X16,X4) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_760,plain,
! [X33,X28] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X28)),c_Lambda_OdB_OAbs(X33)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X33)) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_761,plain,
! [X6,X11,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X11,X4),c_Nat_Osemiring__1__class_Oof__nat(X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_762,plain,
! [X36,X51,X49] :
( c_HOL_Oord__class_Oless(c_Suc(X49),X36,tc_nat)
| ~ c_HOL_Oord__class_Oless(X51,X36,tc_nat)
| ~ c_HOL_Oord__class_Oless(X49,X51,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_763,plain,
! [X11,X51,X49] :
( c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X51),tc_nat)
| ~ c_HOL_Oord__class_Oless(X49,X51,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_764,plain,
! [X11,X51,X49] :
( c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X51),X11),tc_nat)
| ~ c_HOL_Oord__class_Oless(X49,X51,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_765,plain,
! [X17,X18,X16] :
( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X17,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_766,plain,
! [X17,X18,X16] :
( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X18,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_767,plain,
! [X51,X49] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X51),X49),X49,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_768,plain,
! [X51,X49] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X51),X49,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_769,plain,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(X16,c_Orderings_Oord__class_Omax(X16,X18,X4),X4) = c_Orderings_Oord__class_Omax(X16,X18,X4) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_770,axiom,
! [X2,X16,X4] : c_List_Oappend(c_List_Olist_ONil(X4),c_List_Olist_OCons(X16,X2,X4),X4) = c_List_Olist_OCons(X16,X2,X4),
c_0_277 ).
fof(c_0_771,axiom,
! [X2,X16,X4] : c_List_Olist_OCons(X16,X2,X4) = c_List_Oappend(c_List_Olist_ONil(X4),c_List_Olist_OCons(X16,X2,X4),X4),
c_0_278 ).
fof(c_0_772,axiom,
! [X16,X6,X4] : c_List_Oreplicate(c_Suc(X6),X16,X4) = c_List_Olist_OCons(X16,c_List_Oreplicate(X6,X16,X4),X4),
c_0_279 ).
fof(c_0_773,plain,
! [X33,X49] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X33),X49)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_774,axiom,
! [X6,X36,X49] :
( c_Lambda_Oliftn(X6,c_Lambda_OdB_OVar(X49),X36) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X49),X6))
| c_HOL_Oord__class_Oless(X49,X36,tc_nat) ),
c_0_281 ).
fof(c_0_775,plain,
! [X2,X16,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(c_List_Olist_OCons(X16,X2,X4),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),c_List_Olistsum(X2,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_776,plain,
! [X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Nat_Osemiring__1__class_Oof__nat(X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_777,plain,
! [X19,X51,X49] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X51)),X19),X49) = c_Lambda_OdB_OVar(X51)
| ~ c_HOL_Oord__class_Oless(X51,X49,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_778,plain,
! [X6,X11,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X11,X4),c_Nat_Osemiring__1__class_Oof__nat(X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_779,plain,
! [X33] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X33,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_780,axiom,
! [X6,X11,X26] :
( hBOOL(hAPP(hAPP(X26,X6),X11))
| c_HOL_Oord__class_Oless(X6,X11,tc_nat)
| X11 = X6
| c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
c_0_287 ).
fof(c_0_781,axiom,
! [X16,X12,X4] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X16),X16)),
c_0_288 ).
fof(c_0_782,axiom,
! [X12,X9,X4] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X12,X4),X9),X9)),
c_0_289 ).
fof(c_0_783,plain,
! [X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_Nat_Osemiring__1__class_Oof__nat(X6,X4),X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_784,plain,
! [X17,X18,X16,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X17)
| X18 = X17 ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_785,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_786,plain,
! [X18,X16,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X18,X16,X4)
| ~ c_HOL_Oord__class_Oless(X16,X18,X4) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_787,plain,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X16,X18,X4)
| ~ c_HOL_Oord__class_Oless(X18,X16,X4) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_788,plain,
! [X8,X9,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X9,X8,X4)
| ~ c_HOL_Oord__class_Oless(X8,X9,X4) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_789,axiom,
! [X18,X16,X6,X11,X4] :
( c_List_Oreplicate(X11,X16,X4) != c_List_Oreplicate(X6,X18,X4)
| X16 = X18
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_296 ).
fof(c_0_790,plain,
! [X6,X11] :
( ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X11),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_791,axiom,
! [X38,X70,X39,X9,X4] :
( c_List_Olist_OCons(X9,X70,X4) != c_List_Olist_OCons(X39,X38,X4)
| X70 = X38 ),
c_0_298 ).
fof(c_0_792,axiom,
! [X38,X70,X39,X9,X4] :
( c_List_Olist_OCons(X9,X70,X4) != c_List_Olist_OCons(X39,X38,X4)
| X9 = X39 ),
c_0_299 ).
fof(c_0_793,axiom,
! [X30,X1,X2,X4] :
( c_List_Oappend(X2,X1,X4) != c_List_Oappend(X2,X30,X4)
| X1 = X30 ),
c_0_300 ).
fof(c_0_794,axiom,
! [X30,X1,X2,X4] :
( c_List_Oappend(X1,X2,X4) != c_List_Oappend(X30,X2,X4)
| X1 = X30 ),
c_0_301 ).
fof(c_0_795,axiom,
! [X18,X16,X6,X11,X4] :
( c_List_Oreplicate(X11,X16,X4) != c_List_Oreplicate(X6,X18,X4)
| X11 = X6 ),
c_0_302 ).
fof(c_0_796,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X9)
| X8 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_797,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)
| X8 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_798,plain,
! [X7,X8,X9,X4] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7)
| X8 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_799,axiom,
! [X6,X11] : c_Orderings_Oord__class_Omax(c_Suc(X11),c_Suc(X6),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X11,X6,tc_nat)),
c_0_306 ).
fof(c_0_800,axiom,
! [X16,X28] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X16),X28,X16) = c_Lambda_Oliftn(X16,X28,c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_307 ).
fof(c_0_801,plain,
! [X86,X87,X4] :
( X87 = X86
| ~ hBOOL(hAPP(hAPP(c_fequal(X4),X87),X86)) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_802,axiom,
! [X28,X36,X49] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X49)),X28),X36) = c_Lambda_OdB_OVar(X49)
| X49 = X36
| c_HOL_Oord__class_Oless(X36,X49,tc_nat) ),
c_0_309 ).
fof(c_0_803,axiom,
! [X16,X28] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X28),X16) = X28 ),
c_0_310 ).
fof(c_0_804,axiom,
! [X12,X13,X4] : c_Predicate_Oconversep(c_Predicate_Oconversep(X12,X4,X13),X13,X4) = X12,
c_0_311 ).
fof(c_0_805,plain,
! [X33,X49] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X49)),X33)),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_806,plain,
! [X6,X11] :
( c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X11),c_Suc(X6),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_807,axiom,
! [X6,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X11)),X6) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)),
c_0_314 ).
fof(c_0_808,plain,
! [X6,X11] :
( c_HOL_Oord__class_Oless(c_Suc(X11),c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_809,plain,
! [X16,X6] :
( c_HOL_Oord__class_Oless(c_Suc(X16),c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_810,plain,
! [X6,X11] :
( X6 = X11
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X11),tc_nat)
| c_HOL_Oord__class_Oless(X6,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_811,plain,
! [X6,X11] :
( X11 = X6
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X11),tc_nat)
| c_HOL_Oord__class_Oless(X6,X11,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_812,plain,
! [X6,X11] :
( X11 = X6
| c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,c_Suc(X6),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_813,plain,
! [X6,X36,X49] :
( c_Lambda_Oliftn(X6,c_Lambda_OdB_OVar(X49),X36) = c_Lambda_OdB_OVar(X49)
| ~ c_HOL_Oord__class_Oless(X49,X36,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_814,plain,
! [X6,X11] :
( c_HOL_Oord__class_Oless(c_Suc(X11),X6,tc_nat)
| c_Suc(X11) = X6
| ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_815,axiom,
! [X6,X11,X36] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),X6)
| X11 = X6 ),
c_0_322 ).
fof(c_0_816,axiom,
! [X6,X11,X36] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X36) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X36)
| X11 = X6 ),
c_0_323 ).
fof(c_0_817,axiom,
! [X17,X18,X16] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X18) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X17)
| X18 = X17 ),
c_0_324 ).
fof(c_0_818,plain,
! [X6,X11] :
( c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X11),X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_819,axiom,
! [X33,X28] : c_Lambda_Osubstn(X33,X28,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X33),X28),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_326 ).
fof(c_0_820,axiom,
! [X6,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_Suc(X6)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)),
c_0_327 ).
fof(c_0_821,plain,
! [X11,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X4)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X11,X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_822,plain,
! [X6,X11] :
( c_HOL_Oord__class_Oless(X11,c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_823,plain,
! [X36,X49] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X49)),X36) = c_Lambda_OdB_OVar(X49)
| ~ c_HOL_Oord__class_Oless(X49,X36,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_824,plain,
! [X64,X65,X9,X4] :
( hAPP(hAPP(X65,X64),X9) = X9
| ~ c_OrderedGroup_Omonoid__add(X64,X65,X4) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_825,plain,
! [X64,X65,X9,X4] :
( hAPP(hAPP(X65,X9),X64) = X9
| ~ c_OrderedGroup_Omonoid__add(X64,X65,X4) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_826,plain,
! [X6,X9,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X9,X6,X4) != c_HOL_Ozero__class_Ozero(X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_827,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(X9,c_HOL_Ozero__class_Ozero(tc_nat),X4) != c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_334]) ).
fof(c_0_828,axiom,
! [X28,X36,X49] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X49),X28,X36) = c_Lambda_OdB_OVar(X49)
| X49 = X36
| c_HOL_Oord__class_Oless(X36,X49,tc_nat) ),
c_0_335 ).
fof(c_0_829,plain,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| X16 = X18
| c_HOL_Oord__class_Oless(X16,X18,X4)
| c_HOL_Oord__class_Oless(X18,X16,X4) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_830,plain,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X18,X16,X4)
| X16 = X18
| c_HOL_Oord__class_Oless(X16,X18,X4) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_831,plain,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_HOL_Oord__class_Oless(X18,X16,X4)
| c_HOL_Oord__class_Oless(X16,X18,X4)
| X16 = X18 ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_832,plain,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| X16 = X18
| c_HOL_Oord__class_Oless(X18,X16,X4)
| c_HOL_Oord__class_Oless(X16,X18,X4) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_833,plain,
! [X18,X16,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X4)
| c_HOL_Oord__class_Oless(X18,X16,X4)
| c_HOL_Oord__class_Oless(X16,X18,X4)
| X16 = X18 ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_834,axiom,
! [X75,X72,X76,X73] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72) != hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75)
| X72 = X75 ),
c_0_341 ).
fof(c_0_835,axiom,
! [X75,X72,X76,X73] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72) != hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75)
| X73 = X76 ),
c_0_342 ).
fof(c_0_836,axiom,
! [X66,X67,X68,X69] :
( hAPP(hAPP(c_Type_Otype_OFun,X69),X67) != hAPP(hAPP(c_Type_Otype_OFun,X68),X66)
| X69 = X68 ),
c_0_343 ).
fof(c_0_837,axiom,
! [X66,X67,X68,X69] :
( hAPP(hAPP(c_Type_Otype_OFun,X69),X67) != hAPP(hAPP(c_Type_Otype_OFun,X68),X66)
| X67 = X66 ),
c_0_344 ).
fof(c_0_838,plain,
! [X18,X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(X16,X18,X4) = c_Orderings_Oord__class_Omax(X18,X16,X4) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_839,axiom,
! [X18,X16,X4] : c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X16,X4) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X18,X4),
c_0_346 ).
fof(c_0_840,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(X6,c_Suc(X11),tc_nat)
| c_HOL_Oord__class_Oless(X11,X6,tc_nat) ),
c_0_347 ).
fof(c_0_841,axiom,
! [X16] :
( c_HOL_Oord__class_Oless(X16,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,c_Suc(X16),tc_nat) ),
c_0_348 ).
fof(c_0_842,plain,
! [X18,X16,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X18) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X18),X16) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_843,plain,
! [X8,X9,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X8),X9) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_844,plain,
! [X7,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X7),X9) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_845,axiom,
! [X19,X36] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X36)),X19),X36) = X19,
c_0_352 ).
fof(c_0_846,plain,
! [X49,X60,X61] :
( hAPP(X60,X49) = X61
| ~ c_Type_Otyping(X60,c_Lambda_OdB_OVar(X49),X61) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_847,axiom,
! [X6,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X11)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_Suc(X6)),
c_0_354 ).
fof(c_0_848,axiom,
! [X18,X16] :
( c_HOL_Oord__class_Oless(X18,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,X18,tc_nat)
| X16 = X18 ),
c_0_355 ).
fof(c_0_849,axiom,
! [X6,X11] :
( c_HOL_Oord__class_Oless(X6,X11,tc_nat)
| c_HOL_Oord__class_Oless(X11,X6,tc_nat)
| X11 = X6 ),
c_0_356 ).
fof(c_0_850,plain,
! [X6] :
( X6 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_851,axiom,
! [X16,X4] : hBOOL(hAPP(hAPP(c_fequal(X4),X16),X16)),
c_0_358 ).
fof(c_0_852,plain,
! [X6,X9,X4] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X4)
| c_Power_Opower__class_Opower(X9,X6,X4) != c_HOL_Ozero__class_Ozero(X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_853,plain,
! [X16,X9,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X16 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),X9)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_854,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),X9) != c_HOL_Ozero__class_Ozero(X4)
| X9 = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_855,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_362 ).
fof(c_0_856,axiom,
! [X6,X11] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_363 ).
fof(c_0_857,axiom,
! [X1,X2,X4] :
( c_List_Oappend(X2,X1,X4) != c_List_Olist_ONil(X4)
| X1 = c_List_Olist_ONil(X4) ),
c_0_364 ).
fof(c_0_858,axiom,
! [X1,X2,X4] :
( c_List_Oappend(X2,X1,X4) != c_List_Olist_ONil(X4)
| X2 = c_List_Olist_ONil(X4) ),
c_0_365 ).
fof(c_0_859,axiom,
! [X1,X2,X4] :
( c_List_Olist_ONil(X4) != c_List_Oappend(X2,X1,X4)
| X1 = c_List_Olist_ONil(X4) ),
c_0_366 ).
fof(c_0_860,axiom,
! [X1,X2,X4] :
( c_List_Olist_ONil(X4) != c_List_Oappend(X2,X1,X4)
| X2 = c_List_Olist_ONil(X4) ),
c_0_367 ).
fof(c_0_861,plain,
! [X6,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Omult__zero(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),X6,X4) = c_HOL_Ozero__class_Ozero(X4)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_862,axiom,
! [X16,X6,X4] :
( c_List_Olist_ONil(X4) != c_List_Oreplicate(X6,X16,X4)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_369 ).
fof(c_0_863,axiom,
! [X16,X6,X4] :
( c_List_Oreplicate(X6,X16,X4) != c_List_Olist_ONil(X4)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_370 ).
fof(c_0_864,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_371 ).
fof(c_0_865,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_372 ).
fof(c_0_866,axiom,
! [X6,X11] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_373 ).
fof(c_0_867,axiom,
! [X6,X11] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)
| X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_374 ).
fof(c_0_868,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_375]) ).
fof(c_0_869,plain,
! [X16,X4] :
( ~ class_Orderings_Opreorder(X4)
| ~ c_HOL_Oord__class_Oless(X16,X16,X4) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_870,plain,
! [X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X16,X16,X4) ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_871,plain,
! [X16,X4] :
( ~ class_Orderings_Oorder(X4)
| ~ c_HOL_Oord__class_Oless(X16,X16,X4) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_872,axiom,
! [X1,X2,X4] :
( X1 != c_List_Oappend(X2,X1,X4)
| X2 = c_List_Olist_ONil(X4) ),
c_0_379 ).
fof(c_0_873,axiom,
! [X1,X2,X4] :
( c_List_Oappend(X2,X1,X4) != X1
| X2 = c_List_Olist_ONil(X4) ),
c_0_380 ).
fof(c_0_874,axiom,
! [X1,X2,X4] :
( X2 != c_List_Oappend(X2,X1,X4)
| X1 = c_List_Olist_ONil(X4) ),
c_0_381 ).
fof(c_0_875,axiom,
! [X1,X2,X4] :
( c_List_Oappend(X2,X1,X4) != X2
| X1 = c_List_Olist_ONil(X4) ),
c_0_382 ).
fof(c_0_876,axiom,
! [X38,X39,X4] : c_List_Olist_ONil(X4) != c_List_Olist_OCons(X39,X38,X4),
c_0_383 ).
fof(c_0_877,axiom,
! [X6,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X11),
c_0_384 ).
fof(c_0_878,axiom,
! [X38,X39,X4] : c_List_Olist_OCons(X39,X38,X4) != c_List_Olist_ONil(X4),
c_0_385 ).
fof(c_0_879,axiom,
! [X31,X16,X4] : c_List_Olist_OCons(X16,X31,X4) != c_List_Olist_ONil(X4),
c_0_386 ).
fof(c_0_880,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_387 ).
fof(c_0_881,axiom,
! [X6,X11] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_388 ).
fof(c_0_882,plain,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_883,plain,
! [X11] : ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_884,axiom,
! [X2,X16,X4] : X2 != c_List_Olist_OCons(X16,X2,X4),
c_0_391 ).
fof(c_0_885,axiom,
! [X16,X33,X4] : c_List_Olist_OCons(X16,X33,X4) != X33,
c_0_392 ).
fof(c_0_886,axiom,
! [X16,X78] : c_Type_Otyping(X78,c_Lambda_OdB_OVar(X16),hAPP(X78,X16)),
c_0_393 ).
fof(c_0_887,plain,
! [X6,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_Suc(X6),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_394]) ).
fof(c_0_888,plain,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,X6,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_395]) ).
fof(c_0_889,plain,
! [X16] : ~ c_HOL_Oord__class_Oless(X16,X16,tc_nat),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_890,plain,
! [X6,X4] :
( ~ class_Ring__and__Field_Osemiring__0(X4)
| ~ class_Power_Opower(X4)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),X6,X4) = c_HOL_Ozero__class_Ozero(X4)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_891,plain,
! [X12] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X12)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X12)) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_892,plain,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_893,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_400 ).
fof(c_0_894,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_401 ).
fof(c_0_895,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_HOL_Ozero__class_Ozero(tc_nat)
| X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_402 ).
fof(c_0_896,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != c_HOL_Ozero__class_Ozero(tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_403 ).
fof(c_0_897,axiom,
! [X6,X11] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X6) != X11
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_404 ).
fof(c_0_898,axiom,
! [X16,X9] :
( X16 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X9)
| X9 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_405 ).
fof(c_0_899,plain,
! [X16,X4] :
( ~ class_Ring__and__Field_Oidom(X4)
| ~ class_Int_Onumber__ring(X4)
| X16 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X16),c_HOL_Ozero__class_Ozero(X4)) ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_900,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),X9) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_407]) ).
fof(c_0_901,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),X9) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_902,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),X9) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_903,plain,
! [X16,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),X16) = X16 ),
inference(fof_simplification,[status(thm)],[c_0_410]) ).
fof(c_0_904,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_411 ).
fof(c_0_905,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_412 ).
fof(c_0_906,axiom,
! [X4] : c_List_Oappend(c_List_Olist_ONil(X4),c_List_Olist_ONil(X4),X4) = c_List_Olist_ONil(X4),
c_0_413 ).
fof(c_0_907,axiom,
! [X4] : c_List_Olist_ONil(X4) = c_List_Oappend(c_List_Olist_ONil(X4),c_List_Olist_ONil(X4),X4),
c_0_414 ).
fof(c_0_908,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_415 ).
fof(c_0_909,plain,
! [X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),c_HOL_Ozero__class_Ozero(X4)) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_416]) ).
fof(c_0_910,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),c_HOL_Ozero__class_Ozero(X4)) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_417]) ).
fof(c_0_911,plain,
! [X9,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),X9),c_HOL_Ozero__class_Ozero(X4)) = X9 ),
inference(fof_simplification,[status(thm)],[c_0_418]) ).
fof(c_0_912,axiom,
! [X4] : c_Predicate_Oconversep(c_fequal(X4),X4,X4) = c_fequal(X4),
c_0_419 ).
fof(c_0_913,axiom,
! [X20,X75,X76] : hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75) != c_Lambda_OdB_OVar(X20),
c_0_420 ).
fof(c_0_914,axiom,
! [X20,X75,X76] : c_Lambda_OdB_OVar(X20) != hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75),
c_0_421 ).
fof(c_0_915,axiom,
! [X55,X72,X73] : c_Lambda_OdB_OAbs(X55) != hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72),
c_0_422 ).
fof(c_0_916,axiom,
! [X55,X72,X73] : hAPP(hAPP(c_Lambda_OdB_OApp,X73),X72) != c_Lambda_OdB_OAbs(X55),
c_0_423 ).
fof(c_0_917,plain,
! [X16,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(X16,X16,X4) = X16 ),
inference(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_918,axiom,
! [X16] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X16),tc_nat),
c_0_425 ).
fof(c_0_919,axiom,
! [X6] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X6),tc_nat),
c_0_426 ).
fof(c_0_920,axiom,
! [X16,X4] : c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X16,X4) = c_List_Olist_ONil(X4),
c_0_427 ).
fof(c_0_921,axiom,
! [X16,X4] : c_List_Olist_ONil(X4) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X16,X4),
c_0_428 ).
fof(c_0_922,axiom,
! [X1,X4] : X1 = c_List_Oappend(c_List_Olist_ONil(X4),X1,X4),
c_0_429 ).
fof(c_0_923,axiom,
! [X1,X4] : c_List_Oappend(c_List_Olist_ONil(X4),X1,X4) = X1,
c_0_430 ).
fof(c_0_924,axiom,
! [X2,X4] : X2 = c_List_Oappend(X2,c_List_Olist_ONil(X4),X4),
c_0_431 ).
fof(c_0_925,axiom,
! [X16,X4] : X16 = c_List_Oappend(c_List_Olist_ONil(X4),X16,X4),
c_0_432 ).
fof(c_0_926,axiom,
! [X2,X4] : c_List_Oappend(X2,c_List_Olist_ONil(X4),X4) = X2,
c_0_433 ).
fof(c_0_927,axiom,
! [X3,X4] : c_List_Olistsp(X3,c_List_Olist_ONil(X4),X4),
c_0_434 ).
fof(c_0_928,axiom,
! [X6] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_435 ).
fof(c_0_929,axiom,
! [X16] : c_HOL_Oord__class_Oless(X16,c_Suc(X16),tc_nat),
c_0_436 ).
fof(c_0_930,axiom,
! [X6] : c_HOL_Oord__class_Oless(X6,c_Suc(X6),tc_nat),
c_0_437 ).
fof(c_0_931,axiom,
! [X33,X36] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X33,X36) = X33,
c_0_438 ).
fof(c_0_932,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_439 ).
fof(c_0_933,axiom,
! [X6] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) = X6,
c_0_440 ).
fof(c_0_934,axiom,
! [X6] : c_Orderings_Oord__class_Omax(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6,
c_0_441 ).
fof(c_0_935,axiom,
! [X12,X4] : c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X12,X4),X4) = c_Transitive__Closure_Ortranclp(X12,X4),
c_0_442 ).
fof(c_0_936,plain,
! [X6,X11,X4] :
( ~ class_Nat_Osemiring__char__0(X4)
| c_Nat_Osemiring__1__class_Oof__nat(X11,X4) != c_Nat_Osemiring__1__class_Oof__nat(X6,X4)
| X11 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_443]) ).
fof(c_0_937,axiom,
! [X6] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X6) = X6,
c_0_444 ).
fof(c_0_938,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
c_0_445 ).
fof(c_0_939,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
c_0_446 ).
fof(c_0_940,axiom,
! [X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Ozero__class_Ozero(tc_nat)) = X11,
c_0_447 ).
fof(c_0_941,axiom,
! [X16] : X16 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_448 ).
fof(c_0_942,axiom,
! [X6] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X6))),
c_0_449 ).
fof(c_0_943,plain,
! [X84,X85] :
( class_Orderings_Oorder(tc_fun(X84,X85))
| ~ class_Orderings_Oorder(X85) ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_944,plain,
! [X84,X85] :
( class_Orderings_Opreorder(tc_fun(X84,X85))
| ~ class_Orderings_Opreorder(X85) ),
inference(fof_simplification,[status(thm)],[c_0_451]) ).
fof(c_0_945,plain,
! [X4] :
( ~ class_OrderedGroup_Omonoid__add(X4)
| c_List_Olistsum(c_List_Olist_ONil(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_452]) ).
fof(c_0_946,plain,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(fof_simplification,[status(thm)],[c_0_453]) ).
fof(c_0_947,plain,
! [X4] :
( ~ class_OrderedGroup_Osemigroup__add(X4)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_454]) ).
fof(c_0_948,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
c_0_455 ).
fof(c_0_949,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
c_0_456 ).
fof(c_0_950,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
c_0_457 ).
fof(c_0_951,axiom,
! [X54,X20] :
( c_Lambda_OdB_OVar(X20) != c_Lambda_OdB_OVar(X54)
| X20 = X54 ),
c_0_458 ).
fof(c_0_952,axiom,
! [X55,X50] :
( c_Lambda_OdB_OAbs(X50) != c_Lambda_OdB_OAbs(X55)
| X50 = X55 ),
c_0_459 ).
fof(c_0_953,axiom,
! [X54,X20] :
( c_Suc(X20) != c_Suc(X54)
| X20 = X54 ),
c_0_460 ).
fof(c_0_954,axiom,
! [X18,X16] :
( c_Suc(X16) != c_Suc(X18)
| X16 = X18 ),
c_0_461 ).
fof(c_0_955,axiom,
! [X20,X55] : c_Lambda_OdB_OAbs(X55) != c_Lambda_OdB_OVar(X20),
c_0_462 ).
fof(c_0_956,axiom,
! [X20,X55] : c_Lambda_OdB_OVar(X20) != c_Lambda_OdB_OAbs(X55),
c_0_463 ).
fof(c_0_957,axiom,
! [X54] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X54),
c_0_464 ).
fof(c_0_958,axiom,
! [X11] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X11),
c_0_465 ).
fof(c_0_959,axiom,
! [X54] : c_Suc(X54) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_466 ).
fof(c_0_960,axiom,
! [X11] : c_Suc(X11) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_467 ).
fof(c_0_961,axiom,
! [X6] : X6 != c_Suc(X6),
c_0_468 ).
fof(c_0_962,axiom,
! [X6] : c_Suc(X6) != X6,
c_0_469 ).
fof(c_0_963,axiom,
class_Orderings_Oorder(tc_bool),
c_0_470 ).
fof(c_0_964,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_471 ).
fof(c_0_965,axiom,
class_Power_Opower(tc_nat),
c_0_472 ).
fof(c_0_966,axiom,
class_Orderings_Oorder(tc_nat),
c_0_473 ).
fof(c_0_967,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_474 ).
fof(c_0_968,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_475 ).
fof(c_0_969,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_476 ).
fof(c_0_970,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_477 ).
fof(c_0_971,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_478 ).
fof(c_0_972,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
c_0_479 ).
fof(c_0_973,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_480 ).
fof(c_0_974,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_481 ).
fof(c_0_975,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_482 ).
fof(c_0_976,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_483 ).
fof(c_0_977,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_484 ).
fof(c_0_978,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_485 ).
fof(c_0_979,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_486 ).
fof(c_0_980,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_487 ).
fof(c_0_981,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_488 ).
fof(c_0_982,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_489 ).
fof(c_0_983,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_490 ).
fof(c_0_984,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_491 ).
fof(c_0_985,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_492 ).
fof(c_0_986,plain,
! [X83,X84,X85,X86] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),X83),X84)))
| ~ c_Type_Otyping(X85,X83,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X83))
| ~ c_Type_Otyping(c_Type_Oshift(X85,X84,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X86) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_493])])]) ).
fof(c_0_987,plain,
! [X50,X51,X52,X53] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X52,X51,tc_Lambda_OdB,tc_Lambda_OdB)),X50),X53) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X52),X50),X53),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X50,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X53,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X51,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_988,plain,
! [X64,X65,X66,X67,X68,X69,X70] :
( X68 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X70,X68,X67,X64),X70,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X67,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X66),X65,tc_Lambda_OdB,tc_Lambda_OdB),X68)
| ~ c_Type_Otypings(X67,X65,X69)
| ~ c_Type_Otyping(X67,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X66),X65,tc_Lambda_OdB,tc_Lambda_OdB),X64,tc_Lambda_OdB,tc_Lambda_OdB),X70) ),
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_989,plain,
! [X64,X65,X66,X67,X68,X69] :
( c_Type_Otypings(X67,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X64,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X66,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X65,tc_Lambda_OdB,tc_Lambda_OdB),X68)
| ~ c_Type_Otypings(c_Type_Oshift(X67,X66,X69,tc_Type_Otype),X65,X68)
| ~ c_Type_Otyping(X67,X64,X69) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_496])])]) ).
fof(c_0_990,plain,
! [X64,X65,X66,X67,X68,X69,X70] :
( c_Type_Otypings(X67,X64,c_Type_Osko__Type__Xvar__app__types__1__1(X70,X68,X67,X64))
| ~ c_Type_Otyping(X67,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X66),X65,tc_Lambda_OdB,tc_Lambda_OdB),X68)
| ~ c_Type_Otypings(X67,X65,X69)
| ~ c_Type_Otyping(X67,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X66),X65,tc_Lambda_OdB,tc_Lambda_OdB),X64,tc_Lambda_OdB,tc_Lambda_OdB),X70) ),
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_991,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,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)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_498 ).
fof(c_0_992,plain,
! [X78,X79,X80] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X80,X79,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X80,X78,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X79,X78,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_499])])]) ).
fof(c_0_993,plain,
! [X78,X79,X80] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X80,X78,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X79,X78,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X80),X79)) ),
inference(variable_rename,[status(thm)],[c_0_500]) ).
fof(c_0_994,plain,
! [X78,X79,X80] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X80,X78,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X79,X78,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X80),X79)) ),
inference(variable_rename,[status(thm)],[c_0_501]) ).
fof(c_0_995,plain,
! [X78,X79,X80] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X80)),X79),X78,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X79))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X80),X79),c_HOL_Ozero__class_Ozero(tc_nat)),X78,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(variable_rename,[status(thm)],[c_0_502]) ).
fof(c_0_996,plain,
! [X50,X51,X52] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X51,X50,tc_Lambda_OdB,tc_Lambda_OdB)),X52) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X51),X52),c_List_Omap(c_COMBC(c_Lambda_Olift,X52,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X50,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_503]) ).
fof(c_0_997,plain,
! [X60,X61,X62,X63,X64,X65,X66,X67,X68,X69] :
( hAPP(hAPP(X65,hAPP(hAPP(X65,X67),X66)),hAPP(hAPP(X65,X61),X60)) = hAPP(hAPP(X65,X61),hAPP(hAPP(X65,hAPP(hAPP(X65,X67),X66)),X60))
| ~ c_Groebner__Basis_Ogb__semiring(X68,X65,X64,X63,X62,X69) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_504])])]) ).
fof(c_0_998,plain,
! [X60,X61,X62,X63,X64,X65,X66,X67,X68,X69] :
( hAPP(hAPP(X65,hAPP(hAPP(X65,X67),X66)),hAPP(hAPP(X65,X61),X60)) = hAPP(hAPP(X65,hAPP(hAPP(X65,X67),X61)),hAPP(hAPP(X65,X66),X60))
| ~ c_Groebner__Basis_Ogb__semiring(X68,X65,X64,X63,X62,X69) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_505])])]) ).
fof(c_0_999,plain,
! [X60,X61,X62,X63,X64,X65,X66,X67,X68,X69] :
( hAPP(hAPP(X65,hAPP(hAPP(X65,X67),X66)),hAPP(hAPP(X65,X61),X60)) = hAPP(hAPP(X65,X67),hAPP(hAPP(X65,X66),hAPP(hAPP(X65,X61),X60)))
| ~ c_Groebner__Basis_Ogb__semiring(X68,X65,X64,X63,X62,X69) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_506])])]) ).
fof(c_0_1000,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54,X55] :
( hAPP(hAPP(X53,hAPP(hAPP(X53,X54),X52)),hAPP(hAPP(X53,X51),X50)) = hAPP(hAPP(X53,hAPP(hAPP(X53,X54),X51)),hAPP(hAPP(X53,X52),X50))
| ~ c_Groebner__Basis_Ogb__semiring(X53,X49,X48,X47,X46,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_507])])]) ).
fof(c_0_1001,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X52,hAPP(hAPP(X49,X53),X50)),hAPP(hAPP(X49,X51),X50)) = hAPP(hAPP(X49,hAPP(hAPP(X52,X53),X51)),X50)
| ~ c_Groebner__Basis_Ogb__semiring(X52,X49,X48,X47,X46,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_508])])]) ).
fof(c_0_1002,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X49,hAPP(hAPP(X52,X53),X51)),X50) = hAPP(hAPP(X52,hAPP(hAPP(X49,X53),X50)),hAPP(hAPP(X49,X51),X50))
| ~ c_Groebner__Basis_Ogb__semiring(X52,X49,X48,X47,X46,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_509])])]) ).
fof(c_0_1003,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X51,hAPP(hAPP(X52,X47),X46)),X50) = hAPP(hAPP(X52,hAPP(hAPP(X51,X47),X50)),hAPP(hAPP(X51,X46),X50))
| ~ c_Groebner__Basis_Ogb__semiring(X53,X52,X51,X49,X48,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_510])])]) ).
fof(c_0_1004,plain,
! [X54,X55,X56,X57,X58,X59,X60,X61,X62] :
( hAPP(hAPP(X60,hAPP(hAPP(X58,X54),X59)),hAPP(hAPP(X58,X54),X57)) = hAPP(hAPP(X58,X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X57))
| ~ c_Groebner__Basis_Ogb__semiring(X61,X60,X58,X56,X55,X62) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_511])])]) ).
fof(c_0_1005,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X51,hAPP(hAPP(X49,X52),X50)),X50) = hAPP(hAPP(X49,hAPP(hAPP(X51,X52),X46)),X50)
| ~ c_Groebner__Basis_Ogb__semiring(X51,X49,X48,X47,X46,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_512])])]) ).
fof(c_0_1006,plain,
! [X60,X61,X62,X63,X64,X65,X66,X67,X68] :
( hAPP(hAPP(X64,hAPP(hAPP(X64,X66),X65)),X60) = hAPP(hAPP(X64,hAPP(hAPP(X64,X66),X60)),X65)
| ~ c_Groebner__Basis_Ogb__semiring(X67,X64,X63,X62,X61,X68) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_513])])]) ).
fof(c_0_1007,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X52,hAPP(hAPP(X52,X53),X51)),X50) = hAPP(hAPP(X52,hAPP(hAPP(X52,X53),X50)),X51)
| ~ c_Groebner__Basis_Ogb__semiring(X52,X49,X48,X47,X46,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_514])])]) ).
fof(c_0_1008,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X52,X48),hAPP(hAPP(X53,X47),X46)) = hAPP(hAPP(X53,hAPP(hAPP(X52,X48),X47)),hAPP(hAPP(X52,X48),X46))
| ~ c_Groebner__Basis_Ogb__semiring(X53,X52,X51,X50,X49,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_515])])]) ).
fof(c_0_1009,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X51,X50),hAPP(hAPP(X49,X52),X50)) = hAPP(hAPP(X49,hAPP(hAPP(X51,X52),X46)),X50)
| ~ c_Groebner__Basis_Ogb__semiring(X51,X49,X48,X47,X46,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_516])])]) ).
fof(c_0_1010,plain,
! [X60,X61,X62,X63,X64,X65,X66,X67,X68] :
( hAPP(hAPP(X64,hAPP(hAPP(X64,X66),X65)),X60) = hAPP(hAPP(X64,X66),hAPP(hAPP(X64,X65),X60))
| ~ c_Groebner__Basis_Ogb__semiring(X67,X64,X63,X62,X61,X68) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_517])])]) ).
fof(c_0_1011,plain,
! [X59,X60,X61,X62,X63,X64,X65,X66,X67] :
( hAPP(hAPP(X64,X65),hAPP(hAPP(X64,X60),X59)) = hAPP(hAPP(X64,hAPP(hAPP(X64,X65),X60)),X59)
| ~ c_Groebner__Basis_Ogb__semiring(X66,X64,X63,X62,X61,X67) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_518])])]) ).
fof(c_0_1012,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X52,hAPP(hAPP(X52,X53),X51)),X50) = hAPP(hAPP(X52,X53),hAPP(hAPP(X52,X51),X50))
| ~ c_Groebner__Basis_Ogb__semiring(X52,X49,X48,X47,X46,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_519])])]) ).
fof(c_0_1013,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X52,X53),hAPP(hAPP(X52,X51),X50)) = hAPP(hAPP(X52,hAPP(hAPP(X52,X53),X51)),X50)
| ~ c_Groebner__Basis_Ogb__semiring(X52,X49,X48,X47,X46,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_520])])]) ).
fof(c_0_1014,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X53,X48),hAPP(hAPP(X53,X47),X46)) = hAPP(hAPP(X53,hAPP(hAPP(X53,X48),X47)),X46)
| ~ c_Groebner__Basis_Ogb__semiring(X53,X52,X51,X50,X49,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_521])])]) ).
fof(c_0_1015,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X52,X48),hAPP(hAPP(X52,X47),X46)) = hAPP(hAPP(X52,hAPP(hAPP(X52,X48),X47)),X46)
| ~ c_Groebner__Basis_Ogb__semiring(X53,X52,X51,X50,X49,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_522])])]) ).
fof(c_0_1016,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X51,hAPP(hAPP(X50,X46),X49)),X46) = hAPP(hAPP(X50,X46),c_Suc(X49))
| ~ c_Groebner__Basis_Ogb__semiring(X52,X51,X50,X48,X47,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_523])])]) ).
fof(c_0_1017,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X51,X50),X50) = hAPP(hAPP(X49,hAPP(hAPP(X51,X46),X46)),X50)
| ~ c_Groebner__Basis_Ogb__semiring(X51,X49,X48,X47,X46,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_524])])]) ).
fof(c_0_1018,plain,
! [X59,X60,X61,X62,X63,X64,X65,X66,X67] :
( hAPP(hAPP(X64,X65),hAPP(hAPP(X64,X60),X59)) = hAPP(hAPP(X64,X60),hAPP(hAPP(X64,X65),X59))
| ~ c_Groebner__Basis_Ogb__semiring(X66,X64,X63,X62,X61,X67) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_525])])]) ).
fof(c_0_1019,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53,X54] :
( hAPP(hAPP(X52,X53),hAPP(hAPP(X52,X51),X50)) = hAPP(hAPP(X52,X51),hAPP(hAPP(X52,X53),X50))
| ~ c_Groebner__Basis_Ogb__semiring(X52,X49,X48,X47,X46,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_526])])]) ).
fof(c_0_1020,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X49,X46),c_Suc(X50)) = hAPP(hAPP(X51,X46),hAPP(hAPP(X49,X46),X50))
| ~ c_Groebner__Basis_Ogb__semiring(X52,X51,X49,X48,X47,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_527])])]) ).
fof(c_0_1021,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X50,X46),c_Suc(X49)) = hAPP(hAPP(X51,X46),hAPP(hAPP(X50,X46),X49))
| ~ c_Groebner__Basis_Ogb__semiring(X52,X51,X50,X48,X47,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_528])])]) ).
fof(c_0_1022,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X51,X46),hAPP(hAPP(X50,X46),X49)) = hAPP(hAPP(X50,X46),c_Suc(X49))
| ~ c_Groebner__Basis_Ogb__semiring(X52,X51,X50,X48,X47,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_529])])]) ).
fof(c_0_1023,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X49,X51),X50) = hAPP(hAPP(X49,X50),X51)
| ~ c_Groebner__Basis_Ogb__semiring(X52,X49,X48,X47,X46,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_530])])]) ).
fof(c_0_1024,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X51,X52),X50) = hAPP(hAPP(X51,X50),X52)
| ~ c_Groebner__Basis_Ogb__semiring(X51,X49,X48,X47,X46,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_531])])]) ).
fof(c_0_1025,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X52,X47),X46) = hAPP(hAPP(X52,X46),X47)
| ~ c_Groebner__Basis_Ogb__semiring(X52,X51,X50,X49,X48,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_532])])]) ).
fof(c_0_1026,plain,
! [X46,X47,X48,X49,X50,X51,X52,X53] :
( hAPP(hAPP(X51,X47),X46) = hAPP(hAPP(X51,X46),X47)
| ~ c_Groebner__Basis_Ogb__semiring(X52,X51,X50,X49,X48,X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_533])])]) ).
fof(c_0_1027,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X49,X46),c_HOL_Ozero__class_Ozero(tc_nat)) = X47
| ~ c_Groebner__Basis_Ogb__semiring(X51,X50,X49,X48,X47,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_534])])]) ).
fof(c_0_1028,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X50,X47),X51) = X51
| ~ c_Groebner__Basis_Ogb__semiring(X50,X49,X48,X47,X46,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_535])])]) ).
fof(c_0_1029,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X50,X51),X47) = X51
| ~ c_Groebner__Basis_Ogb__semiring(X50,X49,X48,X47,X46,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_536])])]) ).
fof(c_0_1030,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X49,X47),X50) = X47
| ~ c_Groebner__Basis_Ogb__semiring(X51,X49,X48,X47,X46,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_537])])]) ).
fof(c_0_1031,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X49,X50),X47) = X47
| ~ c_Groebner__Basis_Ogb__semiring(X51,X49,X48,X47,X46,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_538])])]) ).
fof(c_0_1032,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X49,X46),X50) = X50
| ~ c_Groebner__Basis_Ogb__semiring(X51,X49,X48,X47,X46,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_539])])]) ).
fof(c_0_1033,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X49,X50),X46) = X50
| ~ c_Groebner__Basis_Ogb__semiring(X51,X49,X48,X47,X46,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_540])])]) ).
fof(c_0_1034,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X51,X48),X46) = X46
| ~ c_Groebner__Basis_Ogb__semiring(X51,X50,X49,X48,X47,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_541])])]) ).
fof(c_0_1035,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X50,X48),X46) = X48
| ~ c_Groebner__Basis_Ogb__semiring(X51,X50,X49,X48,X47,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_542])])]) ).
fof(c_0_1036,plain,
! [X46,X47,X48,X49,X50,X51,X52] :
( hAPP(hAPP(X50,X47),X46) = X46
| ~ c_Groebner__Basis_Ogb__semiring(X51,X50,X49,X48,X47,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_543])])]) ).
fof(c_0_1037,plain,
! [X74,X75,X76,X77,X78,X79] : c_Lambda_OdB_OdB__rec(X76,X75,X74,hAPP(hAPP(c_Lambda_OdB_OApp,X78),X77),X79) = hAPP(hAPP(hAPP(hAPP(X75,X78),X77),c_Lambda_OdB_OdB__rec(X76,X75,X74,X78,X79)),c_Lambda_OdB_OdB__rec(X76,X75,X74,X77,X79)),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_1038,plain,
! [X74,X75,X76,X77,X78,X79] :
( ~ hBOOL(hAPP(X79,c_Lambda_OdB_OdB__case(X76,X75,X74,hAPP(hAPP(c_Lambda_OdB_OApp,X78),X77),t_a)))
| hBOOL(hAPP(X79,hAPP(hAPP(X75,X78),X77))) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_1039,plain,
! [X75,X76,X77,X78,X79,X80] :
( ~ hBOOL(hAPP(X80,c_Lambda_OdB_OdB__case(X79,X78,X77,hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75),t_a)))
| hBOOL(hAPP(X80,hAPP(hAPP(X78,X76),X75))) ),
inference(variable_rename,[status(thm)],[c_0_546]) ).
fof(c_0_1040,plain,
! [X63,X64,X65,X66,X67] :
( X67 = X66
| ~ c_Type_Otyping(X65,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X64),X63,tc_Lambda_OdB,tc_Lambda_OdB),X66)
| ~ c_Type_Otyping(X65,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X64),X63,tc_Lambda_OdB,tc_Lambda_OdB),X67) ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_1041,plain,
! [X72,X73,X74,X75,X76] :
( ~ hBOOL(hAPP(X76,c_Lambda_OdB_OdB__case(X75,X74,X73,c_Lambda_OdB_OVar(X72),t_a)))
| hBOOL(hAPP(X76,hAPP(X75,X72))) ),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_1042,plain,
! [X27,X28,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,c_Lambda_OdB_OVar(X27),t_a)))
| hBOOL(hAPP(X31,hAPP(X30,X27))) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_1043,plain,
! [X32,X33,X34,X35,X36] :
( ~ hBOOL(hAPP(X36,c_Lambda_OdB_OdB__case(X35,X34,X33,c_Lambda_OdB_OAbs(X32),t_a)))
| hBOOL(hAPP(X36,hAPP(X33,X32))) ),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_1044,plain,
! [X51,X52,X53,X54,X55] :
( ~ hBOOL(hAPP(X55,c_Lambda_OdB_OdB__case(X53,X52,X51,c_Lambda_OdB_OAbs(X54),t_a)))
| hBOOL(hAPP(X55,hAPP(X51,X54))) ),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_1045,plain,
! [X78,X79,X80] :
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X80),X79),c_HOL_Ozero__class_Ozero(tc_nat)),X78,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X79,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(X80)),X79),X78,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_1046,plain,
! [X62,X63,X64,X65] :
( c_Type_Otyping(X64,c_Lambda_OdB_OVar(X63),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X65,X64,X63,X62),X65,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X64,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X63),X62,tc_Lambda_OdB,tc_Lambda_OdB),X65) ),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_1047,plain,
! [X62,X63,X64,X65] :
( c_Type_Otyping(X64,X63,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X65,X64,X63,X62),X65,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X64,c_List_Ofoldl(c_Lambda_OdB_OApp,X63,X62,tc_Lambda_OdB,tc_Lambda_OdB),X65) ),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_1048,plain,
! [X62,X63,X64,X65] :
( c_Type_Otyping(X64,X63,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X65,X64,X63,X62),X65,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X64,c_List_Ofoldl(c_Lambda_OdB_OApp,X63,X62,tc_Lambda_OdB,tc_Lambda_OdB),X65) ),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_1049,plain,
! [X64,X65,X66,X67,X68] :
( c_Type_Otyping(X66,c_List_Ofoldl(c_Lambda_OdB_OApp,X65,X64,tc_Lambda_OdB,tc_Lambda_OdB),X68)
| ~ c_Type_Otypings(X66,X64,X67)
| ~ c_Type_Otyping(X66,X65,c_List_Ofoldr(c_Type_Otype_OFun,X67,X68,tc_Type_Otype,tc_Type_Otype)) ),
inference(variable_rename,[status(thm)],[c_0_556]) ).
fof(c_0_1050,plain,
! [X64,X65,X66,X67,X68] :
( c_Type_Otypings(c_Type_Oshift(X66,X65,X67,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X65,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X64,tc_Lambda_OdB,tc_Lambda_OdB),X68)
| ~ c_Type_Otypings(X66,X64,X68) ),
inference(variable_rename,[status(thm)],[c_0_557]) ).
fof(c_0_1051,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_558 ).
fof(c_0_1052,plain,
! [X47] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X47,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X47,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_1053,plain,
! [X7,X8] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X7,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X7,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_560])])]) ).
fof(c_0_1054,plain,
! [X30,X31,X32,X33,X34,X35] : c_List_Ofoldl(X32,X33,c_List_Oappend(X31,X30,X34),X35,X34) = c_List_Ofoldl(X32,c_List_Ofoldl(X32,X33,X31,X35,X34),X30,X35,X34),
inference(variable_rename,[status(thm)],[c_0_561]) ).
fof(c_0_1055,plain,
! [X30,X31,X32,X33,X34,X35] : c_List_Ofoldr(X32,c_List_Oappend(X31,X30,X34),X33,X34,X35) = c_List_Ofoldr(X32,X31,c_List_Ofoldr(X32,X30,X33,X34,X35),X34,X35),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_1056,plain,
! [X62,X63,X64,X65] :
( c_Type_Otypings(X64,X62,c_Type_Osko__Type__Xvar__app__typesE__1__1(X65,X64,X63,X62))
| ~ c_Type_Otyping(X64,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X63),X62,tc_Lambda_OdB,tc_Lambda_OdB),X65) ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_1057,plain,
! [X62,X63,X64,X65] :
( c_Type_Otypings(X64,X62,c_Type_Osko__Type__Xlist__app__typeE__1__1(X65,X64,X63,X62))
| ~ c_Type_Otyping(X64,c_List_Ofoldl(c_Lambda_OdB_OApp,X63,X62,tc_Lambda_OdB,tc_Lambda_OdB),X65) ),
inference(variable_rename,[status(thm)],[c_0_564]) ).
fof(c_0_1058,plain,
! [X62,X63,X64,X65] :
( c_Type_Otypings(X64,X62,c_Type_Osko__Type__Xlist__app__typeD__1__1(X65,X64,X63,X62))
| ~ c_Type_Otyping(X64,c_List_Ofoldl(c_Lambda_OdB_OApp,X63,X62,tc_Lambda_OdB,tc_Lambda_OdB),X65) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_1059,plain,
! [X78,X79,X80,X81] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X81),X80,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X79),X78,tc_Lambda_OdB,tc_Lambda_OdB)
| X80 = X78 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_566])])]) ).
fof(c_0_1060,plain,
! [X78,X79,X80,X81] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X81),X80,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X79),X78,tc_Lambda_OdB,tc_Lambda_OdB)
| X81 = X79 ),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_1061,plain,
! [X78,X79,X80,X81] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X81),X79,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X80),X78,tc_Lambda_OdB,tc_Lambda_OdB)
| X79 = X78 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_568])])]) ).
fof(c_0_1062,plain,
! [X78,X79,X80,X81] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X81),X79,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X80),X78,tc_Lambda_OdB,tc_Lambda_OdB)
| X81 = X80 ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_1063,plain,
! [X31,X32,X33,X34] :
( ~ class_OrderedGroup_Osemigroup__add(X34)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X34),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X34),X33),X32),X31,X34,X34) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X34),X33),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X34),X32,X31,X34,X34)) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_1064,plain,
! [X78,X79,X80,X81] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X81),X78,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X80),X79,tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_571]) ).
fof(c_0_1065,plain,
! [X47,X48,X49] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X49,X47,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X48,X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X49 = X48 ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_1066,plain,
! [X30,X31,X32,X33,X34,X35] : c_List_Ofoldr(X32,c_List_Olist_OCons(X31,X30,X34),X33,X34,X35) = hAPP(hAPP(X32,X31),c_List_Ofoldr(X32,X30,X33,X34,X35)),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_1067,plain,
! [X66,X67,X68,X69,X70] :
( c_List_Ofoldl(X69,hAPP(hAPP(X69,X68),X67),X66,X70,X70) = hAPP(hAPP(X69,X68),c_List_Ofoldl(X69,X67,X66,X70,X70))
| ~ c_OrderedGroup_Osemigroup__add(X69,X70) ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_1068,plain,
! [X66,X67,X68,X69,X70] :
( hAPP(hAPP(X69,X68),c_List_Ofoldl(X69,X67,X66,X70,X70)) = c_List_Ofoldl(X69,X68,X66,X70,X70)
| ~ c_OrderedGroup_Omonoid__add(X67,X69,X70) ),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_1069,plain,
! [X31,X32,X33] :
( ~ class_OrderedGroup_Omonoid__add(X33)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X33),X32),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X33),c_HOL_Ozero__class_Ozero(X33),X31,X33,X33)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X33),X32,X31,X33,X33) ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_1070,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Omonoid__add(X12)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X12),X11,X10,X12,X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X12),X10,c_HOL_Ozero__class_Ozero(X12),X12,X12)) ),
inference(variable_rename,[status(thm)],[c_0_577]) ).
fof(c_0_1071,plain,
! [X51,X52,X53,X54,X55] : c_Lambda_OdB_OdB__rec(X53,X52,X51,c_Lambda_OdB_OAbs(X54),X55) = hAPP(hAPP(X51,X54),c_Lambda_OdB_OdB__rec(X53,X52,X51,X54,X55)),
inference(variable_rename,[status(thm)],[c_0_578]) ).
fof(c_0_1072,plain,
! [X47,X48,X49,X50] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X50),X49) != c_List_Ofoldl(c_Lambda_OdB_OApp,X48,X47,tc_Lambda_OdB,tc_Lambda_OdB)
| X50 = c_List_Ofoldl(c_Lambda_OdB_OApp,X48,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X50,X49,X48,X47),tc_Lambda_OdB,tc_Lambda_OdB)
| X47 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_579]) ).
fof(c_0_1073,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_580 ).
fof(c_0_1074,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_581 ).
fof(c_0_1075,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_582 ).
fof(c_0_1076,plain,
! [X30,X31,X32,X33,X34,X35] : c_List_Ofoldl(X32,X33,c_List_Olist_OCons(X31,X30,X34),X35,X34) = c_List_Ofoldl(X32,hAPP(hAPP(X32,X33),X31),X30,X35,X34),
inference(variable_rename,[status(thm)],[c_0_583]) ).
fof(c_0_1077,plain,
! [X28,X29,X30,X31,X32,X33] : hAPP(c_COMBC(X30,X29,X32,X31,X33),X28) = hAPP(hAPP(X30,X28),X29),
inference(variable_rename,[status(thm)],[c_0_584]) ).
fof(c_0_1078,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Omonoid__add(X6)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6),X5,X6,X6) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X6),X5,c_HOL_Ozero__class_Ozero(X6),X6,X6) ),
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_1079,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Oab__semigroup__add(X12)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X12),X10,X11,X12,X12) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X12),X11,X10,X12,X12) ),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_1080,plain,
! [X62,X63,X64,X65] :
( c_Type_Otyping(X64,X63,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X65,X64,X63,X62)),X65))
| ~ c_Type_Otyping(X64,hAPP(hAPP(c_Lambda_OdB_OApp,X63),X62),X65) ),
inference(variable_rename,[status(thm)],[c_0_587]) ).
fof(c_0_1081,plain,
! [X34,X35,X36] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X36),X35) != c_List_Ofoldl(c_Lambda_OdB_OApp,X34,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X36),X35) = X34 ),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_1082,plain,
! [X78,X79,X80,X81] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X80)),X78) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X81),X79,tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_1083,plain,
! [X78,X79,X80] :
( c_Lambda_OdB_OAbs(X80) != c_List_Ofoldl(c_Lambda_OdB_OApp,X79,X78,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X80) = X79 ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_1084,plain,
! [X78,X79,X80] :
( c_Lambda_OdB_OVar(X80) != c_List_Ofoldl(c_Lambda_OdB_OApp,X79,X78,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X80) = X79 ),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_1085,plain,
! [X78,X79,X80] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X79,X78,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X80)
| X79 = c_Lambda_OdB_OAbs(X80) ),
inference(variable_rename,[status(thm)],[c_0_592]) ).
fof(c_0_1086,plain,
! [X78,X79,X80] :
( c_Lambda_OdB_OVar(X80) != c_List_Ofoldl(c_Lambda_OdB_OApp,X79,X78,tc_Lambda_OdB,tc_Lambda_OdB)
| X78 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_593])])]) ).
fof(c_0_1087,plain,
! [X78,X79,X80] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X79,X78,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X80)
| X78 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_594])])]) ).
fof(c_0_1088,plain,
! [X78,X79,X80] :
( c_Lambda_OdB_OAbs(X80) != c_List_Ofoldl(c_Lambda_OdB_OApp,X79,X78,tc_Lambda_OdB,tc_Lambda_OdB)
| X78 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_595])])]) ).
fof(c_0_1089,plain,
! [X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X21,X22),X19),X20))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X21,X22,X22),X22),X20),X19)) ),
inference(variable_rename,[status(thm)],[c_0_596]) ).
fof(c_0_1090,plain,
! [X19,X20,X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(X23,X20),X22))
| c_ListOrder_Ostep1(X23,X19,X21,X24)
| ~ c_ListOrder_Ostep1(X23,c_List_Oappend(X19,c_List_Olist_OCons(X20,c_List_Olist_ONil(X24),X24),X24),c_List_Oappend(X21,c_List_Olist_OCons(X22,c_List_Olist_ONil(X24),X24),X24),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_597])])]) ).
fof(c_0_1091,plain,
! [X19,X20,X21,X22,X23,X24] :
( X19 = X21
| c_ListOrder_Ostep1(X23,X19,X21,X24)
| ~ c_ListOrder_Ostep1(X23,c_List_Oappend(X19,c_List_Olist_OCons(X20,c_List_Olist_ONil(X24),X24),X24),c_List_Oappend(X21,c_List_Olist_OCons(X22,c_List_Olist_ONil(X24),X24),X24),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_598])])]) ).
fof(c_0_1092,plain,
! [X19,X20,X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(X23,X20),X22))
| X20 = X22
| ~ c_ListOrder_Ostep1(X23,c_List_Oappend(X19,c_List_Olist_OCons(X20,c_List_Olist_ONil(X24),X24),X24),c_List_Oappend(X21,c_List_Olist_OCons(X22,c_List_Olist_ONil(X24),X24),X24),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_599])])]) ).
fof(c_0_1093,plain,
! [X63,X64,X65,X66,X67] : c_Type_Oshift(c_Type_Oshift(X64,X63,X65,X67),c_HOL_Ozero__class_Ozero(tc_nat),X66,X67) = c_Type_Oshift(c_Type_Oshift(X64,c_HOL_Ozero__class_Ozero(tc_nat),X66,X67),c_Suc(X63),X65,X67),
inference(variable_rename,[status(thm)],[c_0_600]) ).
fof(c_0_1094,plain,
! [X19,X20,X21,X22,X23,X24] :
( X19 = X21
| X20 = X22
| ~ c_ListOrder_Ostep1(X23,c_List_Oappend(X19,c_List_Olist_OCons(X20,c_List_Olist_ONil(X24),X24),X24),c_List_Oappend(X21,c_List_Olist_OCons(X22,c_List_Olist_ONil(X24),X24),X24),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_601])])]) ).
fof(c_0_1095,plain,
! [X82,X83,X84,X85,X86,X87,X88] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X88),X87)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X83),X82),X84)))
| ~ c_Type_Otyping(X85,X82,X88)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X82))
| ~ c_Type_Otyping(c_Type_Oshift(X85,X84,X88,tc_Type_Otype),X83,X86)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X83)) ),
inference(variable_rename,[status(thm)],[c_0_602]) ).
fof(c_0_1096,plain,
! [X82,X83,X84,X85,X86,X87,X88] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X88),X87)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X83),X82),X84)))
| ~ c_Type_Otyping(X85,X82,X87)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X82))
| ~ c_Type_Otyping(c_Type_Oshift(X85,X84,X87,tc_Type_Otype),X83,X86)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X83)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_603])])]) ).
fof(c_0_1097,plain,
! [X50,X51,X52,X53] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X50),X52),X53)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X50),X51),X53)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X52),X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_604])])]) ).
fof(c_0_1098,plain,
! [X50,X51,X52,X53] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X52),X50),X53)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X51),X50),X53)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X52),X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_605])])]) ).
fof(c_0_1099,plain,
! [X30,X31,X32,X33,X34] : c_List_Omap(X32,c_List_Oappend(X31,X30,X33),X33,X34) = c_List_Oappend(c_List_Omap(X32,X31,X33,X34),c_List_Omap(X32,X30,X33,X34),X34),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_1100,plain,
! [X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X21,X22,X22),X22),X20),X19))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X21,X22),X19),X20)) ),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_1101,plain,
! [X83,X84,X85,X86] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X83),X84)))
| ~ c_Type_Otyping(X85,X83,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X83))
| ~ c_Type_Otyping(c_Type_Oshift(X85,X84,v_T____,tc_Type_Otype),v_a____,X86) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_608])])]) ).
fof(c_0_1102,plain,
! [X74,X75,X76,X77,X78,X79] : c_Lambda_OdB_OdB__case(X76,X75,X74,hAPP(hAPP(c_Lambda_OdB_OApp,X78),X77),X79) = hAPP(hAPP(X75,X78),X77),
inference(variable_rename,[status(thm)],[c_0_609]) ).
fof(c_0_1103,plain,
! [X29,X30] : hAPP(hAPP(c_Lambda_OdB_OApp,X30),X29) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X30),X29),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_1104,plain,
! [X50,X51,X52,X53] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X50),X52),X53)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X50),X51),X53)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X52),X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_611])])]) ).
fof(c_0_1105,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Omonoid__add(X6)
| c_List_Olistsum(X5,X6) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6),X5,X6,X6) ),
inference(variable_rename,[status(thm)],[c_0_612]) ).
fof(c_0_1106,plain,
! [X5,X6] :
( ~ class_OrderedGroup_Omonoid__add(X6)
| c_List_Olistsum(X5,X6) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X6),X5,c_HOL_Ozero__class_Ozero(X6),X6,X6) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_1107,plain,
! [X24,X25,X26,X27,X28] : c_Lambda_OdB_OdB__rec(X27,X26,X25,c_Lambda_OdB_OVar(X24),X28) = hAPP(X27,X24),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_1108,plain,
! [X51,X52,X53,X54,X55] : c_Lambda_OdB_OdB__case(X53,X52,X51,c_Lambda_OdB_OAbs(X54),X55) = hAPP(X51,X54),
inference(variable_rename,[status(thm)],[c_0_615]) ).
fof(c_0_1109,plain,
! [X24,X25,X26,X27,X28] : c_Lambda_OdB_OdB__case(X27,X26,X25,c_Lambda_OdB_OVar(X24),X28) = hAPP(X27,X24),
inference(variable_rename,[status(thm)],[c_0_616]) ).
fof(c_0_1110,plain,
! [X50,X51,X52,X53] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X52),X50),X53)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X51),X50),X53)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X52),X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_617])])]) ).
fof(c_0_1111,plain,
! [X13] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X13),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X13),
inference(variable_rename,[status(thm)],[c_0_618]) ).
fof(c_0_1112,plain,
! [X34] : X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X34),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X34),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_1113,plain,
! [X13] : c_Lambda_OdB_OAbs(X13) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X13),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_1114,plain,
! [X12] : c_Lambda_OdB_OVar(X12) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X12),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1115,plain,
! [X30,X31,X32,X33] : c_List_Ofoldl(X30,X31,c_List_Olist_ONil(X32),X33,X32) = X31,
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1116,plain,
! [X30,X31,X32,X33] : c_List_Ofoldr(X30,c_List_Olist_ONil(X32),X31,X32,X33) = X31,
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1117,plain,
! [X84,X85,X86,X87,X88,X89] :
( ~ c_Type_Otyping(X87,X84,X88)
| ~ c_Type_Otyping(c_Type_Oshift(X87,X86,X88,tc_Type_Otype),X85,X89)
| c_Type_Otyping(X87,hAPP(hAPP(hAPP(c_Lambda_Osubst,X85),X84),X86),X89) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_624])])]) ).
fof(c_0_1118,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_625]) ).
fof(c_0_1119,plain,
! [X19,X20,X21,X22,X23,X24] :
( c_ListOrder_Ostep1(X23,X19,X21,X24)
| hBOOL(hAPP(hAPP(X23,X20),X22))
| ~ c_ListOrder_Ostep1(X23,c_List_Olist_OCons(X20,X19,X24),c_List_Olist_OCons(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_626]) ).
fof(c_0_1120,plain,
! [X79,X80,X81,X82] :
( c_Type_Otyping(X80,c_Lambda_OdB_OAbs(X79),hAPP(hAPP(c_Type_Otype_OFun,X82),X81))
| ~ c_Type_Otyping(c_Type_Oshift(X80,c_HOL_Ozero__class_Ozero(tc_nat),X82,tc_Type_Otype),X79,X81) ),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1121,plain,
! [X19,X20,X21,X22,X23,X24] :
( c_ListOrder_Ostep1(X23,X19,X21,X24)
| X21 = X19
| ~ c_ListOrder_Ostep1(X23,c_List_Olist_OCons(X20,X19,X24),c_List_Olist_OCons(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1122,plain,
! [X62,X63,X64] :
( c_Type_Otyping(c_Type_Oshift(X63,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X64,X63,X62),tc_Type_Otype),X62,c_Type_Osko__Type__Xtyping__elims__3__2(X64,X63,X62))
| ~ c_Type_Otyping(X63,c_Lambda_OdB_OAbs(X62),X64) ),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_1123,plain,
! [X30,X31,X32,X33,X34] : c_List_Omap(X32,c_List_Olist_OCons(X31,X30,X33),X33,X34) = c_List_Olist_OCons(hAPP(X32,X31),c_List_Omap(X32,X30,X33,X34),X34),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1124,plain,
! [X36,X37,X38,X39,X40] : c_List_Olist_OCons(hAPP(X38,X37),c_List_Omap(X38,X36,X39,X40),X40) = c_List_Omap(X38,c_List_Olist_OCons(X37,X36,X39),X39,X40),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_1125,plain,
! [X32,X33,X34,X35,X36] : c_List_Omap(X34,c_List_Olist_OCons(X33,X32,X35),X35,X36) = c_List_Olist_OCons(hAPP(X34,X33),c_List_Omap(X34,X32,X35,X36),X36),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1126,plain,
! [X37,X38,X39,X40] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X38),X37)),X39),X40) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X38),X39),X40)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X37),X39),X40)),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_1127,plain,
! [X14,X15,X16,X17,X18] :
( hBOOL(hAPP(hAPP(X14,X15),X16))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X14,X18,X17),X16),X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_634])])]) ).
fof(c_0_1128,plain,
! [X16,X17,X18,X19,X20] :
( hBOOL(hAPP(hAPP(X16,X17),X18))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X16,X20,X19),X18),X17)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_635])])]) ).
fof(c_0_1129,plain,
! [X17,X18,X19,X20,X21] :
( c_ListOrder_Ostep1(X20,c_List_Olist_OCons(X19,X17,X21),c_List_Olist_OCons(X19,X18,X21),X21)
| ~ c_ListOrder_Ostep1(X20,X17,X18,X21) ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1130,plain,
! [X49,X50,X51,X52,X53] :
( c_ListOrder_Ostep1(X52,c_List_Oappend(X49,X50,X53),c_List_Oappend(X49,X51,X53),X53)
| ~ c_ListOrder_Ostep1(X52,X50,X51,X53) ),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1131,plain,
! [X17,X18,X19,X20,X21] :
( ~ c_ListOrder_Ostep1(X20,X17,X18,X21)
| c_ListOrder_Ostep1(X20,c_List_Oappend(X17,X19,X21),c_List_Oappend(X18,X19,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1132,plain,
! [X50,X51,X52] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X51),X52)),hAPP(hAPP(c_Lambda_Olift,X50),X52)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X51),X50)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_639])])]) ).
fof(c_0_1133,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_640]) ).
fof(c_0_1134,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_641])])]) ).
fof(c_0_1135,plain,
! [X34,X35] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X35)),X34)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X35),X34),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1136,plain,
! [X19,X20,X21,X22,X23,X24] :
( X22 = X20
| hBOOL(hAPP(hAPP(X23,X20),X22))
| ~ c_ListOrder_Ostep1(X23,c_List_Olist_OCons(X20,X19,X24),c_List_Olist_OCons(X22,X21,X24),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_643])])]) ).
fof(c_0_1137,plain,
! [X19,X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X22,X23),X21),X19))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X22,X23),X20),X19))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X22,X23),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1138,plain,
! [X62,X63,X64,X65] :
( c_Type_Otyping(X64,X62,c_Type_Osko__Type__Xtyping__elims__2__1(X65,X64,X63,X62))
| ~ c_Type_Otyping(X64,hAPP(hAPP(c_Lambda_OdB_OApp,X63),X62),X65) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1139,plain,
! [X19,X20,X21,X22,X23,X24] :
( X22 = X20
| X21 = X19
| ~ c_ListOrder_Ostep1(X23,c_List_Olist_OCons(X20,X19,X24),c_List_Olist_OCons(X22,X21,X24),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_646])])]) ).
fof(c_0_1140,plain,
! [X11,X12,X13,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X15)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X12),X11)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X11)) ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1141,plain,
! [X62,X63,X64] :
( c_Type_Otyping(c_Type_Oshift(X63,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X63,X62),tc_Type_Otype),X62,c_Type_Osko__Type__Xabs__typeE__1__2(X63,X62))
| ~ c_Type_Otyping(X63,c_Lambda_OdB_OAbs(X62),X64) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_648])])]) ).
fof(c_0_1142,plain,
! [X63,X64,X65,X66,X67] :
( c_Type_Otyping(c_Type_Oshift(X65,X64,X66,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X63),X64),X67)
| ~ c_Type_Otyping(X65,X63,X67) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1143,plain,
! [X17,X18,X19,X20] : c_List_Oappend(c_List_Oreplicate(X19,X18,X20),c_List_Olist_OCons(X18,X17,X20),X20) = c_List_Olist_OCons(X18,c_List_Oappend(c_List_Oreplicate(X19,X18,X20),X17,X20),X20),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1144,plain,
! [X14,X15,X16,X17,X18] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X14,X18,X17),X16),X15))
| ~ hBOOL(hAPP(hAPP(X14,X15),X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_651])])]) ).
fof(c_0_1145,plain,
! [X14,X15,X16,X17,X18] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X14,X18,X17),X15),X16))
| ~ hBOOL(hAPP(hAPP(X14,X16),X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_652])])]) ).
fof(c_0_1146,plain,
! [X34,X35,X36] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X36),X34)),hAPP(hAPP(c_Lambda_OdB_OApp,X35),X34)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X36),X35)) ),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1147,plain,
! [X34,X35,X36] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X34),X36)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X35)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X36),X35)) ),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1148,plain,
! [X50,X51,X52] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X51),X52)),hAPP(hAPP(c_Lambda_Olift,X50),X52)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X51),X50)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_655])])]) ).
fof(c_0_1149,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X17),X16),X14))
| ~ hBOOL(hAPP(hAPP(X13,X15),X14))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1150,plain,
! [X13,X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X17),X16),X14))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X17),X15),X14))
| ~ hBOOL(hAPP(hAPP(X13,X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1151,plain,
! [X62,X63,X64,X65,X66] :
( hAPP(c_Type_Oshift(X64,X63,X65,X66),X62) = hAPP(X64,X62)
| ~ c_HOL_Oord__class_Oless(X62,X63,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_658])])]) ).
fof(c_0_1152,plain,
! [X32,X33,X34,X35,X36] :
( ~ hBOOL(hAPP(hAPP(X35,X32),X33))
| c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X32,X34,X36),c_List_Olist_OCons(X33,X34,X36),X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_659])])]) ).
fof(c_0_1153,plain,
! [X19,X20,X21,X22,X23] :
( c_List_Oappend(X21,c_List_Olist_OCons(X22,c_List_Olist_ONil(X23),X23),X23) != c_List_Oappend(X19,c_List_Olist_OCons(X20,c_List_Olist_ONil(X23),X23),X23)
| X22 = X20 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_660])])]) ).
fof(c_0_1154,plain,
! [X19,X20,X21,X22,X23] :
( c_List_Oappend(X21,c_List_Olist_OCons(X22,c_List_Olist_ONil(X23),X23),X23) != c_List_Oappend(X19,c_List_Olist_OCons(X20,c_List_Olist_ONil(X23),X23),X23)
| X21 = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_661])])]) ).
fof(c_0_1155,plain,
! [X37,X38,X39,X40] : c_List_Oappend(c_List_Oreplicate(X38,X37,X40),c_List_Oreplicate(X39,X37,X40),X40) = c_List_Oappend(c_List_Oreplicate(X39,X37,X40),c_List_Oreplicate(X38,X37,X40),X40),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1156,plain,
! [X19,X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),c_Orderings_Oord__class_Omax(X21,X20,X22)),X19) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),X19),X22) ),
inference(variable_rename,[status(thm)],[c_0_663]) ).
fof(c_0_1157,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X11)),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X10)),X11) ),
inference(variable_rename,[status(thm)],[c_0_664]) ).
fof(c_0_1158,plain,
! [X62,X63,X64,X65] : hAPP(c_Type_Oshift(X63,X62,X64,X65),X62) = X64,
inference(variable_rename,[status(thm)],[c_0_665]) ).
fof(c_0_1159,plain,
! [X37,X38,X39,X40] : c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X38),X37),X39,X40) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X38,X39,X40)),c_Lambda_Osubstn(X37,X39,X40)),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1160,plain,
! [X37,X38,X39,X40] : c_Lambda_Oliftn(X39,hAPP(hAPP(c_Lambda_OdB_OApp,X38),X37),X40) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X39,X38,X40)),c_Lambda_Oliftn(X39,X37,X40)),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1161,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X13)
| c_HOL_Oord__class_Oless(X12,X11,X13)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X10),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X10),X11),X13) ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1162,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X13)
| c_HOL_Oord__class_Oless(X12,X11,X13)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X11),X10),X13) ),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1163,plain,
! [X52,X53,X54] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X52),c_Lambda_OdB_OVar(X54)),X53)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X52)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_670])])]) ).
fof(c_0_1164,plain,
! [X62,X63,X64] :
( X64 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X64,X63,X62)),c_Type_Osko__Type__Xtyping__elims__3__2(X64,X63,X62))
| ~ c_Type_Otyping(X63,c_Lambda_OdB_OAbs(X62),X64) ),
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1165,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_672]) ).
fof(c_0_1166,plain,
! [X50,X51,X52] : c_List_Oappend(c_List_Oreplicate(X51,X50,X52),c_List_Olist_OCons(X50,c_List_Olist_ONil(X52),X52),X52) = c_List_Olist_OCons(X50,c_List_Oreplicate(X51,X50,X52),X52),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1167,plain,
! [X11,X12,X13,X14,X15] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X15)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X14),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X11),X15)
| ~ c_HOL_Oord__class_Oless(X12,X11,X15)
| ~ c_HOL_Oord__class_Oless(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1168,plain,
! [X30,X31,X32,X33,X34] : c_List_Omap(X32,c_List_Oreplicate(X31,X30,X33),X33,X34) = c_List_Oreplicate(X31,hAPP(X32,X30),X34),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1169,plain,
! [X13,X14,X15,X16] :
( c_Wellfounded_Oaccp(X13,X14,X16)
| ~ c_Wellfounded_Oaccp(X13,X15,X16)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X16),X14),X15)) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1170,plain,
! [X13,X14,X15,X16] :
( c_Wellfounded_Oaccp(X13,X14,X16)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X16),X14),X15))
| ~ c_Wellfounded_Oaccp(X13,X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1171,plain,
! [X37,X38,X39] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X38),X37)),X39) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X38),X39)),hAPP(hAPP(c_Lambda_Olift,X37),X39)),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1172,plain,
! [X37,X38,X39] :
( c_HOL_Oord__class_Oless(X38,X37,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X39),X38),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X39),X37),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_679])])]) ).
fof(c_0_1173,plain,
! [X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)),X19) ),
inference(variable_rename,[status(thm)],[c_0_680]) ).
fof(c_0_1174,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X13)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X11)),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X11),X10)) ),
inference(variable_rename,[status(thm)],[c_0_681]) ).
fof(c_0_1175,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Oab__semigroup__add(X13)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X11)),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X11),X10)) ),
inference(variable_rename,[status(thm)],[c_0_682]) ).
fof(c_0_1176,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X12),X11)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X12)),X11) ),
inference(variable_rename,[status(thm)],[c_0_683]) ).
fof(c_0_1177,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X11)),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X11),X10)) ),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1178,plain,
! [X17,X18,X19,X20] : c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X19),X17,X20) = c_List_Oappend(c_List_Oreplicate(X18,X17,X20),c_List_Oreplicate(X19,X17,X20),X20),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1179,plain,
! [X79,X80,X81,X82,X83] :
( c_Type_Otyping(X81,hAPP(hAPP(c_Lambda_OdB_OApp,X80),X79),X82)
| ~ c_Type_Otyping(X81,X79,X83)
| ~ c_Type_Otyping(X81,X80,hAPP(hAPP(c_Type_Otype_OFun,X83),X82)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_686])])]) ).
fof(c_0_1180,plain,
! [X53,X54,X55,X56] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X56),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X55),X53),tc_nat)
| ~ c_HOL_Oord__class_Oless(X54,X53,tc_nat)
| ~ c_HOL_Oord__class_Oless(X56,X55,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1181,plain,
! [X30,X31,X32,X33] :
( c_List_Omap(X31,X30,X32,X33) != c_List_Olist_ONil(X33)
| X30 = c_List_Olist_ONil(X32) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_688])])]) ).
fof(c_0_1182,plain,
! [X30,X31,X32,X33] :
( c_List_Olist_ONil(X33) != c_List_Omap(X31,X30,X32,X33)
| X30 = c_List_Olist_ONil(X32) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_689])])]) ).
fof(c_0_1183,plain,
! [X13,X14,X15] : ~ c_ListOrder_Ostep1(X14,X13,c_List_Olist_ONil(X15),X15),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1184,plain,
! [X13,X14,X15] : ~ c_ListOrder_Ostep1(X14,c_List_Olist_ONil(X15),X13,X15),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1185,plain,
! [X62,X63,X64,X65] :
( c_Type_Otyping(X64,X62,X65)
| ~ c_Type_Otyping(X64,X63,X65)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X63),X62)) ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1186,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_OrderedGroup_Oab__group__add(X24)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X24),X22),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X24),X21),X20)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X24),X21),X23)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X24),X22),X20) = X23 ),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1187,plain,
! [X37,X38,X39] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X37),X39)),X38),X39) = X37,
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1188,plain,
! [X19,X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_HOL_Oord__class_Oless(X19,X20,X22)
| c_HOL_Oord__class_Oless(X19,X21,X22)
| ~ c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X21,X20,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1189,plain,
! [X34,X35,X36] : c_Lambda_Osubstn(X34,X35,X36) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X34),c_Lambda_Oliftn(X36,X35,c_HOL_Ozero__class_Ozero(tc_nat))),X36),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1190,plain,
! [X37,X38,X39] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X38),X37)),X39) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X38),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X37),X39)),
inference(variable_rename,[status(thm)],[c_0_697]) ).
fof(c_0_1191,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X10,X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_698]) ).
fof(c_0_1192,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X12)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10),c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X12),X12)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X12),X12) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1193,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X13)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X10),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X10),X11),X13)
| ~ c_HOL_Oord__class_Oless(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1194,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X13)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X10),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X10),X11),X13)
| ~ c_HOL_Oord__class_Oless(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1195,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X13)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X11),X10),X13)
| ~ c_HOL_Oord__class_Oless(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1196,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X13)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X11),X10),X13)
| ~ c_HOL_Oord__class_Oless(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1197,plain,
! [X10,X11,X12,X13] :
( ~ class_Ring__and__Field_Oordered__semidom(X13)
| c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X10),X13)
| ~ c_HOL_Oord__class_Oless(X11,X10,X13)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),X12,X13) ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1198,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12),tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_705])])]) ).
fof(c_0_1199,plain,
! [X19,X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X21,X20,X22),X19,X22)
| ~ c_HOL_Oord__class_Oless(X20,X19,X22)
| ~ c_HOL_Oord__class_Oless(X21,X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1200,plain,
! [X66,X67,X68,X69,X70] :
( hAPP(hAPP(X66,hAPP(hAPP(X66,X69),X68)),X67) = hAPP(hAPP(X66,X69),hAPP(hAPP(X66,X68),X67))
| ~ c_OrderedGroup_Osemigroup__add(X66,X70) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_707])])]) ).
fof(c_0_1201,plain,
! [X5,X6,X7,X8] :
( c_List_Olistsp(X7,c_List_Oappend(X6,X5,X8),X8)
| ~ c_List_Olistsp(X7,X5,X8)
| ~ c_List_Olistsp(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1202,plain,
! [X19,X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_Orderings_Oord__class_Omax(X21,c_Orderings_Oord__class_Omax(X20,X19,X22),X22) = c_Orderings_Oord__class_Omax(X20,c_Orderings_Oord__class_Omax(X21,X19,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1203,plain,
! [X19,X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X21,X20,X22),X19,X22) = c_Orderings_Oord__class_Omax(X21,c_Orderings_Oord__class_Omax(X20,X19,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1204,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),X11) ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1205,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X11)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1206,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1207,plain,
! [X47,X48,X49,X50] : c_List_Oappend(X47,c_List_Oappend(X48,X49,X50),X50) = c_List_Oappend(c_List_Oappend(X47,X48,X50),X49,X50),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1208,plain,
! [X31,X32,X33,X34] : c_List_Oappend(c_List_Oappend(X31,X33,X34),X32,X34) = c_List_Oappend(X31,c_List_Oappend(X33,X32,X34),X34),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1209,plain,
! [X49,X50,X51,X52] : c_List_Oappend(X50,c_List_Oappend(X49,X51,X52),X52) = c_List_Oappend(c_List_Oappend(X50,X49,X52),X51,X52),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1210,plain,
! [X31,X32,X33,X34] : c_List_Oappend(c_List_Oappend(X33,X32,X34),X31,X34) = c_List_Oappend(X33,c_List_Oappend(X32,X31,X34),X34),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1211,plain,
! [X38,X39,X40,X41] : c_List_Olist_OCons(X40,c_List_Oappend(X39,X38,X41),X41) = c_List_Oappend(c_List_Olist_OCons(X40,X39,X41),X38,X41),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1212,plain,
! [X32,X33,X34,X35] : c_List_Olist_OCons(X34,c_List_Oappend(X33,X32,X35),X35) = c_List_Oappend(c_List_Olist_OCons(X34,X33,X35),X32,X35),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1213,plain,
! [X17,X18,X19,X20] : c_List_Oappend(c_List_Olist_OCons(X19,X18,X20),X17,X20) = c_List_Olist_OCons(X19,c_List_Oappend(X18,X17,X20),X20),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1214,plain,
! [X32,X33,X34,X35] : c_List_Oappend(c_List_Olist_OCons(X34,X33,X35),X32,X35) = c_List_Olist_OCons(X34,c_List_Oappend(X33,X32,X35),X35),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1215,plain,
! [X37,X38,X39] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X39),X38),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X39),X37),tc_nat)
| ~ c_HOL_Oord__class_Oless(X38,X37,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_722])])]) ).
fof(c_0_1216,plain,
! [X52,X53,X54] :
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X54),X52),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X53),X52),tc_nat)
| ~ c_HOL_Oord__class_Oless(X54,X53,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1217,plain,
! [X19,X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_HOL_Oord__class_Oless(X20,X19,X22)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X21,X20,X22),X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1218,plain,
! [X19,X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_HOL_Oord__class_Oless(X21,X19,X22)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X21,X20,X22),X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_725]) ).
fof(c_0_1219,plain,
! [X19,X20,X21,X22] :
( ~ class_OrderedGroup_Oab__group__add(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X19)) ),
inference(variable_rename,[status(thm)],[c_0_726]) ).
fof(c_0_1220,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X13)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X11),X10)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X10)) ),
inference(variable_rename,[status(thm)],[c_0_727]) ).
fof(c_0_1221,plain,
! [X11,X12,X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X12),X11)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),X11)) ),
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1222,plain,
! [X19,X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X21,X22),X20),X19))
| ~ hBOOL(hAPP(hAPP(X21,X20),X19)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_729])])]) ).
fof(c_0_1223,plain,
! [X37,X38,X39] : c_Lambda_Oliftn(c_Suc(X38),X37,X39) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X38,X37,X39)),X39),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1224,plain,
! [X5,X6,X7,X8] :
( c_List_Olistsp(X7,X5,X8)
| ~ c_List_Olistsp(X7,c_List_Oappend(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1225,plain,
! [X5,X6,X7,X8] :
( c_List_Olistsp(X7,X6,X8)
| ~ c_List_Olistsp(X7,c_List_Oappend(X6,X5,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1226,plain,
! [X53,X54,X55,X56] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X54),X55) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X56),X53)
| ~ c_HOL_Oord__class_Oless(X56,X55,tc_nat)
| c_HOL_Oord__class_Oless(X54,X53,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1227,plain,
! [X52,X53,X54] :
( c_HOL_Oord__class_Oless(X54,X52,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X54),X53),X52,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1228,plain,
! [X19,X20,X21] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X19)),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1229,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X12)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),c_Power_Opower__class_Opower(X11,X10,X12),X12)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X12),X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1230,plain,
! [X13,X14,X15,X16] :
( c_Wellfounded_Oaccp(X13,X15,X16)
| ~ hBOOL(hAPP(hAPP(X13,X15),X14))
| ~ c_Wellfounded_Oaccp(X13,X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_737]) ).
fof(c_0_1231,plain,
! [X19,X20,X21,X22] :
( c_Wellfounded_Oaccp(X20,X19,X22)
| ~ hBOOL(hAPP(hAPP(X20,X19),X21))
| ~ c_Wellfounded_Oaccp(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1232,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),X11)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X11),X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1233,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X11)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1234,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10),c_HOL_Ozero__class_Ozero(X11),X11)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1235,plain,
! [X13] :
( hBOOL(hAPP(c_InductTermi_OIT,X13))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X13,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1236,plain,
! [X62,X63,X64,X65] :
( c_Type_Otyping(X64,X62,X65)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X63),X62))
| ~ c_Type_Otyping(X64,X63,X65) ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1237,plain,
! [X5,X6,X7] :
( ~ class_OrderedGroup_Omonoid__add(X7)
| c_List_Olistsum(c_List_Oappend(X6,X5,X7),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X7),c_List_Olistsum(X6,X7)),c_List_Olistsum(X5,X7)) ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1238,plain,
! [X30,X31,X32] : c_List_Olist_ONil(X32) = c_List_Omap(X30,c_List_Olist_ONil(X31),X31,X32),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1239,plain,
! [X30,X31,X32] : c_List_Omap(X30,c_List_Olist_ONil(X31),X31,X32) = c_List_Olist_ONil(X32),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1240,plain,
! [X19,X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X21,X20,X22),X22)
| ~ c_HOL_Oord__class_Oless(X19,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1241,plain,
! [X19,X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X21,X20,X22),X22)
| ~ c_HOL_Oord__class_Oless(X19,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1242,plain,
! [X17,X18,X19,X20] :
( ~ class_Orderings_Olinorder(X20)
| c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omax(X19,X18,X20),X20)
| ~ c_HOL_Oord__class_Oless(X17,X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1243,plain,
! [X17,X18,X19,X20] :
( ~ class_Orderings_Olinorder(X20)
| c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omax(X19,X18,X20),X20)
| ~ c_HOL_Oord__class_Oless(X17,X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1244,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Osemiring__1(X14)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),c_Nat_Osemiring__1__class_Oof__nat(X13,X14)),c_Nat_Osemiring__1__class_Oof__nat(X12,X14)) ),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1245,plain,
! [X17,X18] : c_HOL_Oord__class_Oless(X18,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1246,plain,
! [X50,X51] : c_HOL_Oord__class_Oless(X51,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X50),X51)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1247,plain,
! [X50,X51] : c_HOL_Oord__class_Oless(X51,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X51),X50)),tc_nat),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1248,plain,
! [X50,X51] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X50),c_Lambda_OdB_OVar(X51))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X50)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_755])])]) ).
fof(c_0_1249,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_756]) ).
fof(c_0_1250,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_757])])]) ).
fof(c_0_1251,plain,
! [X19,X20,X21,X22] :
( ~ class_Orderings_Opreorder(X22)
| c_HOL_Oord__class_Oless(X21,X19,X22)
| ~ c_HOL_Oord__class_Oless(X20,X19,X22)
| ~ c_HOL_Oord__class_Oless(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1252,plain,
! [X19,X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| c_HOL_Oord__class_Oless(X19,X21,X22)
| ~ c_HOL_Oord__class_Oless(X19,X20,X22)
| ~ c_HOL_Oord__class_Oless(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1253,plain,
! [X34,X35] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X35)),c_Lambda_OdB_OAbs(X34)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X34)) ),
inference(variable_rename,[status(thm)],[c_0_760]) ).
fof(c_0_1254,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X13,X14),c_Nat_Osemiring__1__class_Oof__nat(X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_761]) ).
fof(c_0_1255,plain,
! [X52,X53,X54] :
( c_HOL_Oord__class_Oless(c_Suc(X54),X52,tc_nat)
| ~ c_HOL_Oord__class_Oless(X53,X52,tc_nat)
| ~ c_HOL_Oord__class_Oless(X54,X53,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_762]) ).
fof(c_0_1256,plain,
! [X52,X53,X54] :
( c_HOL_Oord__class_Oless(X54,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X52),X53),tc_nat)
| ~ c_HOL_Oord__class_Oless(X54,X53,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_763]) ).
fof(c_0_1257,plain,
! [X52,X53,X54] :
( c_HOL_Oord__class_Oless(X54,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X53),X52),tc_nat)
| ~ c_HOL_Oord__class_Oless(X54,X53,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_764]) ).
fof(c_0_1258,plain,
! [X19,X20,X21] :
( c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19),tc_nat)
| ~ c_HOL_Oord__class_Oless(X21,X19,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_765]) ).
fof(c_0_1259,plain,
! [X19,X20,X21] :
( c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19),tc_nat)
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_766]) ).
fof(c_0_1260,plain,
! [X52,X53] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X52),X53),X53,tc_nat),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1261,plain,
! [X52,X53] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X53),X52),X53,tc_nat),
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1262,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| c_Orderings_Oord__class_Omax(X20,c_Orderings_Oord__class_Omax(X20,X19,X21),X21) = c_Orderings_Oord__class_Omax(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_769]) ).
fof(c_0_1263,plain,
! [X17,X18,X19] : c_List_Oappend(c_List_Olist_ONil(X19),c_List_Olist_OCons(X18,X17,X19),X19) = c_List_Olist_OCons(X18,X17,X19),
inference(variable_rename,[status(thm)],[c_0_770]) ).
fof(c_0_1264,plain,
! [X17,X18,X19] : c_List_Olist_OCons(X18,X17,X19) = c_List_Oappend(c_List_Olist_ONil(X19),c_List_Olist_OCons(X18,X17,X19),X19),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1265,plain,
! [X17,X18,X19] : c_List_Oreplicate(c_Suc(X18),X17,X19) = c_List_Olist_OCons(X17,c_List_Oreplicate(X18,X17,X19),X19),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1266,plain,
! [X50,X51] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X50),X51)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X50)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_773])])]) ).
fof(c_0_1267,plain,
! [X50,X51,X52] :
( c_Lambda_Oliftn(X50,c_Lambda_OdB_OVar(X52),X51) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X52),X50))
| c_HOL_Oord__class_Oless(X52,X51,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1268,plain,
! [X17,X18,X19] :
( ~ class_OrderedGroup_Omonoid__add(X19)
| c_List_Olistsum(c_List_Olist_OCons(X18,X17,X19),X19) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),X18),c_List_Olistsum(X17,X19)) ),
inference(variable_rename,[status(thm)],[c_0_775]) ).
fof(c_0_1269,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Nat_Osemiring__1__class_Oof__nat(X7,X8),X8) ),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1270,plain,
! [X52,X53,X54] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X53)),X52),X54) = c_Lambda_OdB_OVar(X53)
| ~ c_HOL_Oord__class_Oless(X53,X54,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1271,plain,
! [X12,X13,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X14)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X13,X14),c_Nat_Osemiring__1__class_Oof__nat(X12,X14),X14)
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1272,plain,
! [X34] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X34,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1273,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(hAPP(X29,X27),X28))
| c_HOL_Oord__class_Oless(X27,X28,tc_nat)
| X28 = X27
| c_HOL_Oord__class_Oless(X28,X27,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_780])])]) ).
fof(c_0_1274,plain,
! [X17,X18,X19] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X18,X19),X17),X17)),
inference(variable_rename,[status(thm)],[c_0_781]) ).
fof(c_0_1275,plain,
! [X13,X14,X15] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X15),X14),X14)),
inference(variable_rename,[status(thm)],[c_0_782]) ).
fof(c_0_1276,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Nat_Osemiring__1__class_Oof__nat(X7,X8),X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1277,plain,
! [X19,X20,X21,X22] :
( ~ class_Ring__and__Field_Oidom(X22)
| ~ class_Int_Onumber__ring(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X19)
| X20 = X19 ),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1278,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_785]) ).
fof(c_0_1279,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Opreorder(X21)
| ~ c_HOL_Oord__class_Oless(X19,X20,X21)
| ~ c_HOL_Oord__class_Oless(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_786]) ).
fof(c_0_1280,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| ~ c_HOL_Oord__class_Oless(X20,X19,X21)
| ~ c_HOL_Oord__class_Oless(X19,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_787]) ).
fof(c_0_1281,plain,
! [X10,X11,X12] :
( ~ class_Orderings_Oorder(X12)
| ~ c_HOL_Oord__class_Oless(X11,X10,X12)
| ~ c_HOL_Oord__class_Oless(X10,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1282,plain,
! [X19,X20,X21,X22,X23] :
( c_List_Oreplicate(X22,X20,X23) != c_List_Oreplicate(X21,X19,X23)
| X20 = X19
| X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_789])])]) ).
fof(c_0_1283,plain,
! [X12,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,c_Suc(X13),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_790]) ).
fof(c_0_1284,plain,
! [X71,X72,X73,X74,X75] :
( c_List_Olist_OCons(X74,X72,X75) != c_List_Olist_OCons(X73,X71,X75)
| X72 = X71 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_791])])]) ).
fof(c_0_1285,plain,
! [X71,X72,X73,X74,X75] :
( c_List_Olist_OCons(X74,X72,X75) != c_List_Olist_OCons(X73,X71,X75)
| X74 = X73 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_792])])]) ).
fof(c_0_1286,plain,
! [X31,X32,X33,X34] :
( c_List_Oappend(X33,X32,X34) != c_List_Oappend(X33,X31,X34)
| X32 = X31 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_793])])]) ).
fof(c_0_1287,plain,
! [X31,X32,X33,X34] :
( c_List_Oappend(X32,X33,X34) != c_List_Oappend(X31,X33,X34)
| X32 = X31 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_794])])]) ).
fof(c_0_1288,plain,
! [X19,X20,X21,X22,X23] :
( c_List_Oreplicate(X22,X20,X23) != c_List_Oreplicate(X21,X19,X23)
| X22 = X21 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_795])])]) ).
fof(c_0_1289,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X13)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X10),X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_796]) ).
fof(c_0_1290,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X13)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X10)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_797]) ).
fof(c_0_1291,plain,
! [X10,X11,X12,X13] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X13)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X10)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_798]) ).
fof(c_0_1292,plain,
! [X12,X13] : c_Orderings_Oord__class_Omax(c_Suc(X13),c_Suc(X12),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X13,X12,tc_nat)),
inference(variable_rename,[status(thm)],[c_0_799]) ).
fof(c_0_1293,plain,
! [X29,X30] :
( c_HOL_Oord__class_Oless(X29,X29,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X29),X30,X29) = c_Lambda_Oliftn(X29,X30,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_800])])]) ).
fof(c_0_1294,plain,
! [X88,X89,X90] :
( X89 = X88
| ~ hBOOL(hAPP(hAPP(c_fequal(X90),X89),X88)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_801])])]) ).
fof(c_0_1295,plain,
! [X50,X51,X52] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X52)),X50),X51) = c_Lambda_OdB_OVar(X52)
| X52 = X51
| c_HOL_Oord__class_Oless(X51,X52,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_802]) ).
fof(c_0_1296,plain,
! [X29,X30] :
( c_HOL_Oord__class_Oless(X29,X29,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X29)),X30),X29) = X30 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_803])])]) ).
fof(c_0_1297,plain,
! [X14,X15,X16] : c_Predicate_Oconversep(c_Predicate_Oconversep(X14,X16,X15),X15,X16) = X14,
inference(variable_rename,[status(thm)],[c_0_804]) ).
fof(c_0_1298,plain,
! [X50,X51] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X51)),X50)),
inference(variable_rename,[status(thm)],[c_0_805]) ).
fof(c_0_1299,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X13),c_Suc(X12),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_806]) ).
fof(c_0_1300,plain,
! [X12,X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X13)),X12) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12)),
inference(variable_rename,[status(thm)],[c_0_807]) ).
fof(c_0_1301,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(c_Suc(X13),c_Suc(X12),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1302,plain,
! [X17,X18] :
( c_HOL_Oord__class_Oless(c_Suc(X17),c_Suc(X18),tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X18,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_809]) ).
fof(c_0_1303,plain,
! [X12,X13] :
( X12 = X13
| ~ c_HOL_Oord__class_Oless(X12,c_Suc(X13),tc_nat)
| c_HOL_Oord__class_Oless(X12,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_810]) ).
fof(c_0_1304,plain,
! [X12,X13] :
( X13 = X12
| ~ c_HOL_Oord__class_Oless(X12,c_Suc(X13),tc_nat)
| c_HOL_Oord__class_Oless(X12,X13,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_811]) ).
fof(c_0_1305,plain,
! [X12,X13] :
( X13 = X12
| c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,c_Suc(X12),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_812]) ).
fof(c_0_1306,plain,
! [X50,X51,X52] :
( c_Lambda_Oliftn(X50,c_Lambda_OdB_OVar(X52),X51) = c_Lambda_OdB_OVar(X52)
| ~ c_HOL_Oord__class_Oless(X52,X51,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_813]) ).
fof(c_0_1307,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(c_Suc(X13),X12,tc_nat)
| c_Suc(X13) = X12
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_814]) ).
fof(c_0_1308,plain,
! [X37,X38,X39] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X39),X38) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X39),X37)
| X38 = X37 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_815])])]) ).
fof(c_0_1309,plain,
! [X37,X38,X39] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X38),X39) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X37),X39)
| X38 = X37 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_816])])]) ).
fof(c_0_1310,plain,
! [X19,X20,X21] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X20) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X19)
| X20 = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_817])])]) ).
fof(c_0_1311,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X13),X12,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_818]) ).
fof(c_0_1312,plain,
! [X34,X35] : c_Lambda_Osubstn(X34,X35,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X34),X35),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_819]) ).
fof(c_0_1313,plain,
! [X12,X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_Suc(X12)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12)),
inference(variable_rename,[status(thm)],[c_0_820]) ).
fof(c_0_1314,plain,
! [X12,X13] :
( ~ class_Ring__and__Field_Oordered__semidom(X13)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X12,X13),c_HOL_Ozero__class_Ozero(X13),X13) ),
inference(variable_rename,[status(thm)],[c_0_821]) ).
fof(c_0_1315,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(X13,c_Suc(X12),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_822]) ).
fof(c_0_1316,plain,
! [X50,X51] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X51)),X50) = c_Lambda_OdB_OVar(X51)
| ~ c_HOL_Oord__class_Oless(X51,X50,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_823]) ).
fof(c_0_1317,plain,
! [X66,X67,X68,X69] :
( hAPP(hAPP(X67,X66),X68) = X68
| ~ c_OrderedGroup_Omonoid__add(X66,X67,X69) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_824])])]) ).
fof(c_0_1318,plain,
! [X66,X67,X68,X69] :
( hAPP(hAPP(X67,X68),X66) = X68
| ~ c_OrderedGroup_Omonoid__add(X66,X67,X69) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_825])])]) ).
fof(c_0_1319,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ozero__neq__one(X12)
| ~ class_Ring__and__Field_Ono__zero__divisors(X12)
| ~ class_Ring__and__Field_Omult__zero(X12)
| ~ class_Power_Opower(X12)
| c_Power_Opower__class_Opower(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_826]) ).
fof(c_0_1320,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ozero__neq__one(X11)
| ~ class_Ring__and__Field_Ono__zero__divisors(X11)
| ~ class_Ring__and__Field_Omult__zero(X11)
| ~ class_Power_Opower(X11)
| c_Power_Opower__class_Opower(X10,c_HOL_Ozero__class_Ozero(tc_nat),X11) != c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_827]) ).
fof(c_0_1321,plain,
! [X50,X51,X52] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X52),X50,X51) = c_Lambda_OdB_OVar(X52)
| X52 = X51
| c_HOL_Oord__class_Oless(X51,X52,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_828]) ).
fof(c_0_1322,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| X20 = X19
| c_HOL_Oord__class_Oless(X20,X19,X21)
| c_HOL_Oord__class_Oless(X19,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_829]) ).
fof(c_0_1323,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| c_HOL_Oord__class_Oless(X19,X20,X21)
| X20 = X19
| c_HOL_Oord__class_Oless(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_830]) ).
fof(c_0_1324,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| c_HOL_Oord__class_Oless(X19,X20,X21)
| c_HOL_Oord__class_Oless(X20,X19,X21)
| X20 = X19 ),
inference(variable_rename,[status(thm)],[c_0_831]) ).
fof(c_0_1325,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| X20 = X19
| c_HOL_Oord__class_Oless(X19,X20,X21)
| c_HOL_Oord__class_Oless(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_832]) ).
fof(c_0_1326,plain,
! [X19,X20,X21] :
( ~ class_Ring__and__Field_Oordered__idom(X21)
| c_HOL_Oord__class_Oless(X19,X20,X21)
| c_HOL_Oord__class_Oless(X20,X19,X21)
| X20 = X19 ),
inference(variable_rename,[status(thm)],[c_0_833]) ).
fof(c_0_1327,plain,
! [X77,X78,X79,X80] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X80),X78) != hAPP(hAPP(c_Lambda_OdB_OApp,X79),X77)
| X78 = X77 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_834])])]) ).
fof(c_0_1328,plain,
! [X77,X78,X79,X80] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X80),X78) != hAPP(hAPP(c_Lambda_OdB_OApp,X79),X77)
| X80 = X79 ),
inference(variable_rename,[status(thm)],[c_0_835]) ).
fof(c_0_1329,plain,
! [X70,X71,X72,X73] :
( hAPP(hAPP(c_Type_Otype_OFun,X73),X71) != hAPP(hAPP(c_Type_Otype_OFun,X72),X70)
| X73 = X72 ),
inference(variable_rename,[status(thm)],[c_0_836]) ).
fof(c_0_1330,plain,
! [X70,X71,X72,X73] :
( hAPP(hAPP(c_Type_Otype_OFun,X73),X71) != hAPP(hAPP(c_Type_Otype_OFun,X72),X70)
| X71 = X70 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_837])])]) ).
fof(c_0_1331,plain,
! [X19,X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| c_Orderings_Oord__class_Omax(X20,X19,X21) = c_Orderings_Oord__class_Omax(X19,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_838]) ).
fof(c_0_1332,plain,
! [X19,X20,X21] : c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X20,X21) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X19,X21),
inference(variable_rename,[status(thm)],[c_0_839]) ).
fof(c_0_1333,plain,
! [X12,X13] :
( c_HOL_Oord__class_Oless(X12,c_Suc(X13),tc_nat)
| c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_840]) ).
fof(c_0_1334,plain,
! [X17] :
( c_HOL_Oord__class_Oless(X17,X17,tc_nat)
| c_HOL_Oord__class_Oless(X17,c_Suc(X17),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_841]) ).
fof(c_0_1335,plain,
! [X19,X20,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X20),X19) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),X19),X20) ),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1336,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X10),X11) ),
inference(variable_rename,[status(thm)],[c_0_843]) ).
fof(c_0_1337,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X10),X11) ),
inference(variable_rename,[status(thm)],[c_0_844]) ).
fof(c_0_1338,plain,
! [X37,X38] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X38)),X37),X38) = X37,
inference(variable_rename,[status(thm)],[c_0_845]) ).
fof(c_0_1339,plain,
! [X62,X63,X64] :
( hAPP(X63,X62) = X64
| ~ c_Type_Otyping(X63,c_Lambda_OdB_OVar(X62),X64) ),
inference(variable_rename,[status(thm)],[c_0_846]) ).
fof(c_0_1340,plain,
! [X12,X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X13)),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_Suc(X12)),
inference(variable_rename,[status(thm)],[c_0_847]) ).
fof(c_0_1341,plain,
! [X19,X20] :
( c_HOL_Oord__class_Oless(X19,X20,tc_nat)
| c_HOL_Oord__class_Oless(X20,X19,tc_nat)
| X20 = X19 ),
inference(variable_rename,[status(thm)],[c_0_848]) ).
fof(c_0_1342,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_849]) ).
fof(c_0_1343,plain,
! [X7] :
( X7 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_850]) ).
fof(c_0_1344,plain,
! [X17,X18] : hBOOL(hAPP(hAPP(c_fequal(X18),X17),X17)),
inference(variable_rename,[status(thm)],[c_0_851]) ).
fof(c_0_1345,plain,
! [X10,X11,X12] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X12)
| c_Power_Opower__class_Opower(X11,X10,X12) != c_HOL_Ozero__class_Ozero(X12)
| X11 = c_HOL_Ozero__class_Ozero(X12) ),
inference(variable_rename,[status(thm)],[c_0_852]) ).
fof(c_0_1346,plain,
! [X17,X18,X19] :
( ~ class_Ring__and__Field_Oidom(X19)
| ~ class_Int_Onumber__ring(X19)
| X17 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X19),X17),X18)
| X18 = c_HOL_Ozero__class_Ozero(X19) ),
inference(variable_rename,[status(thm)],[c_0_853]) ).
fof(c_0_1347,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),X10) != c_HOL_Ozero__class_Ozero(X11)
| X10 = c_HOL_Ozero__class_Ozero(X11) ),
inference(variable_rename,[status(thm)],[c_0_854]) ).
fof(c_0_1348,plain,
! [X12,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X13 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_855]) ).
fof(c_0_1349,plain,
! [X12,X13] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12)
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X13 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_856]) ).
fof(c_0_1350,plain,
! [X5,X6,X7] :
( c_List_Oappend(X6,X5,X7) != c_List_Olist_ONil(X7)
| X5 = c_List_Olist_ONil(X7) ),
inference(variable_rename,[status(thm)],[c_0_857]) ).
fof(c_0_1351,plain,
! [X5,X6,X7] :
( c_List_Oappend(X6,X5,X7) != c_List_Olist_ONil(X7)
| X6 = c_List_Olist_ONil(X7) ),
inference(variable_rename,[status(thm)],[c_0_858]) ).
fof(c_0_1352,plain,
! [X5,X6,X7] :
( c_List_Olist_ONil(X7) != c_List_Oappend(X6,X5,X7)
| X5 = c_List_Olist_ONil(X7) ),
inference(variable_rename,[status(thm)],[c_0_859]) ).
fof(c_0_1353,plain,
! [X5,X6,X7] :
( c_List_Olist_ONil(X7) != c_List_Oappend(X6,X5,X7)
| X6 = c_List_Olist_ONil(X7) ),
inference(variable_rename,[status(thm)],[c_0_860]) ).
fof(c_0_1354,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Ozero__neq__one(X8)
| ~ class_Ring__and__Field_Ono__zero__divisors(X8)
| ~ class_Ring__and__Field_Omult__zero(X8)
| ~ class_Power_Opower(X8)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X8),X7,X8) = c_HOL_Ozero__class_Ozero(X8)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_861]) ).
fof(c_0_1355,plain,
! [X17,X18,X19] :
( c_List_Olist_ONil(X19) != c_List_Oreplicate(X18,X17,X19)
| X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_862])])]) ).
fof(c_0_1356,plain,
! [X17,X18,X19] :
( c_List_Oreplicate(X18,X17,X19) != c_List_Olist_ONil(X19)
| X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_863])])]) ).
fof(c_0_1357,plain,
! [X12,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X13 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_864]) ).
fof(c_0_1358,plain,
! [X12,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_865])])]) ).
fof(c_0_1359,plain,
! [X12,X13] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X13 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(variable_rename,[status(thm)],[c_0_866]) ).
fof(c_0_1360,plain,
! [X12,X13] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12)
| X12 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_867])])]) ).
fof(c_0_1361,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_868 ).
fof(c_0_1362,plain,
! [X17,X18] :
( ~ class_Orderings_Opreorder(X18)
| ~ c_HOL_Oord__class_Oless(X17,X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_869]) ).
fof(c_0_1363,plain,
! [X17,X18] :
( ~ class_Orderings_Olinorder(X18)
| ~ c_HOL_Oord__class_Oless(X17,X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_870]) ).
fof(c_0_1364,plain,
! [X17,X18] :
( ~ class_Orderings_Oorder(X18)
| ~ c_HOL_Oord__class_Oless(X17,X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_871]) ).
fof(c_0_1365,plain,
! [X5,X6,X7] :
( X5 != c_List_Oappend(X6,X5,X7)
| X6 = c_List_Olist_ONil(X7) ),
inference(variable_rename,[status(thm)],[c_0_872]) ).
fof(c_0_1366,plain,
! [X5,X6,X7] :
( c_List_Oappend(X6,X5,X7) != X5
| X6 = c_List_Olist_ONil(X7) ),
inference(variable_rename,[status(thm)],[c_0_873]) ).
fof(c_0_1367,plain,
! [X5,X6,X7] :
( X6 != c_List_Oappend(X6,X5,X7)
| X5 = c_List_Olist_ONil(X7) ),
inference(variable_rename,[status(thm)],[c_0_874]) ).
fof(c_0_1368,plain,
! [X5,X6,X7] :
( c_List_Oappend(X6,X5,X7) != X6
| X5 = c_List_Olist_ONil(X7) ),
inference(variable_rename,[status(thm)],[c_0_875]) ).
fof(c_0_1369,plain,
! [X40,X41,X42] : c_List_Olist_ONil(X42) != c_List_Olist_OCons(X41,X40,X42),
inference(variable_rename,[status(thm)],[c_0_876]) ).
fof(c_0_1370,plain,
! [X12,X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X13),
inference(variable_rename,[status(thm)],[c_0_877]) ).
fof(c_0_1371,plain,
! [X40,X41,X42] : c_List_Olist_OCons(X41,X40,X42) != c_List_Olist_ONil(X42),
inference(variable_rename,[status(thm)],[c_0_878]) ).
fof(c_0_1372,plain,
! [X32,X33,X34] : c_List_Olist_OCons(X33,X32,X34) != c_List_Olist_ONil(X34),
inference(variable_rename,[status(thm)],[c_0_879]) ).
fof(c_0_1373,plain,
! [X12,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_880]) ).
fof(c_0_1374,plain,
! [X12,X13] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_881]) ).
fof(c_0_1375,plain,
! [X7] : ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_882]) ).
fof(c_0_1376,plain,
! [X12] : ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(variable_rename,[status(thm)],[c_0_883]) ).
fof(c_0_1377,plain,
! [X17,X18,X19] : X17 != c_List_Olist_OCons(X18,X17,X19),
inference(variable_rename,[status(thm)],[c_0_884]) ).
fof(c_0_1378,plain,
! [X34,X35,X36] : c_List_Olist_OCons(X34,X35,X36) != X35,
inference(variable_rename,[status(thm)],[c_0_885]) ).
fof(c_0_1379,plain,
! [X79,X80] : c_Type_Otyping(X80,c_Lambda_OdB_OVar(X79),hAPP(X80,X79)),
inference(variable_rename,[status(thm)],[c_0_886]) ).
fof(c_0_1380,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Osemiring__0(X8)
| ~ class_Power_Opower(X8)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X8),c_Suc(X7),X8) = c_HOL_Ozero__class_Ozero(X8) ),
inference(variable_rename,[status(thm)],[c_0_887]) ).
fof(c_0_1381,plain,
! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat),
inference(variable_rename,[status(thm)],[c_0_888]) ).
fof(c_0_1382,plain,
! [X17] : ~ c_HOL_Oord__class_Oless(X17,X17,tc_nat),
inference(variable_rename,[status(thm)],[c_0_889]) ).
fof(c_0_1383,plain,
! [X7,X8] :
( ~ class_Ring__and__Field_Osemiring__0(X8)
| ~ class_Power_Opower(X8)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X8),X7,X8) = c_HOL_Ozero__class_Ozero(X8)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_890]) ).
fof(c_0_1384,plain,
! [X13] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X13)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X13)) ),
inference(variable_rename,[status(thm)],[c_0_891]) ).
fof(c_0_1385,plain,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5)) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_892]) ).
fof(c_0_1386,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_893 ).
fof(c_0_1387,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_894 ).
fof(c_0_1388,plain,
! [X12,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12) != c_HOL_Ozero__class_Ozero(tc_nat)
| X13 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_895]) ).
fof(c_0_1389,plain,
! [X12,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12) != c_HOL_Ozero__class_Ozero(tc_nat)
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_896])])]) ).
fof(c_0_1390,plain,
! [X12,X13] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X12) != X13
| X12 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_897])])]) ).
fof(c_0_1391,plain,
! [X17,X18] :
( X17 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18)
| X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_898]) ).
fof(c_0_1392,plain,
! [X17,X18] :
( ~ class_Ring__and__Field_Oidom(X18)
| ~ class_Int_Onumber__ring(X18)
| X17 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X18),X17),c_HOL_Ozero__class_Ozero(X18)) ),
inference(variable_rename,[status(thm)],[c_0_899]) ).
fof(c_0_1393,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),c_HOL_Ozero__class_Ozero(X11)),X10) = X10 ),
inference(variable_rename,[status(thm)],[c_0_900]) ).
fof(c_0_1394,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Omonoid__add(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),c_HOL_Ozero__class_Ozero(X11)),X10) = X10 ),
inference(variable_rename,[status(thm)],[c_0_901]) ).
fof(c_0_1395,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),c_HOL_Ozero__class_Ozero(X11)),X10) = X10 ),
inference(variable_rename,[status(thm)],[c_0_902]) ).
fof(c_0_1396,plain,
! [X17,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X18),c_HOL_Ozero__class_Ozero(X18)),X17) = X17 ),
inference(variable_rename,[status(thm)],[c_0_903]) ).
fof(c_0_1397,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_904 ).
fof(c_0_1398,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_905 ).
fof(c_0_1399,plain,
! [X5] : c_List_Oappend(c_List_Olist_ONil(X5),c_List_Olist_ONil(X5),X5) = c_List_Olist_ONil(X5),
inference(variable_rename,[status(thm)],[c_0_906]) ).
fof(c_0_1400,plain,
! [X5] : c_List_Olist_ONil(X5) = c_List_Oappend(c_List_Olist_ONil(X5),c_List_Olist_ONil(X5),X5),
inference(variable_rename,[status(thm)],[c_0_907]) ).
fof(c_0_1401,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_908 ).
fof(c_0_1402,plain,
! [X10,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),c_HOL_Ozero__class_Ozero(X11)) = X10 ),
inference(variable_rename,[status(thm)],[c_0_909]) ).
fof(c_0_1403,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Omonoid__add(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),c_HOL_Ozero__class_Ozero(X11)) = X10 ),
inference(variable_rename,[status(thm)],[c_0_910]) ).
fof(c_0_1404,plain,
! [X10,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X11)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X11),X10),c_HOL_Ozero__class_Ozero(X11)) = X10 ),
inference(variable_rename,[status(thm)],[c_0_911]) ).
fof(c_0_1405,plain,
! [X5] : c_Predicate_Oconversep(c_fequal(X5),X5,X5) = c_fequal(X5),
inference(variable_rename,[status(thm)],[c_0_912]) ).
fof(c_0_1406,plain,
! [X77,X78,X79] : hAPP(hAPP(c_Lambda_OdB_OApp,X79),X78) != c_Lambda_OdB_OVar(X77),
inference(variable_rename,[status(thm)],[c_0_913]) ).
fof(c_0_1407,plain,
! [X77,X78,X79] : c_Lambda_OdB_OVar(X77) != hAPP(hAPP(c_Lambda_OdB_OApp,X79),X78),
inference(variable_rename,[status(thm)],[c_0_914]) ).
fof(c_0_1408,plain,
! [X74,X75,X76] : c_Lambda_OdB_OAbs(X74) != hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75),
inference(variable_rename,[status(thm)],[c_0_915]) ).
fof(c_0_1409,plain,
! [X74,X75,X76] : hAPP(hAPP(c_Lambda_OdB_OApp,X76),X75) != c_Lambda_OdB_OAbs(X74),
inference(variable_rename,[status(thm)],[c_0_916]) ).
fof(c_0_1410,plain,
! [X17,X18] :
( ~ class_Orderings_Olinorder(X18)
| c_Orderings_Oord__class_Omax(X17,X17,X18) = X17 ),
inference(variable_rename,[status(thm)],[c_0_917]) ).
fof(c_0_1411,plain,
! [X17] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X17),tc_nat),
inference(variable_rename,[status(thm)],[c_0_918]) ).
fof(c_0_1412,plain,
! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X7),tc_nat),
inference(variable_rename,[status(thm)],[c_0_919]) ).
fof(c_0_1413,plain,
! [X17,X18] : c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X17,X18) = c_List_Olist_ONil(X18),
inference(variable_rename,[status(thm)],[c_0_920]) ).
fof(c_0_1414,plain,
! [X17,X18] : c_List_Olist_ONil(X18) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X17,X18),
inference(variable_rename,[status(thm)],[c_0_921]) ).
fof(c_0_1415,plain,
! [X5,X6] : X5 = c_List_Oappend(c_List_Olist_ONil(X6),X5,X6),
inference(variable_rename,[status(thm)],[c_0_922]) ).
fof(c_0_1416,plain,
! [X5,X6] : c_List_Oappend(c_List_Olist_ONil(X6),X5,X6) = X5,
inference(variable_rename,[status(thm)],[c_0_923]) ).
fof(c_0_1417,plain,
! [X5,X6] : X5 = c_List_Oappend(X5,c_List_Olist_ONil(X6),X6),
inference(variable_rename,[status(thm)],[c_0_924]) ).
fof(c_0_1418,plain,
! [X17,X18] : X17 = c_List_Oappend(c_List_Olist_ONil(X18),X17,X18),
inference(variable_rename,[status(thm)],[c_0_925]) ).
fof(c_0_1419,plain,
! [X5,X6] : c_List_Oappend(X5,c_List_Olist_ONil(X6),X6) = X5,
inference(variable_rename,[status(thm)],[c_0_926]) ).
fof(c_0_1420,plain,
! [X5,X6] : c_List_Olistsp(X5,c_List_Olist_ONil(X6),X6),
inference(variable_rename,[status(thm)],[c_0_927]) ).
fof(c_0_1421,plain,
! [X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_928]) ).
fof(c_0_1422,plain,
! [X17] : c_HOL_Oord__class_Oless(X17,c_Suc(X17),tc_nat),
inference(variable_rename,[status(thm)],[c_0_929]) ).
fof(c_0_1423,plain,
! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat),
inference(variable_rename,[status(thm)],[c_0_930]) ).
fof(c_0_1424,plain,
! [X37,X38] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X37,X38) = X37,
inference(variable_rename,[status(thm)],[c_0_931]) ).
fof(c_0_1425,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_932 ).
fof(c_0_1426,plain,
! [X7] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) = X7,
inference(variable_rename,[status(thm)],[c_0_933]) ).
fof(c_0_1427,plain,
! [X7] : c_Orderings_Oord__class_Omax(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X7,
inference(variable_rename,[status(thm)],[c_0_934]) ).
fof(c_0_1428,plain,
! [X13,X14] : c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X13,X14),X14) = c_Transitive__Closure_Ortranclp(X13,X14),
inference(variable_rename,[status(thm)],[c_0_935]) ).
fof(c_0_1429,plain,
! [X12,X13,X14] :
( ~ class_Nat_Osemiring__char__0(X14)
| c_Nat_Osemiring__1__class_Oof__nat(X13,X14) != c_Nat_Osemiring__1__class_Oof__nat(X12,X14)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_936]) ).
fof(c_0_1430,plain,
! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X7) = X7,
inference(variable_rename,[status(thm)],[c_0_937]) ).
fof(c_0_1431,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
c_0_938 ).
fof(c_0_1432,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
c_0_939 ).
fof(c_0_1433,plain,
! [X12] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Ozero__class_Ozero(tc_nat)) = X12,
inference(variable_rename,[status(thm)],[c_0_940]) ).
fof(c_0_1434,plain,
! [X17] : X17 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(variable_rename,[status(thm)],[c_0_941]) ).
fof(c_0_1435,plain,
! [X7] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X7))),
inference(variable_rename,[status(thm)],[c_0_942]) ).
fof(c_0_1436,plain,
! [X86,X87] :
( class_Orderings_Oorder(tc_fun(X86,X87))
| ~ class_Orderings_Oorder(X87) ),
inference(variable_rename,[status(thm)],[c_0_943]) ).
fof(c_0_1437,plain,
! [X86,X87] :
( class_Orderings_Opreorder(tc_fun(X86,X87))
| ~ class_Orderings_Opreorder(X87) ),
inference(variable_rename,[status(thm)],[c_0_944]) ).
fof(c_0_1438,plain,
! [X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| c_List_Olistsum(c_List_Olist_ONil(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_945]) ).
fof(c_0_1439,plain,
! [X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X5) = c_HOL_Ozero__class_Ozero(X5) ),
inference(variable_rename,[status(thm)],[c_0_946]) ).
fof(c_0_1440,plain,
! [X5] :
( ~ class_OrderedGroup_Osemigroup__add(X5)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X5),X5) ),
inference(variable_rename,[status(thm)],[c_0_947]) ).
fof(c_0_1441,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
c_0_948 ).
fof(c_0_1442,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
c_0_949 ).
fof(c_0_1443,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
c_0_950 ).
fof(c_0_1444,plain,
! [X55,X56] :
( c_Lambda_OdB_OVar(X56) != c_Lambda_OdB_OVar(X55)
| X56 = X55 ),
inference(variable_rename,[status(thm)],[c_0_951]) ).
fof(c_0_1445,plain,
! [X56,X57] :
( c_Lambda_OdB_OAbs(X57) != c_Lambda_OdB_OAbs(X56)
| X57 = X56 ),
inference(variable_rename,[status(thm)],[c_0_952]) ).
fof(c_0_1446,plain,
! [X55,X56] :
( c_Suc(X56) != c_Suc(X55)
| X56 = X55 ),
inference(variable_rename,[status(thm)],[c_0_953]) ).
fof(c_0_1447,plain,
! [X19,X20] :
( c_Suc(X20) != c_Suc(X19)
| X20 = X19 ),
inference(variable_rename,[status(thm)],[c_0_954]) ).
fof(c_0_1448,plain,
! [X56,X57] : c_Lambda_OdB_OAbs(X57) != c_Lambda_OdB_OVar(X56),
inference(variable_rename,[status(thm)],[c_0_955]) ).
fof(c_0_1449,plain,
! [X56,X57] : c_Lambda_OdB_OVar(X56) != c_Lambda_OdB_OAbs(X57),
inference(variable_rename,[status(thm)],[c_0_956]) ).
fof(c_0_1450,plain,
! [X55] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X55),
inference(variable_rename,[status(thm)],[c_0_957]) ).
fof(c_0_1451,plain,
! [X12] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X12),
inference(variable_rename,[status(thm)],[c_0_958]) ).
fof(c_0_1452,plain,
! [X55] : c_Suc(X55) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_959]) ).
fof(c_0_1453,plain,
! [X12] : c_Suc(X12) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(variable_rename,[status(thm)],[c_0_960]) ).
fof(c_0_1454,plain,
! [X7] : X7 != c_Suc(X7),
inference(variable_rename,[status(thm)],[c_0_961]) ).
fof(c_0_1455,plain,
! [X7] : c_Suc(X7) != X7,
inference(variable_rename,[status(thm)],[c_0_962]) ).
fof(c_0_1456,axiom,
class_Orderings_Oorder(tc_bool),
c_0_963 ).
fof(c_0_1457,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_964 ).
fof(c_0_1458,axiom,
class_Power_Opower(tc_nat),
c_0_965 ).
fof(c_0_1459,axiom,
class_Orderings_Oorder(tc_nat),
c_0_966 ).
fof(c_0_1460,axiom,
class_Orderings_Olinorder(tc_nat),
c_0_967 ).
fof(c_0_1461,axiom,
class_Orderings_Opreorder(tc_nat),
c_0_968 ).
fof(c_0_1462,axiom,
class_Nat_Osemiring__char__0(tc_nat),
c_0_969 ).
fof(c_0_1463,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_970 ).
fof(c_0_1464,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_971 ).
fof(c_0_1465,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
c_0_972 ).
fof(c_0_1466,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_973 ).
fof(c_0_1467,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_974 ).
fof(c_0_1468,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_975 ).
fof(c_0_1469,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_976 ).
fof(c_0_1470,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_977 ).
fof(c_0_1471,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_978 ).
fof(c_0_1472,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_979 ).
fof(c_0_1473,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_980 ).
fof(c_0_1474,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_981 ).
fof(c_0_1475,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_982 ).
fof(c_0_1476,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_983 ).
fof(c_0_1477,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_984 ).
fof(c_0_1478,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_985 ).
cnf(c_0_1479,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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,hAPP(hAPP(hAPP(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_986]) ).
cnf(c_0_1480,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_987]) ).
cnf(c_0_1481,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_988]) ).
cnf(c_0_1482,plain,
( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_989]) ).
cnf(c_0_1483,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_990]) ).
cnf(c_0_1484,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,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)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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_991]) ).
cnf(c_0_1485,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_992]) ).
cnf(c_0_1486,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_993]) ).
cnf(c_0_1487,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_994]) ).
cnf(c_0_1488,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,hAPP(hAPP(hAPP(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_995]) ).
cnf(c_0_1489,plain,
hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1490,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1491,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_998]) ).
cnf(c_0_1492,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10)))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_999]) ).
cnf(c_0_1493,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1000]) ).
cnf(c_0_1494,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1001]) ).
cnf(c_0_1495,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1002]) ).
cnf(c_0_1496,plain,
( hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1003]) ).
cnf(c_0_1497,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1004]) ).
cnf(c_0_1498,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1005]) ).
cnf(c_0_1499,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1500,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1501,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1502,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1503,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1010]) ).
cnf(c_0_1504,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1011]) ).
cnf(c_0_1505,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1012]) ).
cnf(c_0_1506,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1013]) ).
cnf(c_0_1507,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1014]) ).
cnf(c_0_1508,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1015]) ).
cnf(c_0_1509,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),X7) = hAPP(hAPP(X3,X7),c_Suc(X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1016]) ).
cnf(c_0_1510,plain,
( hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1017]) ).
cnf(c_0_1511,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1018]) ).
cnf(c_0_1512,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1019]) ).
cnf(c_0_1513,plain,
( hAPP(hAPP(X3,X7),c_Suc(X8)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1020]) ).
cnf(c_0_1514,plain,
( hAPP(hAPP(X3,X7),c_Suc(X8)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1021]) ).
cnf(c_0_1515,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8)) = hAPP(hAPP(X3,X7),c_Suc(X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1022]) ).
cnf(c_0_1516,plain,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1023]) ).
cnf(c_0_1517,plain,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1024]) ).
cnf(c_0_1518,plain,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1025]) ).
cnf(c_0_1519,plain,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1026]) ).
cnf(c_0_1520,plain,
( hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1027]) ).
cnf(c_0_1521,plain,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1028]) ).
cnf(c_0_1522,plain,
( hAPP(hAPP(X1,X7),X4) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1029]) ).
cnf(c_0_1523,plain,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1030]) ).
cnf(c_0_1524,plain,
( hAPP(hAPP(X2,X7),X4) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1031]) ).
cnf(c_0_1525,plain,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1032]) ).
cnf(c_0_1526,plain,
( hAPP(hAPP(X2,X7),X5) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1033]) ).
cnf(c_0_1527,plain,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1034]) ).
cnf(c_0_1528,plain,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1035]) ).
cnf(c_0_1529,plain,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1036]) ).
cnf(c_0_1530,plain,
c_Lambda_OdB_OdB__rec(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(hAPP(hAPP(X2,X4),X5),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X6)),c_Lambda_OdB_OdB__rec(X1,X2,X3,X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_1037]) ).
cnf(c_0_1531,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_1038]) ).
cnf(c_0_1532,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_1039]) ).
cnf(c_0_1533,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_1040]) ).
cnf(c_0_1534,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_1041]) ).
cnf(c_0_1535,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_1042]) ).
cnf(c_0_1536,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_1043]) ).
cnf(c_0_1537,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_1044]) ).
cnf(c_0_1538,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,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_1045]) ).
cnf(c_0_1539,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_1046]) ).
cnf(c_0_1540,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_1047]) ).
cnf(c_0_1541,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_1048]) ).
cnf(c_0_1542,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_1049]) ).
cnf(c_0_1543,plain,
( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1050]) ).
cnf(c_0_1544,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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_1051]) ).
cnf(c_0_1545,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_1052]) ).
cnf(c_0_1546,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_1053]) ).
cnf(c_0_1547,plain,
c_List_Ofoldl(X1,X2,c_List_Oappend(X3,X4,X5),X6,X5) = c_List_Ofoldl(X1,c_List_Ofoldl(X1,X2,X3,X6,X5),X4,X6,X5),
inference(split_conjunct,[status(thm)],[c_0_1054]) ).
cnf(c_0_1548,plain,
c_List_Ofoldr(X1,c_List_Oappend(X2,X3,X4),X5,X4,X6) = c_List_Ofoldr(X1,X2,c_List_Ofoldr(X1,X3,X5,X4,X6),X4,X6),
inference(split_conjunct,[status(thm)],[c_0_1055]) ).
cnf(c_0_1549,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_1056]) ).
cnf(c_0_1550,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_1057]) ).
cnf(c_0_1551,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_1058]) ).
cnf(c_0_1552,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_1059]) ).
cnf(c_0_1553,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_1060]) ).
cnf(c_0_1554,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_1061]) ).
cnf(c_0_1555,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_1062]) ).
cnf(c_0_1556,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_1063]) ).
cnf(c_0_1557,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_1064]) ).
cnf(c_0_1558,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_1065]) ).
cnf(c_0_1559,plain,
c_List_Ofoldr(X1,c_List_Olist_OCons(X2,X3,X4),X5,X4,X6) = hAPP(hAPP(X1,X2),c_List_Ofoldr(X1,X3,X5,X4,X6)),
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1560,plain,
( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1561,plain,
( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1068]) ).
cnf(c_0_1562,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_1069]) ).
cnf(c_0_1563,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_1070]) ).
cnf(c_0_1564,plain,
c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(hAPP(X3,X4),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X5)),
inference(split_conjunct,[status(thm)],[c_0_1071]) ).
cnf(c_0_1565,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| X2 = c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_1072]) ).
cnf(c_0_1566,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_1073]) ).
cnf(c_0_1567,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_1074]) ).
cnf(c_0_1568,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_1075]) ).
cnf(c_0_1569,plain,
c_List_Ofoldl(X1,X2,c_List_Olist_OCons(X3,X4,X5),X6,X5) = c_List_Ofoldl(X1,hAPP(hAPP(X1,X2),X3),X4,X6,X5),
inference(split_conjunct,[status(thm)],[c_0_1076]) ).
cnf(c_0_1570,plain,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
inference(split_conjunct,[status(thm)],[c_0_1077]) ).
cnf(c_0_1571,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_1078]) ).
cnf(c_0_1572,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_1079]) ).
cnf(c_0_1573,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_1080]) ).
cnf(c_0_1574,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_1081]) ).
cnf(c_0_1575,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_1082]) ).
cnf(c_0_1576,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_1083]) ).
cnf(c_0_1577,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_1084]) ).
cnf(c_0_1578,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_1085]) ).
cnf(c_0_1579,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_1086]) ).
cnf(c_0_1580,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_1087]) ).
cnf(c_0_1581,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_1088]) ).
cnf(c_0_1582,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_1089]) ).
cnf(c_0_1583,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1090]) ).
cnf(c_0_1584,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1091]) ).
cnf(c_0_1585,plain,
( X3 = X6
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1092]) ).
cnf(c_0_1586,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_1093]) ).
cnf(c_0_1587,plain,
( X3 = X6
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1588,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_1095]) ).
cnf(c_0_1589,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_1096]) ).
cnf(c_0_1590,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(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_1097]) ).
cnf(c_0_1591,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(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_1098]) ).
cnf(c_0_1592,plain,
c_List_Omap(X1,c_List_Oappend(X2,X3,X4),X4,X5) = c_List_Oappend(c_List_Omap(X1,X2,X4,X5),c_List_Omap(X1,X3,X4,X5),X5),
inference(split_conjunct,[status(thm)],[c_0_1099]) ).
cnf(c_0_1593,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_1100]) ).
cnf(c_0_1594,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_1101]) ).
cnf(c_0_1595,plain,
c_Lambda_OdB_OdB__case(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(X2,X4),X5),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1596,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_1103]) ).
cnf(c_0_1597,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1598,plain,
( c_List_Olistsum(X1,X2) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1599,plain,
( c_List_Olistsum(X1,X2) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1600,plain,
c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1601,plain,
c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1602,plain,
c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1603,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1604,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_1111]) ).
cnf(c_0_1605,plain,
X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X1),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X1),tc_Lambda_OdB,tc_Lambda_OdB),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1606,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_1113]) ).
cnf(c_0_1607,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_1114]) ).
cnf(c_0_1608,plain,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1609,plain,
c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1610,plain,
( c_Type_Otyping(X1,hAPP(hAPP(hAPP(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_1117]) ).
cnf(c_0_1611,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_1118]) ).
cnf(c_0_1612,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1613,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_1120]) ).
cnf(c_0_1614,plain,
( X6 = X3
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1615,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_1122]) ).
cnf(c_0_1616,plain,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1617,plain,
c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5) = c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1618,plain,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1619,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1620,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_1127]) ).
cnf(c_0_1621,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_1128]) ).
cnf(c_0_1622,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1623,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1624,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1625,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(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_1132]) ).
cnf(c_0_1626,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_1133]) ).
cnf(c_0_1627,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_1134]) ).
cnf(c_0_1628,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1629,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1136]) ).
cnf(c_0_1630,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_1137]) ).
cnf(c_0_1631,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_1138]) ).
cnf(c_0_1632,plain,
( X6 = X3
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1139]) ).
cnf(c_0_1633,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_1140]) ).
cnf(c_0_1634,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_1141]) ).
cnf(c_0_1635,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1142]) ).
cnf(c_0_1636,plain,
c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,X4,X3),X3) = c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X1,X2,X3),X4,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1143]) ).
cnf(c_0_1637,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_1144]) ).
cnf(c_0_1638,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_1145]) ).
cnf(c_0_1639,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_1146]) ).
cnf(c_0_1640,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_1147]) ).
cnf(c_0_1641,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1148]) ).
cnf(c_0_1642,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_1149]) ).
cnf(c_0_1643,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_1150]) ).
cnf(c_0_1644,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_1151]) ).
cnf(c_0_1645,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1152]) ).
cnf(c_0_1646,plain,
( X1 = X2
| c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1153]) ).
cnf(c_0_1647,plain,
( X1 = X2
| c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1154]) ).
cnf(c_0_1648,plain,
c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X2,X3),X3) = c_List_Oappend(c_List_Oreplicate(X4,X2,X3),c_List_Oreplicate(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1649,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1650,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_1157]) ).
cnf(c_0_1651,plain,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
inference(split_conjunct,[status(thm)],[c_0_1158]) ).
cnf(c_0_1652,plain,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)),
inference(split_conjunct,[status(thm)],[c_0_1159]) ).
cnf(c_0_1653,plain,
c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X4)),c_Lambda_Oliftn(X1,X3,X4)),
inference(split_conjunct,[status(thm)],[c_0_1160]) ).
cnf(c_0_1654,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_1161]) ).
cnf(c_0_1655,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_1162]) ).
cnf(c_0_1656,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1163]) ).
cnf(c_0_1657,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_1164]) ).
cnf(c_0_1658,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_1165]) ).
cnf(c_0_1659,plain,
c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1166]) ).
cnf(c_0_1660,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_1167]) ).
cnf(c_0_1661,plain,
c_List_Omap(X1,c_List_Oreplicate(X2,X3,X4),X4,X5) = c_List_Oreplicate(X2,hAPP(X1,X3),X5),
inference(split_conjunct,[status(thm)],[c_0_1168]) ).
cnf(c_0_1662,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_1169]) ).
cnf(c_0_1663,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_1170]) ).
cnf(c_0_1664,plain,
hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_1171]) ).
cnf(c_0_1665,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_1172]) ).
cnf(c_0_1666,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_1173]) ).
cnf(c_0_1667,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_1174]) ).
cnf(c_0_1668,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_1175]) ).
cnf(c_0_1669,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_1176]) ).
cnf(c_0_1670,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_1177]) ).
cnf(c_0_1671,plain,
c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,X4) = c_List_Oappend(c_List_Oreplicate(X1,X3,X4),c_List_Oreplicate(X2,X3,X4),X4),
inference(split_conjunct,[status(thm)],[c_0_1178]) ).
cnf(c_0_1672,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_1179]) ).
cnf(c_0_1673,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_1180]) ).
cnf(c_0_1674,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1181]) ).
cnf(c_0_1675,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X3) != c_List_Omap(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1182]) ).
cnf(c_0_1676,plain,
~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1183]) ).
cnf(c_0_1677,plain,
~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
inference(split_conjunct,[status(thm)],[c_0_1184]) ).
cnf(c_0_1678,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_1185]) ).
cnf(c_0_1679,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_1186]) ).
cnf(c_0_1680,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1187]) ).
cnf(c_0_1681,plain,
( c_HOL_Oord__class_Oless(X1,X2,X4)
| c_HOL_Oord__class_Oless(X1,X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1188]) ).
cnf(c_0_1682,plain,
c_Lambda_Osubstn(X1,X2,X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3),
inference(split_conjunct,[status(thm)],[c_0_1189]) ).
cnf(c_0_1683,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_1190]) ).
cnf(c_0_1684,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_1191]) ).
cnf(c_0_1685,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_1192]) ).
cnf(c_0_1686,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_1193]) ).
cnf(c_0_1687,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_1194]) ).
cnf(c_0_1688,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_1195]) ).
cnf(c_0_1689,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_1196]) ).
cnf(c_0_1690,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_1197]) ).
cnf(c_0_1691,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_1198]) ).
cnf(c_0_1692,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1199]) ).
cnf(c_0_1693,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1200]) ).
cnf(c_0_1694,plain,
( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X2,X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1201]) ).
cnf(c_0_1695,plain,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1202]) ).
cnf(c_0_1696,plain,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1203]) ).
cnf(c_0_1697,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_1204]) ).
cnf(c_0_1698,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_1205]) ).
cnf(c_0_1699,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_1206]) ).
cnf(c_0_1700,plain,
c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
inference(split_conjunct,[status(thm)],[c_0_1207]) ).
cnf(c_0_1701,plain,
c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1208]) ).
cnf(c_0_1702,plain,
c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
inference(split_conjunct,[status(thm)],[c_0_1209]) ).
cnf(c_0_1703,plain,
c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1210]) ).
cnf(c_0_1704,plain,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
inference(split_conjunct,[status(thm)],[c_0_1211]) ).
cnf(c_0_1705,plain,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
inference(split_conjunct,[status(thm)],[c_0_1212]) ).
cnf(c_0_1706,plain,
c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1213]) ).
cnf(c_0_1707,plain,
c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3) = c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1214]) ).
cnf(c_0_1708,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_1215]) ).
cnf(c_0_1709,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_1216]) ).
cnf(c_0_1710,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1217]) ).
cnf(c_0_1711,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1218]) ).
cnf(c_0_1712,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_1219]) ).
cnf(c_0_1713,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_1220]) ).
cnf(c_0_1714,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_1221]) ).
cnf(c_0_1715,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_1222]) ).
cnf(c_0_1716,plain,
c_Lambda_Oliftn(c_Suc(X1),X2,X3) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X1,X2,X3)),X3),
inference(split_conjunct,[status(thm)],[c_0_1223]) ).
cnf(c_0_1717,plain,
( c_List_Olistsp(X1,X3,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1224]) ).
cnf(c_0_1718,plain,
( c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1225]) ).
cnf(c_0_1719,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_1226]) ).
cnf(c_0_1720,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_1227]) ).
cnf(c_0_1721,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_1228]) ).
cnf(c_0_1722,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1229]) ).
cnf(c_0_1723,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_1230]) ).
cnf(c_0_1724,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_1231]) ).
cnf(c_0_1725,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_1232]) ).
cnf(c_0_1726,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_1233]) ).
cnf(c_0_1727,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_1234]) ).
cnf(c_0_1728,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_1235]) ).
cnf(c_0_1729,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_1236]) ).
cnf(c_0_1730,plain,
( c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3))
| ~ class_OrderedGroup_Omonoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1237]) ).
cnf(c_0_1731,plain,
c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
inference(split_conjunct,[status(thm)],[c_0_1238]) ).
cnf(c_0_1732,plain,
c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
inference(split_conjunct,[status(thm)],[c_0_1239]) ).
cnf(c_0_1733,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1240]) ).
cnf(c_0_1734,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1241]) ).
cnf(c_0_1735,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1242]) ).
cnf(c_0_1736,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1243]) ).
cnf(c_0_1737,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_1244]) ).
cnf(c_0_1738,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_1245]) ).
cnf(c_0_1739,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_1246]) ).
cnf(c_0_1740,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_1247]) ).
cnf(c_0_1741,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_1248]) ).
cnf(c_0_1742,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_1249]) ).
cnf(c_0_1743,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_1250]) ).
cnf(c_0_1744,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_1251]) ).
cnf(c_0_1745,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_1252]) ).
cnf(c_0_1746,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_1253]) ).
cnf(c_0_1747,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_1254]) ).
cnf(c_0_1748,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_1255]) ).
cnf(c_0_1749,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_1256]) ).
cnf(c_0_1750,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_1257]) ).
cnf(c_0_1751,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_1258]) ).
cnf(c_0_1752,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_1259]) ).
cnf(c_0_1753,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_1260]) ).
cnf(c_0_1754,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_1261]) ).
cnf(c_0_1755,plain,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1262]) ).
cnf(c_0_1756,plain,
c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_OCons(X2,X3,X1),X1) = c_List_Olist_OCons(X2,X3,X1),
inference(split_conjunct,[status(thm)],[c_0_1263]) ).
cnf(c_0_1757,plain,
c_List_Olist_OCons(X1,X2,X3) = c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1264]) ).
cnf(c_0_1758,plain,
c_List_Oreplicate(c_Suc(X1),X2,X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1265]) ).
cnf(c_0_1759,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1266]) ).
cnf(c_0_1760,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1267]) ).
cnf(c_0_1761,plain,
( c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3))
| ~ class_OrderedGroup_Omonoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1268]) ).
cnf(c_0_1762,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_1269]) ).
cnf(c_0_1763,plain,
( hAPP(hAPP(hAPP(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_1270]) ).
cnf(c_0_1764,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_1271]) ).
cnf(c_0_1765,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_1272]) ).
cnf(c_0_1766,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_1273]) ).
cnf(c_0_1767,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(split_conjunct,[status(thm)],[c_0_1274]) ).
cnf(c_0_1768,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(split_conjunct,[status(thm)],[c_0_1275]) ).
cnf(c_0_1769,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_1276]) ).
cnf(c_0_1770,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_1277]) ).
cnf(c_0_1771,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_1278]) ).
cnf(c_0_1772,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_1279]) ).
cnf(c_0_1773,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_1280]) ).
cnf(c_0_1774,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_1281]) ).
cnf(c_0_1775,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1282]) ).
cnf(c_0_1776,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_1283]) ).
cnf(c_0_1777,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1284]) ).
cnf(c_0_1778,plain,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1285]) ).
cnf(c_0_1779,plain,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1286]) ).
cnf(c_0_1780,plain,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1287]) ).
cnf(c_0_1781,plain,
( X1 = X2
| c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1288]) ).
cnf(c_0_1782,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_1289]) ).
cnf(c_0_1783,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_1290]) ).
cnf(c_0_1784,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_1291]) ).
cnf(c_0_1785,plain,
c_Orderings_Oord__class_Omax(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X1,X2,tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1292]) ).
cnf(c_0_1786,plain,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1293]) ).
cnf(c_0_1787,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1294]) ).
cnf(c_0_1788,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1295]) ).
cnf(c_0_1789,plain,
( hAPP(hAPP(hAPP(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_1296]) ).
cnf(c_0_1790,plain,
c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1297]) ).
cnf(c_0_1791,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1298]) ).
cnf(c_0_1792,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_1299]) ).
cnf(c_0_1793,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_1300]) ).
cnf(c_0_1794,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_1301]) ).
cnf(c_0_1795,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_1302]) ).
cnf(c_0_1796,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_1303]) ).
cnf(c_0_1797,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_1304]) ).
cnf(c_0_1798,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_1305]) ).
cnf(c_0_1799,plain,
( c_Lambda_Oliftn(X3,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_1306]) ).
cnf(c_0_1800,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_1307]) ).
cnf(c_0_1801,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_1308]) ).
cnf(c_0_1802,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_1309]) ).
cnf(c_0_1803,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_1310]) ).
cnf(c_0_1804,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_1311]) ).
cnf(c_0_1805,plain,
c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(split_conjunct,[status(thm)],[c_0_1312]) ).
cnf(c_0_1806,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_1313]) ).
cnf(c_0_1807,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_1314]) ).
cnf(c_0_1808,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_1315]) ).
cnf(c_0_1809,plain,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_1316]) ).
cnf(c_0_1810,plain,
( hAPP(hAPP(X2,X1),X4) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1317]) ).
cnf(c_0_1811,plain,
( hAPP(hAPP(X2,X4),X1) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1318]) ).
cnf(c_0_1812,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1319]) ).
cnf(c_0_1813,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1320]) ).
cnf(c_0_1814,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1321]) ).
cnf(c_0_1815,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_1322]) ).
cnf(c_0_1816,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_1323]) ).
cnf(c_0_1817,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_1324]) ).
cnf(c_0_1818,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_1325]) ).
cnf(c_0_1819,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_1326]) ).
cnf(c_0_1820,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_1327]) ).
cnf(c_0_1821,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_1328]) ).
cnf(c_0_1822,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_1329]) ).
cnf(c_0_1823,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_1330]) ).
cnf(c_0_1824,plain,
( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1331]) ).
cnf(c_0_1825,plain,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2),
inference(split_conjunct,[status(thm)],[c_0_1332]) ).
cnf(c_0_1826,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_1333]) ).
cnf(c_0_1827,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_1334]) ).
cnf(c_0_1828,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_1335]) ).
cnf(c_0_1829,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_1336]) ).
cnf(c_0_1830,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_1337]) ).
cnf(c_0_1831,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1338]) ).
cnf(c_0_1832,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1339]) ).
cnf(c_0_1833,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_1340]) ).
cnf(c_0_1834,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_1341]) ).
cnf(c_0_1835,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_1342]) ).
cnf(c_0_1836,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_1343]) ).
cnf(c_0_1837,plain,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
inference(split_conjunct,[status(thm)],[c_0_1344]) ).
cnf(c_0_1838,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1345]) ).
cnf(c_0_1839,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_1346]) ).
cnf(c_0_1840,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_1347]) ).
cnf(c_0_1841,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_1348]) ).
cnf(c_0_1842,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_1349]) ).
cnf(c_0_1843,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1350]) ).
cnf(c_0_1844,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1351]) ).
cnf(c_0_1845,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != c_List_Oappend(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1352]) ).
cnf(c_0_1846,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != c_List_Oappend(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1353]) ).
cnf(c_0_1847,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1354]) ).
cnf(c_0_1848,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Olist_ONil(X2) != c_List_Oreplicate(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1355]) ).
cnf(c_0_1849,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1356]) ).
cnf(c_0_1850,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_1357]) ).
cnf(c_0_1851,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_1358]) ).
cnf(c_0_1852,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_1359]) ).
cnf(c_0_1853,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_1360]) ).
cnf(c_0_1854,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_1361]) ).
cnf(c_0_1855,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1362]) ).
cnf(c_0_1856,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1363]) ).
cnf(c_0_1857,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1364]) ).
cnf(c_0_1858,plain,
( X1 = c_List_Olist_ONil(X2)
| X3 != c_List_Oappend(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1365]) ).
cnf(c_0_1859,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1366]) ).
cnf(c_0_1860,plain,
( X1 = c_List_Olist_ONil(X2)
| X3 != c_List_Oappend(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1367]) ).
cnf(c_0_1861,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_1368]) ).
cnf(c_0_1862,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
inference(split_conjunct,[status(thm)],[c_0_1369]) ).
cnf(c_0_1863,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_1370]) ).
cnf(c_0_1864,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
inference(split_conjunct,[status(thm)],[c_0_1371]) ).
cnf(c_0_1865,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
inference(split_conjunct,[status(thm)],[c_0_1372]) ).
cnf(c_0_1866,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_1373]) ).
cnf(c_0_1867,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_1374]) ).
cnf(c_0_1868,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1375]) ).
cnf(c_0_1869,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1376]) ).
cnf(c_0_1870,plain,
X1 != c_List_Olist_OCons(X2,X1,X3),
inference(split_conjunct,[status(thm)],[c_0_1377]) ).
cnf(c_0_1871,plain,
c_List_Olist_OCons(X1,X2,X3) != X2,
inference(split_conjunct,[status(thm)],[c_0_1378]) ).
cnf(c_0_1872,plain,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_1379]) ).
cnf(c_0_1873,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1380]) ).
cnf(c_0_1874,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1381]) ).
cnf(c_0_1875,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1382]) ).
cnf(c_0_1876,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1383]) ).
cnf(c_0_1877,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1384]) ).
cnf(c_0_1878,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_1385]) ).
cnf(c_0_1879,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_1386]) ).
cnf(c_0_1880,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_1387]) ).
cnf(c_0_1881,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_1388]) ).
cnf(c_0_1882,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_1389]) ).
cnf(c_0_1883,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_1390]) ).
cnf(c_0_1884,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_1391]) ).
cnf(c_0_1885,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_1392]) ).
cnf(c_0_1886,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_1393]) ).
cnf(c_0_1887,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_1394]) ).
cnf(c_0_1888,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_1395]) ).
cnf(c_0_1889,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_1396]) ).
cnf(c_0_1890,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_1397]) ).
cnf(c_0_1891,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_1398]) ).
cnf(c_0_1892,plain,
c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_1893,plain,
c_List_Olist_ONil(X1) = c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_1400]) ).
cnf(c_0_1894,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_1401]) ).
cnf(c_0_1895,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_1402]) ).
cnf(c_0_1896,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_1403]) ).
cnf(c_0_1897,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_1404]) ).
cnf(c_0_1898,plain,
c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
inference(split_conjunct,[status(thm)],[c_0_1405]) ).
cnf(c_0_1899,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
inference(split_conjunct,[status(thm)],[c_0_1406]) ).
cnf(c_0_1900,plain,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1407]) ).
cnf(c_0_1901,plain,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_1408]) ).
cnf(c_0_1902,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
inference(split_conjunct,[status(thm)],[c_0_1409]) ).
cnf(c_0_1903,plain,
( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1410]) ).
cnf(c_0_1904,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_1411]) ).
cnf(c_0_1905,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_1412]) ).
cnf(c_0_1906,plain,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
inference(split_conjunct,[status(thm)],[c_0_1413]) ).
cnf(c_0_1907,plain,
c_List_Olist_ONil(X1) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X2,X1),
inference(split_conjunct,[status(thm)],[c_0_1414]) ).
cnf(c_0_1908,plain,
X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_1909,plain,
c_List_Oappend(c_List_Olist_ONil(X1),X2,X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1416]) ).
cnf(c_0_1910,plain,
X1 = c_List_Oappend(X1,c_List_Olist_ONil(X2),X2),
inference(split_conjunct,[status(thm)],[c_0_1417]) ).
cnf(c_0_1911,plain,
X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_1912,plain,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_1913,plain,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
inference(split_conjunct,[status(thm)],[c_0_1420]) ).
cnf(c_0_1914,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_1421]) ).
cnf(c_0_1915,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_1916,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1423]) ).
cnf(c_0_1917,plain,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1424]) ).
cnf(c_0_1918,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_1425]) ).
cnf(c_0_1919,plain,
c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1426]) ).
cnf(c_0_1920,plain,
c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(split_conjunct,[status(thm)],[c_0_1427]) ).
cnf(c_0_1921,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_1428]) ).
cnf(c_0_1922,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_1429]) ).
cnf(c_0_1923,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_1430]) ).
cnf(c_0_1924,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(split_conjunct,[status(thm)],[c_0_1431]) ).
cnf(c_0_1925,plain,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
inference(split_conjunct,[status(thm)],[c_0_1432]) ).
cnf(c_0_1926,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_1433]) ).
cnf(c_0_1927,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_1434]) ).
cnf(c_0_1928,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
inference(split_conjunct,[status(thm)],[c_0_1435]) ).
cnf(c_0_1929,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1436]) ).
cnf(c_0_1930,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1437]) ).
cnf(c_0_1931,plain,
( c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1438]) ).
cnf(c_0_1932,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_1439]) ).
cnf(c_0_1933,plain,
( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1440]) ).
cnf(c_0_1934,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
inference(split_conjunct,[status(thm)],[c_0_1441]) ).
cnf(c_0_1935,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(split_conjunct,[status(thm)],[c_0_1442]) ).
cnf(c_0_1936,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
inference(split_conjunct,[status(thm)],[c_0_1443]) ).
cnf(c_0_1937,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1444]) ).
cnf(c_0_1938,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1445]) ).
cnf(c_0_1939,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1446]) ).
cnf(c_0_1940,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1447]) ).
cnf(c_0_1941,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
inference(split_conjunct,[status(thm)],[c_0_1448]) ).
cnf(c_0_1942,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(split_conjunct,[status(thm)],[c_0_1449]) ).
cnf(c_0_1943,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1450]) ).
cnf(c_0_1944,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1451]) ).
cnf(c_0_1945,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1452]) ).
cnf(c_0_1946,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1453]) ).
cnf(c_0_1947,plain,
X1 != c_Suc(X1),
inference(split_conjunct,[status(thm)],[c_0_1454]) ).
cnf(c_0_1948,plain,
c_Suc(X1) != X1,
inference(split_conjunct,[status(thm)],[c_0_1455]) ).
cnf(c_0_1949,plain,
class_Orderings_Oorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1456]) ).
cnf(c_0_1950,plain,
class_Orderings_Opreorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1457]) ).
cnf(c_0_1951,plain,
class_Power_Opower(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1458]) ).
cnf(c_0_1952,plain,
class_Orderings_Oorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1459]) ).
cnf(c_0_1953,plain,
class_Orderings_Olinorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1460]) ).
cnf(c_0_1954,plain,
class_Orderings_Opreorder(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1461]) ).
cnf(c_0_1955,plain,
class_Nat_Osemiring__char__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1462]) ).
cnf(c_0_1956,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1463]) ).
cnf(c_0_1957,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1464]) ).
cnf(c_0_1958,plain,
class_Ring__and__Field_Osemiring__0(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1465]) ).
cnf(c_0_1959,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1466]) ).
cnf(c_0_1960,plain,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1467]) ).
cnf(c_0_1961,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1468]) ).
cnf(c_0_1962,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1469]) ).
cnf(c_0_1963,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1470]) ).
cnf(c_0_1964,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1471]) ).
cnf(c_0_1965,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1472]) ).
cnf(c_0_1966,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1473]) ).
cnf(c_0_1967,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1474]) ).
cnf(c_0_1968,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1475]) ).
cnf(c_0_1969,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1476]) ).
cnf(c_0_1970,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1477]) ).
cnf(c_0_1971,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(split_conjunct,[status(thm)],[c_0_1478]) ).
cnf(c_0_1972,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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,hAPP(hAPP(hAPP(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_1479,
[final] ).
cnf(c_0_1973,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4),
c_0_1480,
[final] ).
cnf(c_0_1974,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_1481,
[final] ).
cnf(c_0_1975,plain,
( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
c_0_1482,
[final] ).
cnf(c_0_1976,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_1483,
[final] ).
cnf(c_0_1977,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,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)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_1484,
[final] ).
cnf(c_0_1978,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_1485,
[final] ).
cnf(c_0_1979,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_1486,
[final] ).
cnf(c_0_1980,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_1487,
[final] ).
cnf(c_0_1981,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,hAPP(hAPP(hAPP(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_1488,
[final] ).
cnf(c_0_1982,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),
c_0_1489,
[final] ).
cnf(c_0_1983,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1490,
[final] ).
cnf(c_0_1984,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1491,
[final] ).
cnf(c_0_1985,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10)))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1492,
[final] ).
cnf(c_0_1986,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1493,
[final] ).
cnf(c_0_1987,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1494,
[final] ).
cnf(c_0_1988,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1495,
[final] ).
cnf(c_0_1989,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9)) = hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1496,
[final] ).
cnf(c_0_1990,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1497,
[final] ).
cnf(c_0_1991,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1498,
[final] ).
cnf(c_0_1992,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1499,
[final] ).
cnf(c_0_1993,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1500,
[final] ).
cnf(c_0_1994,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1501,
[final] ).
cnf(c_0_1995,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1502,
[final] ).
cnf(c_0_1996,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1503,
[final] ).
cnf(c_0_1997,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1504,
[final] ).
cnf(c_0_1998,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1505,
[final] ).
cnf(c_0_1999,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1506,
[final] ).
cnf(c_0_2000,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1507,
[final] ).
cnf(c_0_2001,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1508,
[final] ).
cnf(c_0_2002,plain,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),X7) = hAPP(hAPP(X3,X7),c_Suc(X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1509,
[final] ).
cnf(c_0_2003,plain,
( hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1510,
[final] ).
cnf(c_0_2004,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1511,
[final] ).
cnf(c_0_2005,plain,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1512,
[final] ).
cnf(c_0_2006,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8)) = hAPP(hAPP(X3,X7),c_Suc(X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1513,
[final] ).
cnf(c_0_2007,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8)) = hAPP(hAPP(X3,X7),c_Suc(X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1514,
[final] ).
cnf(c_0_2008,plain,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8)) = hAPP(hAPP(X3,X7),c_Suc(X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1515,
[final] ).
cnf(c_0_2009,plain,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1516,
[final] ).
cnf(c_0_2010,plain,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1517,
[final] ).
cnf(c_0_2011,plain,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1518,
[final] ).
cnf(c_0_2012,plain,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1519,
[final] ).
cnf(c_0_2013,plain,
( hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1520,
[final] ).
cnf(c_0_2014,plain,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1521,
[final] ).
cnf(c_0_2015,plain,
( hAPP(hAPP(X1,X7),X4) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1522,
[final] ).
cnf(c_0_2016,plain,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1523,
[final] ).
cnf(c_0_2017,plain,
( hAPP(hAPP(X2,X7),X4) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1524,
[final] ).
cnf(c_0_2018,plain,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1525,
[final] ).
cnf(c_0_2019,plain,
( hAPP(hAPP(X2,X7),X5) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1526,
[final] ).
cnf(c_0_2020,plain,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1527,
[final] ).
cnf(c_0_2021,plain,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1528,
[final] ).
cnf(c_0_2022,plain,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
c_0_1529,
[final] ).
cnf(c_0_2023,plain,
hAPP(hAPP(hAPP(hAPP(X2,X4),X5),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X6)),c_Lambda_OdB_OdB__rec(X1,X2,X3,X5,X6)) = c_Lambda_OdB_OdB__rec(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6),
c_0_1530,
[final] ).
cnf(c_0_2024,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
c_0_1531,
[final] ).
cnf(c_0_2025,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
c_0_1532,
[final] ).
cnf(c_0_2026,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_1533,
[final] ).
cnf(c_0_2027,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
c_0_1534,
[final] ).
cnf(c_0_2028,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
c_0_1535,
[final] ).
cnf(c_0_2029,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
c_0_1536,
[final] ).
cnf(c_0_2030,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
c_0_1537,
[final] ).
cnf(c_0_2031,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,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
c_0_1538,
[final] ).
cnf(c_0_2032,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_1539,
[final] ).
cnf(c_0_2033,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_1540,
[final] ).
cnf(c_0_2034,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_1541,
[final] ).
cnf(c_0_2035,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_1542,
[final] ).
cnf(c_0_2036,plain,
( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X1,X2,X3) ),
c_0_1543,
[final] ).
cnf(c_0_2037,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_1544,
[final] ).
cnf(c_0_2038,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
c_0_1545,
[final] ).
cnf(c_0_2039,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_1546,
[final] ).
cnf(c_0_2040,plain,
c_List_Ofoldl(X1,c_List_Ofoldl(X1,X2,X3,X6,X5),X4,X6,X5) = c_List_Ofoldl(X1,X2,c_List_Oappend(X3,X4,X5),X6,X5),
c_0_1547,
[final] ).
cnf(c_0_2041,plain,
c_List_Ofoldr(X1,X2,c_List_Ofoldr(X1,X3,X5,X4,X6),X4,X6) = c_List_Ofoldr(X1,c_List_Oappend(X2,X3,X4),X5,X4,X6),
c_0_1548,
[final] ).
cnf(c_0_2042,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_1549,
[final] ).
cnf(c_0_2043,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_1550,
[final] ).
cnf(c_0_2044,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_1551,
[final] ).
cnf(c_0_2045,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_1552,
[final] ).
cnf(c_0_2046,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_1553,
[final] ).
cnf(c_0_2047,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_1554,
[final] ).
cnf(c_0_2048,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_1555,
[final] ).
cnf(c_0_2049,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_1556,
[final] ).
cnf(c_0_2050,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_1557,
[final] ).
cnf(c_0_2051,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_1558,
[final] ).
cnf(c_0_2052,plain,
c_List_Ofoldr(X1,c_List_Olist_OCons(X2,X3,X4),X5,X4,X6) = hAPP(hAPP(X1,X2),c_List_Ofoldr(X1,X3,X5,X4,X6)),
c_0_1559,
[final] ).
cnf(c_0_2053,plain,
( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
c_0_1560,
[final] ).
cnf(c_0_2054,plain,
( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
c_0_1561,
[final] ).
cnf(c_0_2055,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_1562,
[final] ).
cnf(c_0_2056,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_1563,
[final] ).
cnf(c_0_2057,plain,
hAPP(hAPP(X3,X4),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X5)) = c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5),
c_0_1564,
[final] ).
cnf(c_0_2058,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_1565,
[final] ).
cnf(c_0_2059,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_1566,
[final] ).
cnf(c_0_2060,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_1567,
[final] ).
cnf(c_0_2061,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_1568,
[final] ).
cnf(c_0_2062,plain,
c_List_Ofoldl(X1,X2,c_List_Olist_OCons(X3,X4,X5),X6,X5) = c_List_Ofoldl(X1,hAPP(hAPP(X1,X2),X3),X4,X6,X5),
c_0_1569,
[final] ).
cnf(c_0_2063,plain,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
c_0_1570,
[final] ).
cnf(c_0_2064,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_1571,
[final] ).
cnf(c_0_2065,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_1572,
[final] ).
cnf(c_0_2066,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_1573,
[final] ).
cnf(c_0_2067,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_1574,
[final] ).
cnf(c_0_2068,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_1575,
[final] ).
cnf(c_0_2069,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_1576,
[final] ).
cnf(c_0_2070,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_1577,
[final] ).
cnf(c_0_2071,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_1578,
[final] ).
cnf(c_0_2072,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_1579,
[final] ).
cnf(c_0_2073,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_1580,
[final] ).
cnf(c_0_2074,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_1581,
[final] ).
cnf(c_0_2075,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_1582,
[final] ).
cnf(c_0_2076,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_1583,
[final] ).
cnf(c_0_2077,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_1584,
[final] ).
cnf(c_0_2078,plain,
( X3 = X6
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_1585,
[final] ).
cnf(c_0_2079,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_1586,
[final] ).
cnf(c_0_2080,plain,
( X3 = X6
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_1587,
[final] ).
cnf(c_0_2081,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_1588,
[final] ).
cnf(c_0_2082,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_1589,
[final] ).
cnf(c_0_2083,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1590,
[final] ).
cnf(c_0_2084,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1591,
[final] ).
cnf(c_0_2085,plain,
c_List_Oappend(c_List_Omap(X1,X2,X4,X5),c_List_Omap(X1,X3,X4,X5),X5) = c_List_Omap(X1,c_List_Oappend(X2,X3,X4),X4,X5),
c_0_1592,
[final] ).
cnf(c_0_2086,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_1593,
[final] ).
cnf(c_0_2087,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_1594,
[final] ).
cnf(c_0_2088,plain,
c_Lambda_OdB_OdB__case(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(X2,X4),X5),
c_0_1595,
[final] ).
cnf(c_0_2089,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_1596,
[final] ).
cnf(c_0_2090,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1597,
[final] ).
cnf(c_0_2091,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2) = c_List_Olistsum(X1,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
c_0_1598,
[final] ).
cnf(c_0_2092,plain,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2) = c_List_Olistsum(X1,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
c_0_1599,
[final] ).
cnf(c_0_2093,plain,
c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
c_0_1600,
[final] ).
cnf(c_0_2094,plain,
c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X3,X4),
c_0_1601,
[final] ).
cnf(c_0_2095,plain,
c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
c_0_1602,
[final] ).
cnf(c_0_2096,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1603,
[final] ).
cnf(c_0_2097,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_1604,
[final] ).
cnf(c_0_2098,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X1),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1,
c_0_1605,
[final] ).
cnf(c_0_2099,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_1606,
[final] ).
cnf(c_0_2100,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_1607,
[final] ).
cnf(c_0_2101,plain,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
c_0_1608,
[final] ).
cnf(c_0_2102,plain,
c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
c_0_1609,
[final] ).
cnf(c_0_2103,plain,
( c_Type_Otyping(X1,hAPP(hAPP(hAPP(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_1610,
[final] ).
cnf(c_0_2104,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_1611,
[final] ).
cnf(c_0_2105,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_1612,
[final] ).
cnf(c_0_2106,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_1613,
[final] ).
cnf(c_0_2107,plain,
( X6 = X3
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_1614,
[final] ).
cnf(c_0_2108,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_1615,
[final] ).
cnf(c_0_2109,plain,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
c_0_1616,
[final] ).
cnf(c_0_2110,plain,
c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5) = c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5),
c_0_1617,
[final] ).
cnf(c_0_2111,plain,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
c_0_1618,
[final] ).
cnf(c_0_2112,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4),
c_0_1619,
[final] ).
cnf(c_0_2113,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
c_0_1620,
[final] ).
cnf(c_0_2114,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
c_0_1621,
[final] ).
cnf(c_0_2115,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
c_0_1622,
[final] ).
cnf(c_0_2116,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
c_0_1623,
[final] ).
cnf(c_0_2117,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
c_0_1624,
[final] ).
cnf(c_0_2118,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_1625,
[final] ).
cnf(c_0_2119,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_1626,
[final] ).
cnf(c_0_2120,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_1627,
[final] ).
cnf(c_0_2121,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
c_0_1628,
[final] ).
cnf(c_0_2122,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_1629,
[final] ).
cnf(c_0_2123,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_1630,
[final] ).
cnf(c_0_2124,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_1631,
[final] ).
cnf(c_0_2125,plain,
( X6 = X3
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_1632,
[final] ).
cnf(c_0_2126,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_1633,
[final] ).
cnf(c_0_2127,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_1634,
[final] ).
cnf(c_0_2128,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
c_0_1635,
[final] ).
cnf(c_0_2129,plain,
c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X1,X2,X3),X4,X3),X3) = c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,X4,X3),X3),
c_0_1636,
[final] ).
cnf(c_0_2130,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1637,
[final] ).
cnf(c_0_2131,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1638,
[final] ).
cnf(c_0_2132,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_1639,
[final] ).
cnf(c_0_2133,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_1640,
[final] ).
cnf(c_0_2134,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_1641,
[final] ).
cnf(c_0_2135,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_1642,
[final] ).
cnf(c_0_2136,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_1643,
[final] ).
cnf(c_0_2137,plain,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1644,
[final] ).
cnf(c_0_2138,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
c_0_1645,
[final] ).
cnf(c_0_2139,plain,
( X1 = X2
| c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
c_0_1646,
[final] ).
cnf(c_0_2140,plain,
( X1 = X2
| c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
c_0_1647,
[final] ).
cnf(c_0_2141,plain,
c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X2,X3),X3) = c_List_Oappend(c_List_Oreplicate(X4,X2,X3),c_List_Oreplicate(X1,X2,X3),X3),
c_0_1648,
[final] ).
cnf(c_0_2142,plain,
( c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_1649,
[final] ).
cnf(c_0_2143,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_1650,
[final] ).
cnf(c_0_2144,plain,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
c_0_1651,
[final] ).
cnf(c_0_2145,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)) = c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4),
c_0_1652,
[final] ).
cnf(c_0_2146,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X4)),c_Lambda_Oliftn(X1,X3,X4)) = c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4),
c_0_1653,
[final] ).
cnf(c_0_2147,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_1654,
[final] ).
cnf(c_0_2148,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_1655,
[final] ).
cnf(c_0_2149,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1656,
[final] ).
cnf(c_0_2150,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_1657,
[final] ).
cnf(c_0_2151,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_1658,
[final] ).
cnf(c_0_2152,plain,
c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
c_0_1659,
[final] ).
cnf(c_0_2153,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_1660,
[final] ).
cnf(c_0_2154,plain,
c_List_Omap(X1,c_List_Oreplicate(X2,X3,X4),X4,X5) = c_List_Oreplicate(X2,hAPP(X1,X3),X5),
c_0_1661,
[final] ).
cnf(c_0_2155,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_1662,
[final] ).
cnf(c_0_2156,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_1663,
[final] ).
cnf(c_0_2157,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),
c_0_1664,
[final] ).
cnf(c_0_2158,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_1665,
[final] ).
cnf(c_0_2159,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_1666,
[final] ).
cnf(c_0_2160,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_1667,
[final] ).
cnf(c_0_2161,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_1668,
[final] ).
cnf(c_0_2162,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_1669,
[final] ).
cnf(c_0_2163,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_1670,
[final] ).
cnf(c_0_2164,plain,
c_List_Oappend(c_List_Oreplicate(X1,X3,X4),c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,X4),
c_0_1671,
[final] ).
cnf(c_0_2165,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_1672,
[final] ).
cnf(c_0_2166,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_1673,
[final] ).
cnf(c_0_2167,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
c_0_1674,
[final] ).
cnf(c_0_2168,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
c_0_1675,
[final] ).
cnf(c_0_2169,plain,
~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
c_0_1676,
[final] ).
cnf(c_0_2170,plain,
~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
c_0_1677,
[final] ).
cnf(c_0_2171,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_1678,
[final] ).
cnf(c_0_2172,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_1679,
[final] ).
cnf(c_0_2173,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
c_0_1680,
[final] ).
cnf(c_0_2174,plain,
( c_HOL_Oord__class_Oless(X1,X2,X4)
| c_HOL_Oord__class_Oless(X1,X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
c_0_1681,
[final] ).
cnf(c_0_2175,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3) = c_Lambda_Osubstn(X1,X2,X3),
c_0_1682,
[final] ).
cnf(c_0_2176,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_1683,
[final] ).
cnf(c_0_2177,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_1684,
[final] ).
cnf(c_0_2178,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_1685,
[final] ).
cnf(c_0_2179,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_1686,
[final] ).
cnf(c_0_2180,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_1687,
[final] ).
cnf(c_0_2181,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_1688,
[final] ).
cnf(c_0_2182,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_1689,
[final] ).
cnf(c_0_2183,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_1690,
[final] ).
cnf(c_0_2184,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_1691,
[final] ).
cnf(c_0_2185,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1692,
[final] ).
cnf(c_0_2186,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
c_0_1693,
[final] ).
cnf(c_0_2187,plain,
( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X2,X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
c_0_1694,
[final] ).
cnf(c_0_2188,plain,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
c_0_1695,
[final] ).
cnf(c_0_2189,plain,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1696,
[final] ).
cnf(c_0_2190,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_1697,
[final] ).
cnf(c_0_2191,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_1698,
[final] ).
cnf(c_0_2192,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_1699,
[final] ).
cnf(c_0_2193,plain,
c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4) = c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4),
c_0_1700,
[final] ).
cnf(c_0_2194,plain,
c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3),
c_0_1701,
[final] ).
cnf(c_0_2195,plain,
c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4) = c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4),
c_0_1702,
[final] ).
cnf(c_0_2196,plain,
c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3),
c_0_1703,
[final] ).
cnf(c_0_2197,plain,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
c_0_1704,
[final] ).
cnf(c_0_2198,plain,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
c_0_1705,
[final] ).
cnf(c_0_2199,plain,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3),
c_0_1706,
[final] ).
cnf(c_0_2200,plain,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3),
c_0_1707,
[final] ).
cnf(c_0_2201,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_1708,
[final] ).
cnf(c_0_2202,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_1709,
[final] ).
cnf(c_0_2203,plain,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1710,
[final] ).
cnf(c_0_2204,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1711,
[final] ).
cnf(c_0_2205,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_1712,
[final] ).
cnf(c_0_2206,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_1713,
[final] ).
cnf(c_0_2207,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_1714,
[final] ).
cnf(c_0_2208,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_1715,
[final] ).
cnf(c_0_2209,plain,
hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X1,X2,X3)),X3) = c_Lambda_Oliftn(c_Suc(X1),X2,X3),
c_0_1716,
[final] ).
cnf(c_0_2210,plain,
( c_List_Olistsp(X1,X3,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
c_0_1717,
[final] ).
cnf(c_0_2211,plain,
( c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
c_0_1718,
[final] ).
cnf(c_0_2212,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_1719,
[final] ).
cnf(c_0_2213,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_1720,
[final] ).
cnf(c_0_2214,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_1721,
[final] ).
cnf(c_0_2215,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_1722,
[final] ).
cnf(c_0_2216,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
c_0_1723,
[final] ).
cnf(c_0_2217,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
c_0_1724,
[final] ).
cnf(c_0_2218,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_1725,
[final] ).
cnf(c_0_2219,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_1726,
[final] ).
cnf(c_0_2220,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_1727,
[final] ).
cnf(c_0_2221,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_1728,
[final] ).
cnf(c_0_2222,plain,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
c_0_1729,
[final] ).
cnf(c_0_2223,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__add(X3) ),
c_0_1730,
[final] ).
cnf(c_0_2224,plain,
c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1) = c_List_Olist_ONil(X1),
c_0_1731,
[final] ).
cnf(c_0_2225,plain,
c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
c_0_1732,
[final] ).
cnf(c_0_2226,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1733,
[final] ).
cnf(c_0_2227,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1734,
[final] ).
cnf(c_0_2228,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1735,
[final] ).
cnf(c_0_2229,plain,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1736,
[final] ).
cnf(c_0_2230,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_1737,
[final] ).
cnf(c_0_2231,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
c_0_1738,
[final] ).
cnf(c_0_2232,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
c_0_1739,
[final] ).
cnf(c_0_2233,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
c_0_1740,
[final] ).
cnf(c_0_2234,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_1741,
[final] ).
cnf(c_0_2235,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_1742,
[final] ).
cnf(c_0_2236,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_1743,
[final] ).
cnf(c_0_2237,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_1744,
[final] ).
cnf(c_0_2238,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_1745,
[final] ).
cnf(c_0_2239,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_1746,
[final] ).
cnf(c_0_2240,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_1747,
[final] ).
cnf(c_0_2241,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_1748,
[final] ).
cnf(c_0_2242,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_1749,
[final] ).
cnf(c_0_2243,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_1750,
[final] ).
cnf(c_0_2244,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_1751,
[final] ).
cnf(c_0_2245,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_1752,
[final] ).
cnf(c_0_2246,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
c_0_1753,
[final] ).
cnf(c_0_2247,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
c_0_1754,
[final] ).
cnf(c_0_2248,plain,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1755,
[final] ).
cnf(c_0_2249,plain,
c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_OCons(X2,X3,X1),X1) = c_List_Olist_OCons(X2,X3,X1),
c_0_1756,
[final] ).
cnf(c_0_2250,plain,
c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_OCons(X1,X2,X3),
c_0_1757,
[final] ).
cnf(c_0_2251,plain,
c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(c_Suc(X1),X2,X3),
c_0_1758,
[final] ).
cnf(c_0_2252,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1759,
[final] ).
cnf(c_0_2253,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) ),
c_0_1760,
[final] ).
cnf(c_0_2254,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__add(X3) ),
c_0_1761,
[final] ).
cnf(c_0_2255,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_1762,
[final] ).
cnf(c_0_2256,plain,
( hAPP(hAPP(hAPP(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_1763,
[final] ).
cnf(c_0_2257,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_1764,
[final] ).
cnf(c_0_2258,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_1765,
[final] ).
cnf(c_0_2259,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_1766,
[final] ).
cnf(c_0_2260,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
c_0_1767,
[final] ).
cnf(c_0_2261,plain,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
c_0_1768,
[final] ).
cnf(c_0_2262,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_1769,
[final] ).
cnf(c_0_2263,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_1770,
[final] ).
cnf(c_0_2264,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1771,
[final] ).
cnf(c_0_2265,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1772,
[final] ).
cnf(c_0_2266,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1773,
[final] ).
cnf(c_0_2267,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1774,
[final] ).
cnf(c_0_2268,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
c_0_1775,
[final] ).
cnf(c_0_2269,plain,
( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1776,
[final] ).
cnf(c_0_2270,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
c_0_1777,
[final] ).
cnf(c_0_2271,plain,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
c_0_1778,
[final] ).
cnf(c_0_2272,plain,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
c_0_1779,
[final] ).
cnf(c_0_2273,plain,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
c_0_1780,
[final] ).
cnf(c_0_2274,plain,
( X1 = X2
| c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
c_0_1781,
[final] ).
cnf(c_0_2275,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_1782,
[final] ).
cnf(c_0_2276,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_1783,
[final] ).
cnf(c_0_2277,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_1784,
[final] ).
cnf(c_0_2278,plain,
c_Orderings_Oord__class_Omax(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X1,X2,tc_nat)),
c_0_1785,
[final] ).
cnf(c_0_2279,plain,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1786,
[final] ).
cnf(c_0_2280,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
c_0_1787,
[final] ).
cnf(c_0_2281,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
c_0_1788,
[final] ).
cnf(c_0_2282,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1789,
[final] ).
cnf(c_0_2283,plain,
c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
c_0_1790,
[final] ).
cnf(c_0_2284,plain,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
c_0_1791,
[final] ).
cnf(c_0_2285,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_1792,
[final] ).
cnf(c_0_2286,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_1793,
[final] ).
cnf(c_0_2287,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_1794,
[final] ).
cnf(c_0_2288,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_1795,
[final] ).
cnf(c_0_2289,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_1796,
[final] ).
cnf(c_0_2290,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_1797,
[final] ).
cnf(c_0_2291,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_1798,
[final] ).
cnf(c_0_2292,plain,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1799,
[final] ).
cnf(c_0_2293,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_1800,
[final] ).
cnf(c_0_2294,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_1801,
[final] ).
cnf(c_0_2295,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_1802,
[final] ).
cnf(c_0_2296,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_1803,
[final] ).
cnf(c_0_2297,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
c_0_1804,
[final] ).
cnf(c_0_2298,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),
c_0_1805,
[final] ).
cnf(c_0_2299,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_1806,
[final] ).
cnf(c_0_2300,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_1807,
[final] ).
cnf(c_0_2301,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1808,
[final] ).
cnf(c_0_2302,plain,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1809,
[final] ).
cnf(c_0_2303,plain,
( hAPP(hAPP(X2,X1),X4) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
c_0_1810,
[final] ).
cnf(c_0_2304,plain,
( hAPP(hAPP(X2,X4),X1) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
c_0_1811,
[final] ).
cnf(c_0_2305,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
c_0_1812,
[final] ).
cnf(c_0_2306,plain,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
c_0_1813,
[final] ).
cnf(c_0_2307,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
c_0_1814,
[final] ).
cnf(c_0_2308,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_1815,
[final] ).
cnf(c_0_2309,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_1816,
[final] ).
cnf(c_0_2310,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_1817,
[final] ).
cnf(c_0_2311,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_1818,
[final] ).
cnf(c_0_2312,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_1819,
[final] ).
cnf(c_0_2313,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
c_0_1820,
[final] ).
cnf(c_0_2314,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
c_0_1821,
[final] ).
cnf(c_0_2315,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
c_0_1822,
[final] ).
cnf(c_0_2316,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
c_0_1823,
[final] ).
cnf(c_0_2317,plain,
( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1824,
[final] ).
cnf(c_0_2318,plain,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2),
c_0_1825,
[final] ).
cnf(c_0_2319,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
c_0_1826,
[final] ).
cnf(c_0_2320,plain,
( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1827,
[final] ).
cnf(c_0_2321,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_1828,
[final] ).
cnf(c_0_2322,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_1829,
[final] ).
cnf(c_0_2323,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_1830,
[final] ).
cnf(c_0_2324,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
c_0_1831,
[final] ).
cnf(c_0_2325,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
c_0_1832,
[final] ).
cnf(c_0_2326,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_1833,
[final] ).
cnf(c_0_2327,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1834,
[final] ).
cnf(c_0_2328,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1835,
[final] ).
cnf(c_0_2329,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_1836,
[final] ).
cnf(c_0_2330,plain,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
c_0_1837,
[final] ).
cnf(c_0_2331,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
c_0_1838,
[final] ).
cnf(c_0_2332,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_1839,
[final] ).
cnf(c_0_2333,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_1840,
[final] ).
cnf(c_0_2334,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_1841,
[final] ).
cnf(c_0_2335,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_1842,
[final] ).
cnf(c_0_2336,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1843,
[final] ).
cnf(c_0_2337,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_1844,
[final] ).
cnf(c_0_2338,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1845,
[final] ).
cnf(c_0_2339,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_1846,
[final] ).
cnf(c_0_2340,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
c_0_1847,
[final] ).
cnf(c_0_2341,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_1848,
[final] ).
cnf(c_0_2342,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
c_0_1849,
[final] ).
cnf(c_0_2343,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_1850,
[final] ).
cnf(c_0_2344,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_1851,
[final] ).
cnf(c_0_2345,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_1852,
[final] ).
cnf(c_0_2346,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_1853,
[final] ).
cnf(c_0_2347,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1854,
[final] ).
cnf(c_0_2348,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1855,
[final] ).
cnf(c_0_2349,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1856,
[final] ).
cnf(c_0_2350,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1857,
[final] ).
cnf(c_0_2351,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
c_0_1858,
[final] ).
cnf(c_0_2352,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
c_0_1859,
[final] ).
cnf(c_0_2353,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
c_0_1860,
[final] ).
cnf(c_0_2354,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
c_0_1861,
[final] ).
cnf(c_0_2355,plain,
c_List_Olist_OCons(X2,X3,X1) != c_List_Olist_ONil(X1),
c_0_1862,
[final] ).
cnf(c_0_2356,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_1863,
[final] ).
cnf(c_0_2357,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
c_0_1864,
[final] ).
cnf(c_0_2358,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
c_0_1865,
[final] ).
cnf(c_0_2359,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_1866,
[final] ).
cnf(c_0_2360,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_1867,
[final] ).
cnf(c_0_2361,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1868,
[final] ).
cnf(c_0_2362,plain,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
c_0_1869,
[final] ).
cnf(c_0_2363,plain,
c_List_Olist_OCons(X2,X1,X3) != X1,
c_0_1870,
[final] ).
cnf(c_0_2364,plain,
c_List_Olist_OCons(X1,X2,X3) != X2,
c_0_1871,
[final] ).
cnf(c_0_2365,plain,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
c_0_1872,
[final] ).
cnf(c_0_2366,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
c_0_1873,
[final] ).
cnf(c_0_2367,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_1874,
[final] ).
cnf(c_0_2368,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
c_0_1875,
[final] ).
cnf(c_0_2369,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
c_0_1876,
[final] ).
cnf(c_0_2370,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1877,
[final] ).
cnf(c_0_2371,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_1878,
[final] ).
cnf(c_0_2372,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_1879,
[final] ).
cnf(c_0_2373,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_1880,
[final] ).
cnf(c_0_2374,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_1881,
[final] ).
cnf(c_0_2375,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_1882,
[final] ).
cnf(c_0_2376,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_1883,
[final] ).
cnf(c_0_2377,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
c_0_1884,
[final] ).
cnf(c_0_2378,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_1885,
[final] ).
cnf(c_0_2379,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_1886,
[final] ).
cnf(c_0_2380,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1887,
[final] ).
cnf(c_0_2381,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_1888,
[final] ).
cnf(c_0_2382,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_1889,
[final] ).
cnf(c_0_2383,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_1890,
[final] ).
cnf(c_0_2384,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_1891,
[final] ).
cnf(c_0_2385,plain,
c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
c_0_1892,
[final] ).
cnf(c_0_2386,plain,
c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
c_0_1893,
[final] ).
cnf(c_0_2387,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_1894,
[final] ).
cnf(c_0_2388,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_1895,
[final] ).
cnf(c_0_2389,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1896,
[final] ).
cnf(c_0_2390,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_1897,
[final] ).
cnf(c_0_2391,plain,
c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
c_0_1898,
[final] ).
cnf(c_0_2392,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
c_0_1899,
[final] ).
cnf(c_0_2393,plain,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
c_0_1900,
[final] ).
cnf(c_0_2394,plain,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
c_0_1901,
[final] ).
cnf(c_0_2395,plain,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
c_0_1902,
[final] ).
cnf(c_0_2396,plain,
( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
c_0_1903,
[final] ).
cnf(c_0_2397,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_1904,
[final] ).
cnf(c_0_2398,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
c_0_1905,
[final] ).
cnf(c_0_2399,plain,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
c_0_1906,
[final] ).
cnf(c_0_2400,plain,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X2,X1) = c_List_Olist_ONil(X1),
c_0_1907,
[final] ).
cnf(c_0_2401,plain,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
c_0_1908,
[final] ).
cnf(c_0_2402,plain,
c_List_Oappend(c_List_Olist_ONil(X1),X2,X1) = X2,
c_0_1909,
[final] ).
cnf(c_0_2403,plain,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
c_0_1910,
[final] ).
cnf(c_0_2404,plain,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
c_0_1911,
[final] ).
cnf(c_0_2405,plain,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
c_0_1912,
[final] ).
cnf(c_0_2406,plain,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
c_0_1913,
[final] ).
cnf(c_0_2407,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_1914,
[final] ).
cnf(c_0_2408,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_1915,
[final] ).
cnf(c_0_2409,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
c_0_1916,
[final] ).
cnf(c_0_2410,plain,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
c_0_1917,
[final] ).
cnf(c_0_2411,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_1918,
[final] ).
cnf(c_0_2412,plain,
c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
c_0_1919,
[final] ).
cnf(c_0_2413,plain,
c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
c_0_1920,
[final] ).
cnf(c_0_2414,plain,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
c_0_1921,
[final] ).
cnf(c_0_2415,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_1922,
[final] ).
cnf(c_0_2416,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
c_0_1923,
[final] ).
cnf(c_0_2417,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
c_0_1924,
[final] ).
cnf(c_0_2418,plain,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
c_0_1925,
[final] ).
cnf(c_0_2419,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
c_0_1926,
[final] ).
cnf(c_0_2420,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
c_0_1927,
[final] ).
cnf(c_0_2421,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
c_0_1928,
[final] ).
cnf(c_0_2422,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_1929,
[final] ).
cnf(c_0_2423,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1930,
[final] ).
cnf(c_0_2424,plain,
( c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1931,
[final] ).
cnf(c_0_2425,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_1932,
[final] ).
cnf(c_0_2426,plain,
( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
c_0_1933,
[final] ).
cnf(c_0_2427,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
c_0_1934,
[final] ).
cnf(c_0_2428,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
c_0_1935,
[final] ).
cnf(c_0_2429,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
c_0_1936,
[final] ).
cnf(c_0_2430,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
c_0_1937,
[final] ).
cnf(c_0_2431,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
c_0_1938,
[final] ).
cnf(c_0_2432,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_1939,
[final] ).
cnf(c_0_2433,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_1940,
[final] ).
cnf(c_0_2434,plain,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
c_0_1941,
[final] ).
cnf(c_0_2435,plain,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
c_0_1942,
[final] ).
cnf(c_0_2436,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1943,
[final] ).
cnf(c_0_2437,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1944,
[final] ).
cnf(c_0_2438,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1945,
[final] ).
cnf(c_0_2439,plain,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
c_0_1946,
[final] ).
cnf(c_0_2440,plain,
c_Suc(X1) != X1,
c_0_1947,
[final] ).
cnf(c_0_2441,plain,
c_Suc(X1) != X1,
c_0_1948,
[final] ).
cnf(c_0_2442,plain,
class_Orderings_Oorder(tc_bool),
c_0_1949,
[final] ).
cnf(c_0_2443,plain,
class_Orderings_Opreorder(tc_bool),
c_0_1950,
[final] ).
cnf(c_0_2444,plain,
class_Power_Opower(tc_nat),
c_0_1951,
[final] ).
cnf(c_0_2445,plain,
class_Orderings_Oorder(tc_nat),
c_0_1952,
[final] ).
cnf(c_0_2446,plain,
class_Orderings_Olinorder(tc_nat),
c_0_1953,
[final] ).
cnf(c_0_2447,plain,
class_Orderings_Opreorder(tc_nat),
c_0_1954,
[final] ).
cnf(c_0_2448,plain,
class_Nat_Osemiring__char__0(tc_nat),
c_0_1955,
[final] ).
cnf(c_0_2449,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
c_0_1956,
[final] ).
cnf(c_0_2450,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
c_0_1957,
[final] ).
cnf(c_0_2451,plain,
class_Ring__and__Field_Osemiring__0(tc_nat),
c_0_1958,
[final] ).
cnf(c_0_2452,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
c_0_1959,
[final] ).
cnf(c_0_2453,plain,
class_OrderedGroup_Osemigroup__add(tc_nat),
c_0_1960,
[final] ).
cnf(c_0_2454,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
c_0_1961,
[final] ).
cnf(c_0_2455,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
c_0_1962,
[final] ).
cnf(c_0_2456,plain,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
c_0_1963,
[final] ).
cnf(c_0_2457,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
c_0_1964,
[final] ).
cnf(c_0_2458,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
c_0_1965,
[final] ).
cnf(c_0_2459,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
c_0_1966,
[final] ).
cnf(c_0_2460,plain,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
c_0_1967,
[final] ).
cnf(c_0_2461,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
c_0_1968,
[final] ).
cnf(c_0_2462,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
c_0_1969,
[final] ).
cnf(c_0_2463,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
c_0_1970,
[final] ).
cnf(c_0_2464,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
c_0_1971,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1972_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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,hAPP(hAPP(hAPP(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_1972]) ).
cnf(c_0_1972_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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_1972]) ).
cnf(c_0_1972_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,hAPP(hAPP(hAPP(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,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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_1972]) ).
cnf(c_0_1972_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,hAPP(hAPP(hAPP(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,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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_1972]) ).
cnf(c_0_1974_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_1974]) ).
cnf(c_0_1974_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_1974]) ).
cnf(c_0_1974_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_1974]) ).
cnf(c_0_1974_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_1974]) ).
cnf(c_0_1975_0,axiom,
( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
| ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_2,axiom,
( ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6)
| ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1976_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_1976]) ).
cnf(c_0_1976_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_1976]) ).
cnf(c_0_1976_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_1976]) ).
cnf(c_0_1976_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_1976]) ).
cnf(c_0_1978_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_1978]) ).
cnf(c_0_1978_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_1978]) ).
cnf(c_0_1979_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_1979]) ).
cnf(c_0_1979_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_1979]) ).
cnf(c_0_1980_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_1980]) ).
cnf(c_0_1980_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_1980]) ).
cnf(c_0_1981_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,hAPP(hAPP(hAPP(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_1981]) ).
cnf(c_0_1981_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| 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_1981]) ).
cnf(c_0_1981_2,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| 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_1981]) ).
cnf(c_0_1983_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1984_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1985_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10)))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10))) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1986_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10)) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1987_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1988_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1989_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9)) = hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9)) = hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1990_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1991_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1992_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1993_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1994_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1995_0,axiom,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1996_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1997_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1998_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1999_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_2000_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2001_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2002_0,axiom,
( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),X7) = hAPP(hAPP(X3,X7),c_Suc(X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),X7) = hAPP(hAPP(X3,X7),c_Suc(X8)) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2003_0,axiom,
( hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2004_0,axiom,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2004_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2005_0,axiom,
( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2005_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9)) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2006_0,axiom,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8)) = hAPP(hAPP(X3,X7),c_Suc(X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2006_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8)) = hAPP(hAPP(X3,X7),c_Suc(X8)) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2007_0,axiom,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8)) = hAPP(hAPP(X3,X7),c_Suc(X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8)) = hAPP(hAPP(X3,X7),c_Suc(X8)) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2008_0,axiom,
( hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8)) = hAPP(hAPP(X3,X7),c_Suc(X8))
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),hAPP(hAPP(X3,X7),X8)) = hAPP(hAPP(X3,X7),c_Suc(X8)) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2009_0,axiom,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2010_0,axiom,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2011_0,axiom,
( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2012_0,axiom,
( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2013_0,axiom,
( hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2014_0,axiom,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X4),X7) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2015_0,axiom,
( hAPP(hAPP(X1,X7),X4) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X7),X4) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2016_0,axiom,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X4),X7) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2017_0,axiom,
( hAPP(hAPP(X2,X7),X4) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),X4) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2018_0,axiom,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X5),X7) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2019_0,axiom,
( hAPP(hAPP(X2,X7),X5) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X7),X5) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2020_0,axiom,
( hAPP(hAPP(X1,X4),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X1,X4),X7) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2021_0,axiom,
( hAPP(hAPP(X2,X4),X7) = X4
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X4),X7) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2022_0,axiom,
( hAPP(hAPP(X2,X5),X7) = X7
| ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_1,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X2,X5),X7) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2024_0,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2024_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a)))
| hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2025_0,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2025_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a)))
| hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2026_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_2026]) ).
cnf(c_0_2027_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2028_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2029_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2030_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2031_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,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_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,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_2,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(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| 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_2031]) ).
cnf(c_0_2032_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_2032]) ).
cnf(c_0_2032_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_2032]) ).
cnf(c_0_2033_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_2033]) ).
cnf(c_0_2033_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_2033]) ).
cnf(c_0_2034_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_2034]) ).
cnf(c_0_2034_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_2034]) ).
cnf(c_0_2035_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_2035]) ).
cnf(c_0_2035_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_2035]) ).
cnf(c_0_2035_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_2035]) ).
cnf(c_0_2036_0,axiom,
( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_1,axiom,
( ~ c_Type_Otypings(X1,X2,X3)
| c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2038_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_1,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2039_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_2039]) ).
cnf(c_0_2039_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_2039]) ).
cnf(c_0_2042_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_2042]) ).
cnf(c_0_2042_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_2042]) ).
cnf(c_0_2043_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_2043]) ).
cnf(c_0_2043_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_2043]) ).
cnf(c_0_2044_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_2044]) ).
cnf(c_0_2044_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_2044]) ).
cnf(c_0_2045_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_2045]) ).
cnf(c_0_2045_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_2045]) ).
cnf(c_0_2046_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_2046]) ).
cnf(c_0_2046_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_2046]) ).
cnf(c_0_2047_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_2047]) ).
cnf(c_0_2047_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_2047]) ).
cnf(c_0_2048_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_2048]) ).
cnf(c_0_2048_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_2048]) ).
cnf(c_0_2049_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_2049]) ).
cnf(c_0_2049_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_2049]) ).
cnf(c_0_2051_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_2051]) ).
cnf(c_0_2051_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_2051]) ).
cnf(c_0_2053_0,axiom,
( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_1,axiom,
( ~ c_OrderedGroup_Osemigroup__add(X1,X2)
| c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2054_0,axiom,
( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_1,axiom,
( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
| hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2055_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_2055]) ).
cnf(c_0_2055_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_2055]) ).
cnf(c_0_2056_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_2056]) ).
cnf(c_0_2056_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_2056]) ).
cnf(c_0_2058_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_2,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2064_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_2064]) ).
cnf(c_0_2064_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_2064]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2065_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_2065]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2066_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_2066]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2067_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_2067]) ).
cnf(c_0_2069_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_2069]) ).
cnf(c_0_2069_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_2069]) ).
cnf(c_0_2070_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_2070]) ).
cnf(c_0_2070_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_2070]) ).
cnf(c_0_2071_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_2071]) ).
cnf(c_0_2071_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_2071]) ).
cnf(c_0_2072_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_2072]) ).
cnf(c_0_2072_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_2072]) ).
cnf(c_0_2073_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_2073]) ).
cnf(c_0_2073_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_2073]) ).
cnf(c_0_2074_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_2074]) ).
cnf(c_0_2074_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_2074]) ).
cnf(c_0_2075_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_2075]) ).
cnf(c_0_2075_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_2075]) ).
cnf(c_0_2076_0,axiom,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_1,axiom,
( hBOOL(hAPP(hAPP(X1,X3),X6))
| c_ListOrder_Ostep1(X1,X2,X5,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2077_0,axiom,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_1,axiom,
( X2 = X5
| c_ListOrder_Ostep1(X1,X2,X5,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| X2 = X5
| c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2078_0,axiom,
( X3 = X6
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_1,axiom,
( hBOOL(hAPP(hAPP(X1,X3),X6))
| X3 = X6
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| X3 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2080_0,axiom,
( X3 = X6
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_1,axiom,
( X2 = X5
| X3 = X6
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| X2 = X5
| X3 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2081_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_2081]) ).
cnf(c_0_2081_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_2081]) ).
cnf(c_0_2081_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,hAPP(hAPP(hAPP(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_2081]) ).
cnf(c_0_2081_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,hAPP(hAPP(hAPP(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_2081]) ).
cnf(c_0_2081_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,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_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,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2082_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_2082]) ).
cnf(c_0_2082_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_2082]) ).
cnf(c_0_2082_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,hAPP(hAPP(hAPP(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_2082]) ).
cnf(c_0_2082_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,hAPP(hAPP(hAPP(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_2082]) ).
cnf(c_0_2082_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,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3)))
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_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,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X6),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2083_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(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_2083]) ).
cnf(c_0_2083_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(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2084_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(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_2084]) ).
cnf(c_0_2084_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(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2086_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_2086]) ).
cnf(c_0_2086_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_2086]) ).
cnf(c_0_2087_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_2087]) ).
cnf(c_0_2087_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X2,v_T____,tc_Type_Otype),v_a____,X3)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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_2087]) ).
cnf(c_0_2087_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,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X4),X2)))
| ~ c_Type_Otyping(X1,X4,v_T____) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_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,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2090_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2090_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2091_0,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2) = c_List_Olistsum(X1,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2) = c_List_Olistsum(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2092_0,axiom,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2) = c_List_Olistsum(X1,X2)
| ~ class_OrderedGroup_Omonoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2092_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2) = c_List_Olistsum(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2096_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2096_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2103_0,axiom,
( c_Type_Otyping(X1,hAPP(hAPP(hAPP(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_2103]) ).
cnf(c_0_2103_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2103_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,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2104_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_2104]) ).
cnf(c_0_2104_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_2104]) ).
cnf(c_0_2104_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_2104]) ).
cnf(c_0_2105_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_1,axiom,
( c_ListOrder_Ostep1(X1,X3,X6,X4)
| hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2106_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_2106]) ).
cnf(c_0_2106_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_2106]) ).
cnf(c_0_2107_0,axiom,
( X6 = X3
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_1,axiom,
( c_ListOrder_Ostep1(X1,X3,X6,X4)
| X6 = X3
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| X6 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2108_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_2108]) ).
cnf(c_0_2108_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_2108]) ).
cnf(c_0_2113_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_2113]) ).
cnf(c_0_2113_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_2113]) ).
cnf(c_0_2114_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_2114]) ).
cnf(c_0_2114_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_2114]) ).
cnf(c_0_2115_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2115_1,axiom,
( ~ c_ListOrder_Ostep1(X1,X2,X3,X4)
| c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2116_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2116_1,axiom,
( ~ c_ListOrder_Ostep1(X1,X2,X3,X4)
| c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2117_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2117_1,axiom,
( ~ c_ListOrder_Ostep1(X1,X2,X5,X4)
| c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2118_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(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_2118]) ).
cnf(c_0_2118_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_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2119_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_2119]) ).
cnf(c_0_2119_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_2119]) ).
cnf(c_0_2120_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_2120]) ).
cnf(c_0_2120_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_2120]) ).
cnf(c_0_2122_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_1,axiom,
( X5 = X2
| hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2122_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| X5 = X2
| hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2122]) ).
cnf(c_0_2123_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_2123]) ).
cnf(c_0_2123_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_2123]) ).
cnf(c_0_2123_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_2123]) ).
cnf(c_0_2124_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_2124]) ).
cnf(c_0_2124_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_2124]) ).
cnf(c_0_2125_0,axiom,
( X6 = X3
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_1,axiom,
( X5 = X2
| X6 = X3
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2125_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| X5 = X2
| X6 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2125]) ).
cnf(c_0_2126_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_2126]) ).
cnf(c_0_2126_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_2126]) ).
cnf(c_0_2127_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_2127]) ).
cnf(c_0_2127_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_2127]) ).
cnf(c_0_2128_0,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2128_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2128]) ).
cnf(c_0_2130_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_2130]) ).
cnf(c_0_2130_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_2130]) ).
cnf(c_0_2131_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_2131]) ).
cnf(c_0_2131_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_2131]) ).
cnf(c_0_2132_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_2132]) ).
cnf(c_0_2132_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_2132]) ).
cnf(c_0_2133_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_2133]) ).
cnf(c_0_2133_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_2133]) ).
cnf(c_0_2134_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2134_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2134]) ).
cnf(c_0_2135_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_2135]) ).
cnf(c_0_2135_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_2135]) ).
cnf(c_0_2135_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_2135]) ).
cnf(c_0_2136_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_2136]) ).
cnf(c_0_2136_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_2136]) ).
cnf(c_0_2136_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_2136]) ).
cnf(c_0_2137_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_2137]) ).
cnf(c_0_2137_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_2137]) ).
cnf(c_0_2138_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2138_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2138]) ).
cnf(c_0_2139_0,axiom,
( X1 = X2
| c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2139_1,axiom,
( c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2139]) ).
cnf(c_0_2140_0,axiom,
( X1 = X2
| c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2140_1,axiom,
( c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2140]) ).
cnf(c_0_2142_0,axiom,
( c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2142_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2142]) ).
cnf(c_0_2143_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_2143]) ).
cnf(c_0_2143_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_2143]) ).
cnf(c_0_2147_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_2147]) ).
cnf(c_0_2147_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_2147]) ).
cnf(c_0_2147_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_2147]) ).
cnf(c_0_2148_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_2148]) ).
cnf(c_0_2148_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_2148]) ).
cnf(c_0_2148_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_2148]) ).
cnf(c_0_2149_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2149_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2149]) ).
cnf(c_0_2150_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_2150]) ).
cnf(c_0_2150_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_2150]) ).
cnf(c_0_2151_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_2151]) ).
cnf(c_0_2151_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_2151]) ).
cnf(c_0_2153_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_2153]) ).
cnf(c_0_2153_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_2153]) ).
cnf(c_0_2153_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_2153]) ).
cnf(c_0_2153_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_2153]) ).
cnf(c_0_2155_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_2155]) ).
cnf(c_0_2155_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_2155]) ).
cnf(c_0_2155_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_2155]) ).
cnf(c_0_2156_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_2156]) ).
cnf(c_0_2156_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_2156]) ).
cnf(c_0_2156_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_2156]) ).
cnf(c_0_2158_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_2158]) ).
cnf(c_0_2158_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_2158]) ).
cnf(c_0_2159_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_2159]) ).
cnf(c_0_2159_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_2159]) ).
cnf(c_0_2160_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_2160]) ).
cnf(c_0_2160_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_2160]) ).
cnf(c_0_2161_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_2161]) ).
cnf(c_0_2161_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_2161]) ).
cnf(c_0_2162_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_2162]) ).
cnf(c_0_2162_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_2162]) ).
cnf(c_0_2163_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_2163]) ).
cnf(c_0_2163_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_2163]) ).
cnf(c_0_2165_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_2165]) ).
cnf(c_0_2165_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_2165]) ).
cnf(c_0_2165_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_2165]) ).
cnf(c_0_2166_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_2166]) ).
cnf(c_0_2166_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_2166]) ).
cnf(c_0_2166_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_2166]) ).
cnf(c_0_2167_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2167_1,axiom,
( c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2167]) ).
cnf(c_0_2168_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2168_1,axiom,
( c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2168]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2171_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_2171]) ).
cnf(c_0_2172_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_2172]) ).
cnf(c_0_2172_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_2172]) ).
cnf(c_0_2172_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_2172]) ).
cnf(c_0_2174_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X4)
| c_HOL_Oord__class_Oless(X1,X3,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_1,axiom,
( c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X1,X2,X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_2,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2174_3,axiom,
( ~ class_Orderings_Olinorder(X4)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
| c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2174]) ).
cnf(c_0_2177_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_2177]) ).
cnf(c_0_2177_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_2177]) ).
cnf(c_0_2177_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_2177]) ).
cnf(c_0_2177_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_2177]) ).
cnf(c_0_2178_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_2178]) ).
cnf(c_0_2178_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_2178]) ).
cnf(c_0_2178_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_2178]) ).
cnf(c_0_2178_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_2178]) ).
cnf(c_0_2179_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_2179]) ).
cnf(c_0_2179_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_2179]) ).
cnf(c_0_2179_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_2179]) ).
cnf(c_0_2180_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_2180]) ).
cnf(c_0_2180_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_2180]) ).
cnf(c_0_2180_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_2180]) ).
cnf(c_0_2181_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_2181]) ).
cnf(c_0_2181_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_2181]) ).
cnf(c_0_2181_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_2181]) ).
cnf(c_0_2182_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_2182]) ).
cnf(c_0_2182_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_2182]) ).
cnf(c_0_2182_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_2182]) ).
cnf(c_0_2183_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_2183]) ).
cnf(c_0_2183_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_2183]) ).
cnf(c_0_2183_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_2183]) ).
cnf(c_0_2183_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_2183]) ).
cnf(c_0_2184_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_2184]) ).
cnf(c_0_2184_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_2184]) ).
cnf(c_0_2184_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_2184]) ).
cnf(c_0_2185_0,axiom,
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2185_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2185]) ).
cnf(c_0_2186_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2186_1,axiom,
( ~ c_OrderedGroup_Osemigroup__add(X1,X2)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2186]) ).
cnf(c_0_2187_0,axiom,
( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X2,X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_1,axiom,
( ~ c_List_Olistsp(X1,X2,X3)
| c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2187_2,axiom,
( ~ c_List_Olistsp(X1,X4,X3)
| ~ c_List_Olistsp(X1,X2,X3)
| c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2187]) ).
cnf(c_0_2188_0,axiom,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2188_1,axiom,
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2188]) ).
cnf(c_0_2189_0,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2189_1,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2189]) ).
cnf(c_0_2190_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_2190]) ).
cnf(c_0_2190_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_2190]) ).
cnf(c_0_2190_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_2190]) ).
cnf(c_0_2191_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_2191]) ).
cnf(c_0_2191_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_2191]) ).
cnf(c_0_2191_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_2191]) ).
cnf(c_0_2192_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_2192]) ).
cnf(c_0_2192_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_2192]) ).
cnf(c_0_2192_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_2192]) ).
cnf(c_0_2201_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_2201]) ).
cnf(c_0_2201_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_2201]) ).
cnf(c_0_2202_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_2202]) ).
cnf(c_0_2202_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_2202]) ).
cnf(c_0_2203_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2203_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2203]) ).
cnf(c_0_2204_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2204_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2204]) ).
cnf(c_0_2205_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_2205]) ).
cnf(c_0_2205_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_2205]) ).
cnf(c_0_2206_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_2206]) ).
cnf(c_0_2206_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_2206]) ).
cnf(c_0_2207_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_2207]) ).
cnf(c_0_2207_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_2207]) ).
cnf(c_0_2208_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_2208]) ).
cnf(c_0_2208_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_2208]) ).
cnf(c_0_2210_0,axiom,
( c_List_Olistsp(X1,X3,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2210_1,axiom,
( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)
| c_List_Olistsp(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2210]) ).
cnf(c_0_2211_0,axiom,
( c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2211_1,axiom,
( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)
| c_List_Olistsp(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2211]) ).
cnf(c_0_2212_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_2212]) ).
cnf(c_0_2212_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_2212]) ).
cnf(c_0_2212_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_2212]) ).
cnf(c_0_2213_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_2213]) ).
cnf(c_0_2213_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_2213]) ).
cnf(c_0_2215_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_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),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2215_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(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),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2215]) ).
cnf(c_0_2216_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_2216]) ).
cnf(c_0_2216_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_2216]) ).
cnf(c_0_2216_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_2216]) ).
cnf(c_0_2217_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_2217]) ).
cnf(c_0_2217_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_2217]) ).
cnf(c_0_2217_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_2217]) ).
cnf(c_0_2218_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_2218]) ).
cnf(c_0_2218_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_2218]) ).
cnf(c_0_2218_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_2218]) ).
cnf(c_0_2219_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_2219]) ).
cnf(c_0_2219_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_2219]) ).
cnf(c_0_2219_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_2219]) ).
cnf(c_0_2220_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_2220]) ).
cnf(c_0_2220_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_2220]) ).
cnf(c_0_2220_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_2220]) ).
cnf(c_0_2221_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_2221]) ).
cnf(c_0_2221_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_2221]) ).
cnf(c_0_2222_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_2222]) ).
cnf(c_0_2222_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_2222]) ).
cnf(c_0_2222_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_2222]) ).
cnf(c_0_2223_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2223_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2223]) ).
cnf(c_0_2226_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2226_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2226]) ).
cnf(c_0_2227_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2227_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2227]) ).
cnf(c_0_2228_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2228_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2228]) ).
cnf(c_0_2229_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2229_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2229]) ).
cnf(c_0_2230_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_2230]) ).
cnf(c_0_2230_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_2230]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2234_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_2234]) ).
cnf(c_0_2235_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_2235]) ).
cnf(c_0_2235_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_2235]) ).
cnf(c_0_2236_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_2236]) ).
cnf(c_0_2236_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_2236]) ).
cnf(c_0_2237_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_2237]) ).
cnf(c_0_2237_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_2237]) ).
cnf(c_0_2237_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_2237]) ).
cnf(c_0_2237_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_2237]) ).
cnf(c_0_2238_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_2238]) ).
cnf(c_0_2238_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_2238]) ).
cnf(c_0_2238_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_2238]) ).
cnf(c_0_2238_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_2238]) ).
cnf(c_0_2239_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_2239]) ).
cnf(c_0_2239_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_2239]) ).
cnf(c_0_2240_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_2240]) ).
cnf(c_0_2240_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_2240]) ).
cnf(c_0_2240_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_2240]) ).
cnf(c_0_2241_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_2241]) ).
cnf(c_0_2241_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_2241]) ).
cnf(c_0_2241_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_2241]) ).
cnf(c_0_2242_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_2242]) ).
cnf(c_0_2242_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_2242]) ).
cnf(c_0_2243_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_2243]) ).
cnf(c_0_2243_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_2243]) ).
cnf(c_0_2244_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_2244]) ).
cnf(c_0_2244_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_2244]) ).
cnf(c_0_2245_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_2245]) ).
cnf(c_0_2245_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_2245]) ).
cnf(c_0_2248_0,axiom,
( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2248_1,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2248]) ).
cnf(c_0_2252_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2252_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2252]) ).
cnf(c_0_2253_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2253_1,axiom,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3))
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2253]) ).
cnf(c_0_2254_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3)
| ~ class_OrderedGroup_Omonoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2254_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2254]) ).
cnf(c_0_2255_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_2255]) ).
cnf(c_0_2255_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_2255]) ).
cnf(c_0_2255_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_2255]) ).
cnf(c_0_2256_0,axiom,
( hAPP(hAPP(hAPP(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_2256]) ).
cnf(c_0_2256_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2256]) ).
cnf(c_0_2257_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_2257]) ).
cnf(c_0_2257_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_2257]) ).
cnf(c_0_2257_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_2257]) ).
cnf(c_0_2258_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_2258]) ).
cnf(c_0_2258_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_2258]) ).
cnf(c_0_2259_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_2259]) ).
cnf(c_0_2259_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_2259]) ).
cnf(c_0_2259_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_2259]) ).
cnf(c_0_2259_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_2259]) ).
cnf(c_0_2262_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_2262]) ).
cnf(c_0_2262_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_2262]) ).
cnf(c_0_2262_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_2262]) ).
cnf(c_0_2263_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_2263]) ).
cnf(c_0_2263_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_2263]) ).
cnf(c_0_2263_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_2263]) ).
cnf(c_0_2263_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_2263]) ).
cnf(c_0_2264_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_2264]) ).
cnf(c_0_2264_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_2264]) ).
cnf(c_0_2264_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_2264]) ).
cnf(c_0_2265_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_2265]) ).
cnf(c_0_2265_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_2265]) ).
cnf(c_0_2265_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_2265]) ).
cnf(c_0_2266_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_2266]) ).
cnf(c_0_2266_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_2266]) ).
cnf(c_0_2266_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_2266]) ).
cnf(c_0_2267_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_2267]) ).
cnf(c_0_2267_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_2267]) ).
cnf(c_0_2267_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_2267]) ).
cnf(c_0_2268_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_1,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2268_2,axiom,
( c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2268]) ).
cnf(c_0_2269_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_2269]) ).
cnf(c_0_2269_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_2269]) ).
cnf(c_0_2270_0,axiom,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2270_1,axiom,
( c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2270]) ).
cnf(c_0_2271_0,axiom,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2271_1,axiom,
( c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2271]) ).
cnf(c_0_2272_0,axiom,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2272_1,axiom,
( c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2272]) ).
cnf(c_0_2273_0,axiom,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2273_1,axiom,
( c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2273]) ).
cnf(c_0_2274_0,axiom,
( X1 = X2
| c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2274_1,axiom,
( c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2274]) ).
cnf(c_0_2275_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_2275]) ).
cnf(c_0_2275_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_2275]) ).
cnf(c_0_2275_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_2275]) ).
cnf(c_0_2276_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_2276]) ).
cnf(c_0_2276_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_2276]) ).
cnf(c_0_2276_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_2276]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2277_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_2277]) ).
cnf(c_0_2279_0,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2279_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_2279]) ).
cnf(c_0_2280_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2280_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2280]) ).
cnf(c_0_2281_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2281]) ).
cnf(c_0_2281_2,axiom,
( hAPP(hAPP(hAPP(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_2281]) ).
cnf(c_0_2282_0,axiom,
( hAPP(hAPP(hAPP(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_2282]) ).
cnf(c_0_2282_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2282]) ).
cnf(c_0_2285_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_2285]) ).
cnf(c_0_2285_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_2285]) ).
cnf(c_0_2287_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_2287]) ).
cnf(c_0_2287_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_2287]) ).
cnf(c_0_2288_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_2288]) ).
cnf(c_0_2288_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_2288]) ).
cnf(c_0_2289_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_2289]) ).
cnf(c_0_2289_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_2289]) ).
cnf(c_0_2289_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_2289]) ).
cnf(c_0_2290_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_2290]) ).
cnf(c_0_2290_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_2290]) ).
cnf(c_0_2290_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_2290]) ).
cnf(c_0_2291_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_2291]) ).
cnf(c_0_2291_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_2291]) ).
cnf(c_0_2291_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_2291]) ).
cnf(c_0_2292_0,axiom,
( c_Lambda_Oliftn(X3,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_2292]) ).
cnf(c_0_2292_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2292]) ).
cnf(c_0_2293_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_2293]) ).
cnf(c_0_2293_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_2293]) ).
cnf(c_0_2293_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_2293]) ).
cnf(c_0_2294_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_2294]) ).
cnf(c_0_2294_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_2294]) ).
cnf(c_0_2295_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_2295]) ).
cnf(c_0_2295_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_2295]) ).
cnf(c_0_2296_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_2296]) ).
cnf(c_0_2296_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_2296]) ).
cnf(c_0_2297_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_2297]) ).
cnf(c_0_2297_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_2297]) ).
cnf(c_0_2300_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_2300]) ).
cnf(c_0_2300_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_2300]) ).
cnf(c_0_2301_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_2301]) ).
cnf(c_0_2301_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_2301]) ).
cnf(c_0_2302_0,axiom,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2302_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2302]) ).
cnf(c_0_2303_0,axiom,
( hAPP(hAPP(X2,X1),X4) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2303_1,axiom,
( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
| hAPP(hAPP(X2,X1),X4) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2303]) ).
cnf(c_0_2304_0,axiom,
( hAPP(hAPP(X2,X4),X1) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2304_1,axiom,
( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
| hAPP(hAPP(X2,X4),X1) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2304]) ).
cnf(c_0_2305_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_1,axiom,
( c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_4,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2305_5,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2305]) ).
cnf(c_0_2306_0,axiom,
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_1,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_2,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2306_4,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2306]) ).
cnf(c_0_2307_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2307_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2307]) ).
cnf(c_0_2307_2,axiom,
( c_Lambda_Osubstn(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_2307]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2308_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_2308]) ).
cnf(c_0_2309_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_2309]) ).
cnf(c_0_2309_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_2309]) ).
cnf(c_0_2309_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_2309]) ).
cnf(c_0_2309_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_2309]) ).
cnf(c_0_2310_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_2310]) ).
cnf(c_0_2310_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_2310]) ).
cnf(c_0_2310_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_2310]) ).
cnf(c_0_2310_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_2310]) ).
cnf(c_0_2311_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_2311]) ).
cnf(c_0_2311_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_2311]) ).
cnf(c_0_2311_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_2311]) ).
cnf(c_0_2311_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_2311]) ).
cnf(c_0_2312_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_2312]) ).
cnf(c_0_2312_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_2312]) ).
cnf(c_0_2312_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_2312]) ).
cnf(c_0_2312_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_2312]) ).
cnf(c_0_2313_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_2313]) ).
cnf(c_0_2313_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_2313]) ).
cnf(c_0_2314_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_2314]) ).
cnf(c_0_2314_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_2314]) ).
cnf(c_0_2315_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_2315]) ).
cnf(c_0_2315_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_2315]) ).
cnf(c_0_2316_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_2316]) ).
cnf(c_0_2316_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_2316]) ).
cnf(c_0_2317_0,axiom,
( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2317_1,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2317]) ).
cnf(c_0_2319_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_2319]) ).
cnf(c_0_2319_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_2319]) ).
cnf(c_0_2320_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_2320]) ).
cnf(c_0_2320_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_2320]) ).
cnf(c_0_2321_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_2321]) ).
cnf(c_0_2321_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_2321]) ).
cnf(c_0_2322_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_2322]) ).
cnf(c_0_2322_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_2322]) ).
cnf(c_0_2323_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_2323]) ).
cnf(c_0_2323_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_2323]) ).
cnf(c_0_2325_0,axiom,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2325_1,axiom,
( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_2325]) ).
cnf(c_0_2327_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_2327]) ).
cnf(c_0_2327_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_2327]) ).
cnf(c_0_2327_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_2327]) ).
cnf(c_0_2328_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_2328]) ).
cnf(c_0_2328_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_2328]) ).
cnf(c_0_2328_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_2328]) ).
cnf(c_0_2329_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_2329]) ).
cnf(c_0_2329_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_2329]) ).
cnf(c_0_2331_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_1,axiom,
( c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2331_2,axiom,
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
| c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2331]) ).
cnf(c_0_2332_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_2332]) ).
cnf(c_0_2332_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_2332]) ).
cnf(c_0_2332_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_2332]) ).
cnf(c_0_2332_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_2332]) ).
cnf(c_0_2333_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_2333]) ).
cnf(c_0_2333_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_2333]) ).
cnf(c_0_2333_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_2333]) ).
cnf(c_0_2334_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_2334]) ).
cnf(c_0_2334_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_2334]) ).
cnf(c_0_2334_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_2334]) ).
cnf(c_0_2335_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_2335]) ).
cnf(c_0_2335_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_2335]) ).
cnf(c_0_2335_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_2335]) ).
cnf(c_0_2336_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2336_1,axiom,
( c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2336]) ).
cnf(c_0_2337_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2337_1,axiom,
( c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2337]) ).
cnf(c_0_2338_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2338_1,axiom,
( c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2338]) ).
cnf(c_0_2339_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2339_1,axiom,
( c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2339]) ).
cnf(c_0_2340_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_3,axiom,
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_4,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2340_5,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2340]) ).
cnf(c_0_2341_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2341_1,axiom,
( c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2341]) ).
cnf(c_0_2342_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2342_1,axiom,
( c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2342]) ).
cnf(c_0_2343_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_2343]) ).
cnf(c_0_2343_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_2343]) ).
cnf(c_0_2343_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_2343]) ).
cnf(c_0_2344_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_2344]) ).
cnf(c_0_2344_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_2344]) ).
cnf(c_0_2344_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_2344]) ).
cnf(c_0_2345_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_2345]) ).
cnf(c_0_2345_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_2345]) ).
cnf(c_0_2345_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_2345]) ).
cnf(c_0_2346_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_2346]) ).
cnf(c_0_2346_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_2346]) ).
cnf(c_0_2346_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_2346]) ).
cnf(c_0_2348_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2348_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2348]) ).
cnf(c_0_2349_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2349_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2349]) ).
cnf(c_0_2350_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2350_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2350]) ).
cnf(c_0_2351_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2351_1,axiom,
( c_List_Oappend(X1,X3,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2351]) ).
cnf(c_0_2352_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2352_1,axiom,
( c_List_Oappend(X1,X3,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2352]) ).
cnf(c_0_2353_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2353_1,axiom,
( c_List_Oappend(X3,X1,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2353]) ).
cnf(c_0_2354_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2354_1,axiom,
( c_List_Oappend(X3,X1,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2354]) ).
cnf(c_0_2359_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_2359]) ).
cnf(c_0_2359_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_2359]) ).
cnf(c_0_2359_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_2359]) ).
cnf(c_0_2360_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_2360]) ).
cnf(c_0_2360_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_2360]) ).
cnf(c_0_2360_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_2360]) ).
cnf(c_0_2366_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_1,axiom,
( ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2366_2,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2366]) ).
cnf(c_0_2369_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(X2)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_2,axiom,
( ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2369_3,axiom,
( ~ class_Ring__and__Field_Osemiring__0(X2)
| ~ class_Power_Opower(X2)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_2369]) ).
cnf(c_0_2370_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_2370]) ).
cnf(c_0_2370_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_2370]) ).
cnf(c_0_2371_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_2371]) ).
cnf(c_0_2371_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_2371]) ).
cnf(c_0_2374_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_2374]) ).
cnf(c_0_2374_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_2374]) ).
cnf(c_0_2375_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_2375]) ).
cnf(c_0_2375_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_2375]) ).
cnf(c_0_2376_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_2376]) ).
cnf(c_0_2376_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_2376]) ).
cnf(c_0_2377_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_2377]) ).
cnf(c_0_2377_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_2377]) ).
cnf(c_0_2378_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_2378]) ).
cnf(c_0_2378_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_2378]) ).
cnf(c_0_2378_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_2378]) ).
cnf(c_0_2379_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_2379]) ).
cnf(c_0_2379_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_2379]) ).
cnf(c_0_2380_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_2380]) ).
cnf(c_0_2380_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_2380]) ).
cnf(c_0_2381_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_2381]) ).
cnf(c_0_2381_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_2381]) ).
cnf(c_0_2382_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_2382]) ).
cnf(c_0_2382_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_2382]) ).
cnf(c_0_2388_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_2388]) ).
cnf(c_0_2388_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_2388]) ).
cnf(c_0_2389_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_2389]) ).
cnf(c_0_2389_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_2389]) ).
cnf(c_0_2390_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_2390]) ).
cnf(c_0_2390_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_2390]) ).
cnf(c_0_2396_0,axiom,
( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2396_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2396]) ).
cnf(c_0_2407_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_2407]) ).
cnf(c_0_2407_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_2407]) ).
cnf(c_0_2415_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_2415]) ).
cnf(c_0_2415_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_2415]) ).
cnf(c_0_2415_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_2415]) ).
cnf(c_0_2422_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2422_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2422]) ).
cnf(c_0_2423_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2423_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2423]) ).
cnf(c_0_2424_0,axiom,
( c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2424_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2424]) ).
cnf(c_0_2425_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_2425]) ).
cnf(c_0_2425_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_2425]) ).
cnf(c_0_2426_0,axiom,
( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2426_1,axiom,
( ~ class_OrderedGroup_Osemigroup__add(X1)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2426]) ).
cnf(c_0_2430_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2430_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2430]) ).
cnf(c_0_2431_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2431_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2431]) ).
cnf(c_0_2432_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2432_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2432]) ).
cnf(c_0_2433_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2433_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2433]) ).
cnf(c_0_2050_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_2050]) ).
cnf(c_0_2068_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_2068]) ).
cnf(c_0_2169_0,axiom,
~ c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2169]) ).
cnf(c_0_2170_0,axiom,
~ c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2),
inference(literals_permutation,[status(thm)],[c_0_2170]) ).
cnf(c_0_2246_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_2246]) ).
cnf(c_0_2247_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_2247]) ).
cnf(c_0_2284_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
inference(literals_permutation,[status(thm)],[c_0_2284]) ).
cnf(c_0_2347_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_2347]) ).
cnf(c_0_2355_0,axiom,
c_List_Olist_OCons(X2,X3,X1) != c_List_Olist_ONil(X1),
inference(literals_permutation,[status(thm)],[c_0_2355]) ).
cnf(c_0_2357_0,axiom,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
inference(literals_permutation,[status(thm)],[c_0_2357]) ).
cnf(c_0_2358_0,axiom,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X3),
inference(literals_permutation,[status(thm)],[c_0_2358]) ).
cnf(c_0_2361_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2361]) ).
cnf(c_0_2362_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2362]) ).
cnf(c_0_2363_0,axiom,
c_List_Olist_OCons(X2,X1,X3) != X1,
inference(literals_permutation,[status(thm)],[c_0_2363]) ).
cnf(c_0_2364_0,axiom,
c_List_Olist_OCons(X1,X2,X3) != X2,
inference(literals_permutation,[status(thm)],[c_0_2364]) ).
cnf(c_0_2367_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2367]) ).
cnf(c_0_2368_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2368]) ).
cnf(c_0_2392_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
inference(literals_permutation,[status(thm)],[c_0_2392]) ).
cnf(c_0_2393_0,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2393]) ).
cnf(c_0_2394_0,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
inference(literals_permutation,[status(thm)],[c_0_2394]) ).
cnf(c_0_2395_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
inference(literals_permutation,[status(thm)],[c_0_2395]) ).
cnf(c_0_2434_0,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
inference(literals_permutation,[status(thm)],[c_0_2434]) ).
cnf(c_0_2435_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(literals_permutation,[status(thm)],[c_0_2435]) ).
cnf(c_0_2436_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2436]) ).
cnf(c_0_2437_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2437]) ).
cnf(c_0_2438_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2438]) ).
cnf(c_0_2439_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2439]) ).
cnf(c_0_2440_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_2440]) ).
cnf(c_0_2441_0,axiom,
c_Suc(X1) != X1,
inference(literals_permutation,[status(thm)],[c_0_2441]) ).
cnf(c_0_1973_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1977_0,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,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)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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_1977]) ).
cnf(c_0_1982_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_2023_0,axiom,
hAPP(hAPP(hAPP(hAPP(X2,X4),X5),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X6)),c_Lambda_OdB_OdB__rec(X1,X2,X3,X5,X6)) = c_Lambda_OdB_OdB__rec(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2037_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(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_2037]) ).
cnf(c_0_2040_0,axiom,
c_List_Ofoldl(X1,c_List_Ofoldl(X1,X2,X3,X6,X5),X4,X6,X5) = c_List_Ofoldl(X1,X2,c_List_Oappend(X3,X4,X5),X6,X5),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2041_0,axiom,
c_List_Ofoldr(X1,X2,c_List_Ofoldr(X1,X3,X5,X4,X6),X4,X6) = c_List_Ofoldr(X1,c_List_Oappend(X2,X3,X4),X5,X4,X6),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2052_0,axiom,
c_List_Ofoldr(X1,c_List_Olist_OCons(X2,X3,X4),X5,X4,X6) = hAPP(hAPP(X1,X2),c_List_Ofoldr(X1,X3,X5,X4,X6)),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2057_0,axiom,
hAPP(hAPP(X3,X4),c_Lambda_OdB_OdB__rec(X1,X2,X3,X4,X5)) = c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2059_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_2059]) ).
cnf(c_0_2060_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_2060]) ).
cnf(c_0_2061_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_2061]) ).
cnf(c_0_2062_0,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_OCons(X3,X4,X5),X6,X5) = c_List_Ofoldl(X1,hAPP(hAPP(X1,X2),X3),X4,X6,X5),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2063_0,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2079_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_2079]) ).
cnf(c_0_2085_0,axiom,
c_List_Oappend(c_List_Omap(X1,X2,X4,X5),c_List_Omap(X1,X3,X4,X5),X5) = c_List_Omap(X1,c_List_Oappend(X2,X3,X4),X4,X5),
inference(literals_permutation,[status(thm)],[c_0_2085]) ).
cnf(c_0_2088_0,axiom,
c_Lambda_OdB_OdB__case(X1,X2,X3,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X5),X6) = hAPP(hAPP(X2,X4),X5),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2089_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_2089]) ).
cnf(c_0_2093_0,axiom,
c_Lambda_OdB_OdB__rec(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2094_0,axiom,
c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X3,X4),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2095_0,axiom,
c_Lambda_OdB_OdB__case(X1,X2,X3,c_Lambda_OdB_OVar(X4),X5) = hAPP(X1,X4),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2097_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_2097]) ).
cnf(c_0_2098_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X1),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1,
inference(literals_permutation,[status(thm)],[c_0_2098]) ).
cnf(c_0_2099_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_2099]) ).
cnf(c_0_2100_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_2100]) ).
cnf(c_0_2101_0,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2102_0,axiom,
c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4) = X3,
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2109_0,axiom,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
inference(literals_permutation,[status(thm)],[c_0_2109]) ).
cnf(c_0_2110_0,axiom,
c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5) = c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2111_0,axiom,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2112_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2121_0,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(literals_permutation,[status(thm)],[c_0_2121]) ).
cnf(c_0_2129_0,axiom,
c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X1,X2,X3),X4,X3),X3) = c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,X4,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2129]) ).
cnf(c_0_2141_0,axiom,
c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Oreplicate(X4,X2,X3),X3) = c_List_Oappend(c_List_Oreplicate(X4,X2,X3),c_List_Oreplicate(X1,X2,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2141]) ).
cnf(c_0_2144_0,axiom,
hAPP(c_Type_Oshift(X1,X2,X3,X4),X2) = X3,
inference(literals_permutation,[status(thm)],[c_0_2144]) ).
cnf(c_0_2145_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)) = c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4),
inference(literals_permutation,[status(thm)],[c_0_2145]) ).
cnf(c_0_2146_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X4)),c_Lambda_Oliftn(X1,X3,X4)) = c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4),
inference(literals_permutation,[status(thm)],[c_0_2146]) ).
cnf(c_0_2152_0,axiom,
c_List_Oappend(c_List_Oreplicate(X1,X2,X3),c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) = c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2152]) ).
cnf(c_0_2154_0,axiom,
c_List_Omap(X1,c_List_Oreplicate(X2,X3,X4),X4,X5) = c_List_Oreplicate(X2,hAPP(X1,X3),X5),
inference(literals_permutation,[status(thm)],[c_0_2154]) ).
cnf(c_0_2157_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),
inference(literals_permutation,[status(thm)],[c_0_2157]) ).
cnf(c_0_2164_0,axiom,
c_List_Oappend(c_List_Oreplicate(X1,X3,X4),c_List_Oreplicate(X2,X3,X4),X4) = c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,X4),
inference(literals_permutation,[status(thm)],[c_0_2164]) ).
cnf(c_0_2173_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2173]) ).
cnf(c_0_2175_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3) = c_Lambda_Osubstn(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2175]) ).
cnf(c_0_2176_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_2176]) ).
cnf(c_0_2193_0,axiom,
c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4) = c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4),
inference(literals_permutation,[status(thm)],[c_0_2193]) ).
cnf(c_0_2194_0,axiom,
c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2194]) ).
cnf(c_0_2195_0,axiom,
c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4) = c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4),
inference(literals_permutation,[status(thm)],[c_0_2195]) ).
cnf(c_0_2196_0,axiom,
c_List_Oappend(c_List_Oappend(X1,X2,X3),X4,X3) = c_List_Oappend(X1,c_List_Oappend(X2,X4,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2196]) ).
cnf(c_0_2197_0,axiom,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
inference(literals_permutation,[status(thm)],[c_0_2197]) ).
cnf(c_0_2198_0,axiom,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
inference(literals_permutation,[status(thm)],[c_0_2198]) ).
cnf(c_0_2199_0,axiom,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3),
inference(literals_permutation,[status(thm)],[c_0_2199]) ).
cnf(c_0_2200_0,axiom,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X4,X3),X3) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3),
inference(literals_permutation,[status(thm)],[c_0_2200]) ).
cnf(c_0_2209_0,axiom,
hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X1,X2,X3)),X3) = c_Lambda_Oliftn(c_Suc(X1),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2209]) ).
cnf(c_0_2214_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_2214]) ).
cnf(c_0_2224_0,axiom,
c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1) = c_List_Olist_ONil(X1),
inference(literals_permutation,[status(thm)],[c_0_2224]) ).
cnf(c_0_2225_0,axiom,
c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
inference(literals_permutation,[status(thm)],[c_0_2225]) ).
cnf(c_0_2231_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_2231]) ).
cnf(c_0_2232_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_2232]) ).
cnf(c_0_2233_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_2233]) ).
cnf(c_0_2249_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_OCons(X2,X3,X1),X1) = c_List_Olist_OCons(X2,X3,X1),
inference(literals_permutation,[status(thm)],[c_0_2249]) ).
cnf(c_0_2250_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Olist_OCons(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2250]) ).
cnf(c_0_2251_0,axiom,
c_List_Olist_OCons(X2,c_List_Oreplicate(X1,X2,X3),X3) = c_List_Oreplicate(c_Suc(X1),X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2251]) ).
cnf(c_0_2260_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(literals_permutation,[status(thm)],[c_0_2260]) ).
cnf(c_0_2261_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
inference(literals_permutation,[status(thm)],[c_0_2261]) ).
cnf(c_0_2278_0,axiom,
c_Orderings_Oord__class_Omax(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X1,X2,tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_2278]) ).
cnf(c_0_2283_0,axiom,
c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X2,X3),X3,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2283]) ).
cnf(c_0_2286_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_2286]) ).
cnf(c_0_2298_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),
inference(literals_permutation,[status(thm)],[c_0_2298]) ).
cnf(c_0_2299_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_2299]) ).
cnf(c_0_2318_0,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2),
inference(literals_permutation,[status(thm)],[c_0_2318]) ).
cnf(c_0_2324_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_2324]) ).
cnf(c_0_2326_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_2326]) ).
cnf(c_0_2330_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
inference(literals_permutation,[status(thm)],[c_0_2330]) ).
cnf(c_0_2356_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_2356]) ).
cnf(c_0_2365_0,axiom,
c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2)),
inference(literals_permutation,[status(thm)],[c_0_2365]) ).
cnf(c_0_2372_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_2372]) ).
cnf(c_0_2373_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_2373]) ).
cnf(c_0_2383_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_2383]) ).
cnf(c_0_2384_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_2384]) ).
cnf(c_0_2385_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
inference(literals_permutation,[status(thm)],[c_0_2385]) ).
cnf(c_0_2386_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
inference(literals_permutation,[status(thm)],[c_0_2386]) ).
cnf(c_0_2387_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_2387]) ).
cnf(c_0_2391_0,axiom,
c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
inference(literals_permutation,[status(thm)],[c_0_2391]) ).
cnf(c_0_2397_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_2397]) ).
cnf(c_0_2398_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_2398]) ).
cnf(c_0_2399_0,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
inference(literals_permutation,[status(thm)],[c_0_2399]) ).
cnf(c_0_2400_0,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X2,X1) = c_List_Olist_ONil(X1),
inference(literals_permutation,[status(thm)],[c_0_2400]) ).
cnf(c_0_2401_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2401]) ).
cnf(c_0_2402_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X1),X2,X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_2402]) ).
cnf(c_0_2403_0,axiom,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2403]) ).
cnf(c_0_2404_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2404]) ).
cnf(c_0_2405_0,axiom,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2405]) ).
cnf(c_0_2406_0,axiom,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
inference(literals_permutation,[status(thm)],[c_0_2406]) ).
cnf(c_0_2408_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2408]) ).
cnf(c_0_2409_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2409]) ).
cnf(c_0_2410_0,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2410]) ).
cnf(c_0_2411_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_2411]) ).
cnf(c_0_2412_0,axiom,
c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_2412]) ).
cnf(c_0_2413_0,axiom,
c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(literals_permutation,[status(thm)],[c_0_2413]) ).
cnf(c_0_2414_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_2414]) ).
cnf(c_0_2416_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_2416]) ).
cnf(c_0_2417_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(literals_permutation,[status(thm)],[c_0_2417]) ).
cnf(c_0_2418_0,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
inference(literals_permutation,[status(thm)],[c_0_2418]) ).
cnf(c_0_2419_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_2419]) ).
cnf(c_0_2420_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_2420]) ).
cnf(c_0_2421_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
inference(literals_permutation,[status(thm)],[c_0_2421]) ).
cnf(c_0_2427_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
inference(literals_permutation,[status(thm)],[c_0_2427]) ).
cnf(c_0_2428_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(literals_permutation,[status(thm)],[c_0_2428]) ).
cnf(c_0_2429_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
inference(literals_permutation,[status(thm)],[c_0_2429]) ).
cnf(c_0_2442_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2443_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2444_0,axiom,
class_Power_Opower(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2445_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2446_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2447_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2448_0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2448]) ).
cnf(c_0_2449_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2449]) ).
cnf(c_0_2450_0,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2450]) ).
cnf(c_0_2451_0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2451]) ).
cnf(c_0_2452_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2452]) ).
cnf(c_0_2453_0,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2453]) ).
cnf(c_0_2454_0,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2455_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2456_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2456]) ).
cnf(c_0_2457_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2458_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2459_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2460_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2461_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2462_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2463_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2464_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_1_002,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_2_003,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
c_0_1 ).
cnf(c_0_3_004,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_005,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_970,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox/tmp/iprover_modulo_82bb7c.p',c_0_4) ).
cnf(c_1284,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(copy,[status(esa)],[c_970]) ).
cnf(c_1288,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(copy,[status(esa)],[c_1284]) ).
cnf(c_1289,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(copy,[status(esa)],[c_1288]) ).
cnf(c_1290,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(copy,[status(esa)],[c_1289]) ).
cnf(c_4122,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(copy,[status(esa)],[c_1290]) ).
cnf(c_512,plain,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X1))
| ~ c_Type_Otyping(X2,X0,X3)
| c_Type_Otyping(X2,X1,X3) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_82bb7c.p',c_0_2222_0) ).
cnf(c_3206,plain,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X1))
| ~ c_Type_Otyping(X2,X0,X3)
| c_Type_Otyping(X2,X1,X3) ),
inference(copy,[status(esa)],[c_512]) ).
cnf(c_4126,plain,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),X0,v_T_H____) ),
inference(resolution,[status(thm)],[c_4122,c_3206]) ).
cnf(c_4127,plain,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),X0,v_T_H____) ),
inference(rewriting,[status(thm)],[c_4126]) ).
cnf(c_130,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,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)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/tmp/iprover_modulo_82bb7c.p',c_0_1977_0) ).
cnf(c_2443,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,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)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(copy,[status(esa)],[c_130]) ).
cnf(c_4132,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(resolution,[status(thm)],[c_4127,c_2443]) ).
cnf(c_4133,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(rewriting,[status(thm)],[c_4132]) ).
cnf(c_121,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____),
file('/export/starexec/sandbox/tmp/iprover_modulo_82bb7c.p',c_0_2060_0) ).
cnf(c_2431,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(copy,[status(esa)],[c_121]) ).
cnf(c_4137,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4133,c_2431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL835-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : iprover_modulo %s %d
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jul 3 03:55:13 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % Running in mono-core mode
% 0.17/0.47 % Orienting using strategy Equiv(ClausalAll)
% 0.17/0.47 % Orientation found
% 0.17/0.47 % 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_6581ac.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_82bb7c.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_5c2147 | grep -v "SZS"
% 0.17/0.49
% 0.17/0.49 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.17/0.49
% 0.17/0.49 %
% 0.17/0.49 % ------ iProver source info
% 0.17/0.49
% 0.17/0.49 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.17/0.49 % git: non_committed_changes: true
% 0.17/0.49 % git: last_make_outside_of_git: true
% 0.17/0.49
% 0.17/0.49 %
% 0.17/0.49 % ------ Input Options
% 0.17/0.49
% 0.17/0.49 % --out_options all
% 0.17/0.49 % --tptp_safe_out true
% 0.17/0.49 % --problem_path ""
% 0.17/0.49 % --include_path ""
% 0.17/0.49 % --clausifier .//eprover
% 0.17/0.49 % --clausifier_options --tstp-format
% 0.17/0.49 % --stdin false
% 0.17/0.49 % --dbg_backtrace false
% 0.17/0.49 % --dbg_dump_prop_clauses false
% 0.17/0.49 % --dbg_dump_prop_clauses_file -
% 0.17/0.49 % --dbg_out_stat false
% 0.17/0.49
% 0.17/0.49 % ------ General Options
% 0.17/0.49
% 0.17/0.49 % --fof false
% 0.17/0.49 % --time_out_real 150.
% 0.17/0.49 % --time_out_prep_mult 0.2
% 0.17/0.49 % --time_out_virtual -1.
% 0.17/0.49 % --schedule none
% 0.17/0.49 % --ground_splitting input
% 0.17/0.49 % --splitting_nvd 16
% 0.17/0.49 % --non_eq_to_eq false
% 0.17/0.49 % --prep_gs_sim true
% 0.17/0.49 % --prep_unflatten false
% 0.17/0.49 % --prep_res_sim true
% 0.17/0.49 % --prep_upred true
% 0.17/0.49 % --res_sim_input true
% 0.17/0.49 % --clause_weak_htbl true
% 0.17/0.49 % --gc_record_bc_elim false
% 0.17/0.49 % --symbol_type_check false
% 0.17/0.49 % --clausify_out false
% 0.17/0.49 % --large_theory_mode false
% 0.17/0.49 % --prep_sem_filter none
% 0.17/0.49 % --prep_sem_filter_out false
% 0.17/0.49 % --preprocessed_out false
% 0.17/0.49 % --sub_typing false
% 0.17/0.49 % --brand_transform false
% 0.17/0.49 % --pure_diseq_elim true
% 0.17/0.49 % --min_unsat_core false
% 0.17/0.49 % --pred_elim true
% 0.17/0.49 % --add_important_lit false
% 0.17/0.49 % --soft_assumptions false
% 0.17/0.49 % --reset_solvers false
% 0.17/0.49 % --bc_imp_inh []
% 0.17/0.49 % --conj_cone_tolerance 1.5
% 0.17/0.49 % --prolific_symb_bound 500
% 0.17/0.49 % --lt_threshold 2000
% 0.17/0.49
% 0.17/0.49 % ------ SAT Options
% 0.17/0.49
% 0.17/0.49 % --sat_mode false
% 0.17/0.49 % --sat_fm_restart_options ""
% 0.17/0.49 % --sat_gr_def false
% 0.17/0.49 % --sat_epr_types true
% 0.17/0.49 % --sat_non_cyclic_types false
% 0.17/0.49 % --sat_finite_models false
% 0.17/0.49 % --sat_fm_lemmas false
% 0.17/0.49 % --sat_fm_prep false
% 0.17/0.49 % --sat_fm_uc_incr true
% 0.17/0.49 % --sat_out_model small
% 0.17/0.49 % --sat_out_clauses false
% 0.17/0.49
% 0.17/0.49 % ------ QBF Options
% 0.17/0.49
% 0.17/0.49 % --qbf_mode false
% 0.17/0.49 % --qbf_elim_univ true
% 0.17/0.49 % --qbf_sk_in true
% 0.17/0.49 % --qbf_pred_elim true
% 0.17/0.49 % --qbf_split 32
% 0.17/0.49
% 0.17/0.49 % ------ BMC1 Options
% 0.17/0.49
% 0.17/0.49 % --bmc1_incremental false
% 0.17/0.49 % --bmc1_axioms reachable_all
% 0.17/0.49 % --bmc1_min_bound 0
% 0.17/0.49 % --bmc1_max_bound -1
% 0.17/0.49 % --bmc1_max_bound_default -1
% 0.17/0.49 % --bmc1_symbol_reachability true
% 0.17/0.49 % --bmc1_property_lemmas false
% 0.17/0.49 % --bmc1_k_induction false
% 0.17/0.49 % --bmc1_non_equiv_states false
% 0.17/0.49 % --bmc1_deadlock false
% 0.17/0.49 % --bmc1_ucm false
% 0.17/0.49 % --bmc1_add_unsat_core none
% 0.17/0.49 % --bmc1_unsat_core_children false
% 0.17/0.49 % --bmc1_unsat_core_extrapolate_axioms false
% 0.17/0.49 % --bmc1_out_stat full
% 0.17/0.49 % --bmc1_ground_init false
% 0.17/0.49 % --bmc1_pre_inst_next_state false
% 0.17/0.49 % --bmc1_pre_inst_state false
% 0.17/0.49 % --bmc1_pre_inst_reach_state false
% 0.17/0.49 % --bmc1_out_unsat_core false
% 0.17/0.49 % --bmc1_aig_witness_out false
% 0.17/0.49 % --bmc1_verbose false
% 0.17/0.49 % --bmc1_dump_clauses_tptp false
% 150.28/150.49 % --bmc1_dump_unsat_core_tptp false
% 150.28/150.49 % --bmc1_dump_file -
% 150.28/150.49 % --bmc1_ucm_expand_uc_limit 128
% 150.28/150.49 % --bmc1_ucm_n_expand_iterations 6
% 150.28/150.49 % --bmc1_ucm_extend_mode 1
% 150.28/150.49 % --bmc1_ucm_init_mode 2
% 150.28/150.49 % --bmc1_ucm_cone_mode none
% 150.28/150.49 % --bmc1_ucm_reduced_relation_type 0
% 150.28/150.49 % --bmc1_ucm_relax_model 4
% 150.28/150.49 % --bmc1_ucm_full_tr_after_sat true
% 150.28/150.49 % --bmc1_ucm_expand_neg_assumptions false
% 150.28/150.49 % --bmc1_ucm_layered_model none
% 150.28/150.49 % --bmc1_ucm_max_lemma_size 10
% 150.28/150.49
% 150.28/150.49 % ------ AIG Options
% 150.28/150.49
% 150.28/150.49 % --aig_mode false
% 150.28/150.49
% 150.28/150.49 % ------ Instantiation Options
% 150.28/150.49
% 150.28/150.49 % --instantiation_flag true
% 150.28/150.49 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.28/150.49 % --inst_solver_per_active 750
% 150.28/150.49 % --inst_solver_calls_frac 0.5
% 150.28/150.49 % --inst_passive_queue_type priority_queues
% 150.28/150.49 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.28/150.49 % --inst_passive_queues_freq [25;2]
% 150.28/150.49 % --inst_dismatching true
% 150.28/150.49 % --inst_eager_unprocessed_to_passive true
% 150.28/150.49 % --inst_prop_sim_given true
% 150.28/150.49 % --inst_prop_sim_new false
% 150.28/150.49 % --inst_orphan_elimination true
% 150.28/150.49 % --inst_learning_loop_flag true
% 150.28/150.49 % --inst_learning_start 3000
% 150.28/150.49 % --inst_learning_factor 2
% 150.28/150.49 % --inst_start_prop_sim_after_learn 3
% 150.28/150.49 % --inst_sel_renew solver
% 150.28/150.49 % --inst_lit_activity_flag true
% 150.28/150.49 % --inst_out_proof true
% 150.28/150.49
% 150.28/150.49 % ------ Resolution Options
% 150.28/150.49
% 150.28/150.49 % --resolution_flag true
% 150.28/150.49 % --res_lit_sel kbo_max
% 150.28/150.49 % --res_to_prop_solver none
% 150.28/150.49 % --res_prop_simpl_new false
% 150.28/150.49 % --res_prop_simpl_given false
% 150.28/150.49 % --res_passive_queue_type priority_queues
% 150.28/150.49 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.28/150.49 % --res_passive_queues_freq [15;5]
% 150.28/150.49 % --res_forward_subs full
% 150.28/150.49 % --res_backward_subs full
% 150.28/150.49 % --res_forward_subs_resolution true
% 150.28/150.49 % --res_backward_subs_resolution true
% 150.28/150.49 % --res_orphan_elimination false
% 150.28/150.49 % --res_time_limit 1000.
% 150.28/150.49 % --res_out_proof true
% 150.28/150.49 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_6581ac.s
% 150.28/150.49 % --modulo true
% 150.28/150.49
% 150.28/150.49 % ------ Combination Options
% 150.28/150.49
% 150.28/150.49 % --comb_res_mult 1000
% 150.28/150.49 % --comb_inst_mult 300
% 150.28/150.49 % ------
% 150.28/150.49
% 150.28/150.49 % ------ Parsing...% successful
% 150.28/150.49
% 150.28/150.49 % ------ 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 %
% 150.28/150.49
% 150.28/150.49 % ------ Proving...
% 150.28/150.49 % ------ Problem Properties
% 150.28/150.49
% 150.28/150.49 %
% 150.28/150.49 % EPR false
% 150.28/150.49 % Horn false
% 150.28/150.49 % Has equality true
% 150.28/150.49
% 150.28/150.49 % % ------ Input Options Time Limit: Unbounded
% 150.28/150.49
% 150.28/150.49
% 150.28/150.49 Compiling...
% 150.28/150.49 Loading plugin: done.
% 150.28/150.49 Compiling...
% 150.28/150.49 Loading plugin: done.
% 150.28/150.49 %
% 150.28/150.49
% 150.28/150.49
% 150.28/150.49 % Time Out Real
% 150.28/150.49
% 150.28/150.49 % ------ Statistics
% 150.28/150.49
% 150.28/150.49 % ------ General
% 150.28/150.49
% 150.28/150.49 % num_of_input_clauses: 971
% 150.28/150.49 % num_of_input_neg_conjectures: 1
% 150.28/150.49 % num_of_splits: 0
% 150.28/150.49 % num_of_split_atoms: 0
% 150.28/150.49 % num_of_sem_filtered_clauses: 0
% 150.28/150.49 % num_of_subtypes: 0
% 150.28/150.49 % monotx_restored_types: 0
% 150.28/150.49 % sat_num_of_epr_types: 0
% 150.28/150.49 % sat_num_of_non_cyclic_types: 0
% 150.28/150.49 % sat_guarded_non_collapsed_types: 0
% 150.28/150.49 % is_epr: 0
% 150.28/150.49 % is_horn: 0
% 150.28/150.49 % has_eq: 1
% 150.28/150.49 % num_pure_diseq_elim: 0
% 150.28/150.49 % simp_replaced_by: 0
% 150.28/150.49 % res_preprocessed: 2
% 150.28/150.49 % prep_upred: 0
% 150.28/150.49 % prep_unflattend: 0
% 150.28/150.49 % pred_elim_cands: 0
% 150.28/150.49 % pred_elim: 0
% 150.28/150.49 % pred_elim_cl: 0
% 150.28/150.49 % pred_elim_cycles: 0
% 150.28/150.49 % forced_gc_time: 0
% 150.28/150.49 % gc_basic_clause_elim: 0
% 150.28/150.49 % parsing_time: 0.058
% 150.28/150.49 % sem_filter_time: 0.
% 150.28/150.49 % pred_elim_time: 0.
% 150.28/150.49 % out_proof_time: 0.
% 150.28/150.49 % monotx_time: 0.
% 150.28/150.49 % subtype_inf_time: 0.
% 150.28/150.49 % unif_index_cands_time: 0.
% 150.28/150.49 % unif_index_add_time: 0.002
% 150.28/150.49 % total_time: 150.017
% 150.28/150.49 % num_of_symbols: 124
% 150.28/150.49 % num_of_terms: 3882
% 150.28/150.49
% 150.28/150.49 % ------ Propositional Solver
% 150.28/150.49
% 150.28/150.49 % prop_solver_calls: 1
% 150.28/150.49 % prop_fast_solver_calls: 3
% 150.28/150.49 % prop_num_of_clauses: 927
% 150.28/150.49 % prop_preprocess_simplified: 2883
% 150.28/150.49 % prop_fo_subsumed: 0
% 150.28/150.49 % prop_solver_time: 0.
% 150.28/150.49 % prop_fast_solver_time: 0.
% 150.28/150.49 % prop_unsat_core_time: 0.
% 150.28/150.49
% 150.28/150.49 % ------ QBF
% 150.28/150.49
% 150.28/150.49 % qbf_q_res: 0
% 150.28/150.49 % qbf_num_tautologies: 0
% 150.28/150.49 % qbf_prep_cycles: 0
% 150.28/150.49
% 150.28/150.49 % ------ BMC1
% 150.28/150.49
% 150.28/150.49 % bmc1_current_bound: -1
% 150.28/150.49 % bmc1_last_solved_bound: -1
% 150.28/150.49 % bmc1_unsat_core_size: -1
% 150.28/150.49 % bmc1_unsat_core_parents_size: -1
% 150.28/150.49 % bmc1_merge_next_fun: 0
% 150.28/150.49 % bmc1_unsat_core_clauses_time: 0.
% 150.28/150.49
% 150.28/150.49 % ------ Instantiation
% 150.28/150.49
% 150.28/150.49 % inst_num_of_clauses: 846
% 150.28/150.49 % inst_num_in_passive: 0
% 150.28/150.49 % inst_num_in_active: 0
% 150.28/150.49 % inst_num_in_unprocessed: 971
% 150.28/150.49 % inst_num_of_loops: 0
% 150.28/150.49 % inst_num_of_learning_restarts: 0
% 150.28/150.49 % inst_num_moves_active_passive: 0
% 150.28/150.49 % inst_lit_activity: 0
% 150.28/150.49 % inst_lit_activity_moves: 0
% 150.28/150.49 % inst_num_tautologies: 0
% 150.28/150.49 % inst_num_prop_implied: 0
% 150.28/150.49 % inst_num_existing_simplified: 0
% 150.28/150.49 % inst_num_eq_res_simplified: 0
% 150.28/150.49 % inst_num_child_elim: 0
% 150.28/150.49 % inst_num_of_dismatching_blockings: 0
% 150.28/150.49 % inst_num_of_non_proper_insts: 0
% 150.28/150.49 % inst_num_of_duplicates: 0
% 150.28/150.49 % inst_inst_num_from_inst_to_res: 0
% 150.28/150.49 % inst_dismatching_checking_time: 0.
% 150.28/150.49
% 150.28/150.49 % ------ Resolution
% 150.28/150.49
% 150.28/150.49 % res_num_of_clauses: 770
% 150.28/150.49 % res_num_in_passive: 0
% 150.28/150.49 % res_num_in_active: 320
% 150.28/150.49 % res_num_of_loops: 0
% 150.28/150.49 % res_forward_subset_subsumed: 490
% 150.28/150.49 % res_backward_subset_subsumed: 0
% 150.28/150.49 % res_forward_subsumed: 0
% 150.28/150.49 % res_backward_subsumed: 0
% 150.28/150.49 % res_forward_subsumption_resolution: 0
% 150.28/150.49 % res_backward_subsumption_resolution: 0
% 150.28/150.49 % res_clause_to_clause_subsumption: 0
% 150.28/150.49 % res_orphan_elimination: 0
% 150.28/150.49 % res_tautology_del: 0
% 150.28/150.49 % res_num_eq_res_simplified: 0
% 150.28/150.49 % res_num_sel_changes: 0
% 150.28/150.49 % res_moves_from_active_to_pass: 0
% 150.28/150.49
% 150.28/150.49 % Status Unknown
% 150.31/150.62 % Orienting using strategy ClausalAll
% 150.31/150.62 % Orientation found
% 150.31/150.62 % 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_6581ac.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_82bb7c.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_05d7a8 | grep -v "SZS"
% 150.31/150.63
% 150.31/150.63 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.31/150.63
% 150.31/150.63 %
% 150.31/150.63 % ------ iProver source info
% 150.31/150.63
% 150.31/150.63 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.31/150.63 % git: non_committed_changes: true
% 150.31/150.63 % git: last_make_outside_of_git: true
% 150.31/150.63
% 150.31/150.63 %
% 150.31/150.63 % ------ Input Options
% 150.31/150.63
% 150.31/150.63 % --out_options all
% 150.31/150.63 % --tptp_safe_out true
% 150.31/150.63 % --problem_path ""
% 150.31/150.63 % --include_path ""
% 150.31/150.63 % --clausifier .//eprover
% 150.31/150.63 % --clausifier_options --tstp-format
% 150.31/150.63 % --stdin false
% 150.31/150.63 % --dbg_backtrace false
% 150.31/150.63 % --dbg_dump_prop_clauses false
% 150.31/150.63 % --dbg_dump_prop_clauses_file -
% 150.31/150.63 % --dbg_out_stat false
% 150.31/150.63
% 150.31/150.63 % ------ General Options
% 150.31/150.63
% 150.31/150.63 % --fof false
% 150.31/150.63 % --time_out_real 150.
% 150.31/150.63 % --time_out_prep_mult 0.2
% 150.31/150.63 % --time_out_virtual -1.
% 150.31/150.63 % --schedule none
% 150.31/150.63 % --ground_splitting input
% 150.31/150.63 % --splitting_nvd 16
% 150.31/150.63 % --non_eq_to_eq false
% 150.31/150.63 % --prep_gs_sim true
% 150.31/150.63 % --prep_unflatten false
% 150.31/150.63 % --prep_res_sim true
% 150.31/150.63 % --prep_upred true
% 150.31/150.63 % --res_sim_input true
% 150.31/150.63 % --clause_weak_htbl true
% 150.31/150.63 % --gc_record_bc_elim false
% 150.31/150.63 % --symbol_type_check false
% 150.31/150.63 % --clausify_out false
% 150.31/150.63 % --large_theory_mode false
% 150.31/150.63 % --prep_sem_filter none
% 150.31/150.63 % --prep_sem_filter_out false
% 150.31/150.63 % --preprocessed_out false
% 150.31/150.63 % --sub_typing false
% 150.31/150.63 % --brand_transform false
% 150.31/150.63 % --pure_diseq_elim true
% 150.31/150.63 % --min_unsat_core false
% 150.31/150.63 % --pred_elim true
% 150.31/150.63 % --add_important_lit false
% 150.31/150.63 % --soft_assumptions false
% 150.31/150.63 % --reset_solvers false
% 150.31/150.63 % --bc_imp_inh []
% 150.31/150.63 % --conj_cone_tolerance 1.5
% 150.31/150.63 % --prolific_symb_bound 500
% 150.31/150.63 % --lt_threshold 2000
% 150.31/150.63
% 150.31/150.63 % ------ SAT Options
% 150.31/150.63
% 150.31/150.63 % --sat_mode false
% 150.31/150.63 % --sat_fm_restart_options ""
% 150.31/150.63 % --sat_gr_def false
% 150.31/150.63 % --sat_epr_types true
% 150.31/150.63 % --sat_non_cyclic_types false
% 150.31/150.63 % --sat_finite_models false
% 150.31/150.63 % --sat_fm_lemmas false
% 150.31/150.63 % --sat_fm_prep false
% 150.31/150.63 % --sat_fm_uc_incr true
% 150.31/150.63 % --sat_out_model small
% 150.31/150.63 % --sat_out_clauses false
% 150.31/150.63
% 150.31/150.63 % ------ QBF Options
% 150.31/150.63
% 150.31/150.63 % --qbf_mode false
% 150.31/150.63 % --qbf_elim_univ true
% 150.31/150.63 % --qbf_sk_in true
% 150.31/150.63 % --qbf_pred_elim true
% 150.31/150.63 % --qbf_split 32
% 150.31/150.63
% 150.31/150.63 % ------ BMC1 Options
% 150.31/150.63
% 150.31/150.63 % --bmc1_incremental false
% 150.31/150.63 % --bmc1_axioms reachable_all
% 150.31/150.63 % --bmc1_min_bound 0
% 150.31/150.63 % --bmc1_max_bound -1
% 150.31/150.63 % --bmc1_max_bound_default -1
% 150.31/150.63 % --bmc1_symbol_reachability true
% 150.31/150.63 % --bmc1_property_lemmas false
% 150.31/150.63 % --bmc1_k_induction false
% 150.31/150.63 % --bmc1_non_equiv_states false
% 150.31/150.63 % --bmc1_deadlock false
% 150.31/150.63 % --bmc1_ucm false
% 150.31/150.63 % --bmc1_add_unsat_core none
% 150.31/150.63 % --bmc1_unsat_core_children false
% 150.31/150.63 % --bmc1_unsat_core_extrapolate_axioms false
% 150.31/150.63 % --bmc1_out_stat full
% 150.31/150.63 % --bmc1_ground_init false
% 150.31/150.63 % --bmc1_pre_inst_next_state false
% 150.31/150.63 % --bmc1_pre_inst_state false
% 150.31/150.63 % --bmc1_pre_inst_reach_state false
% 150.31/150.63 % --bmc1_out_unsat_core false
% 150.31/150.63 % --bmc1_aig_witness_out false
% 150.31/150.63 % --bmc1_verbose false
% 150.31/150.63 % --bmc1_dump_clauses_tptp false
% 152.90/153.46 % --bmc1_dump_unsat_core_tptp false
% 152.90/153.46 % --bmc1_dump_file -
% 152.90/153.46 % --bmc1_ucm_expand_uc_limit 128
% 152.90/153.46 % --bmc1_ucm_n_expand_iterations 6
% 152.90/153.46 % --bmc1_ucm_extend_mode 1
% 152.90/153.46 % --bmc1_ucm_init_mode 2
% 152.90/153.46 % --bmc1_ucm_cone_mode none
% 152.90/153.46 % --bmc1_ucm_reduced_relation_type 0
% 152.90/153.46 % --bmc1_ucm_relax_model 4
% 152.90/153.46 % --bmc1_ucm_full_tr_after_sat true
% 152.90/153.46 % --bmc1_ucm_expand_neg_assumptions false
% 152.90/153.46 % --bmc1_ucm_layered_model none
% 152.90/153.46 % --bmc1_ucm_max_lemma_size 10
% 152.90/153.46
% 152.90/153.46 % ------ AIG Options
% 152.90/153.46
% 152.90/153.46 % --aig_mode false
% 152.90/153.46
% 152.90/153.46 % ------ Instantiation Options
% 152.90/153.46
% 152.90/153.46 % --instantiation_flag true
% 152.90/153.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 152.90/153.46 % --inst_solver_per_active 750
% 152.90/153.46 % --inst_solver_calls_frac 0.5
% 152.90/153.46 % --inst_passive_queue_type priority_queues
% 152.90/153.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 152.90/153.46 % --inst_passive_queues_freq [25;2]
% 152.90/153.46 % --inst_dismatching true
% 152.90/153.46 % --inst_eager_unprocessed_to_passive true
% 152.90/153.46 % --inst_prop_sim_given true
% 152.90/153.46 % --inst_prop_sim_new false
% 152.90/153.46 % --inst_orphan_elimination true
% 152.90/153.46 % --inst_learning_loop_flag true
% 152.90/153.46 % --inst_learning_start 3000
% 152.90/153.46 % --inst_learning_factor 2
% 152.90/153.46 % --inst_start_prop_sim_after_learn 3
% 152.90/153.46 % --inst_sel_renew solver
% 152.90/153.46 % --inst_lit_activity_flag true
% 152.90/153.46 % --inst_out_proof true
% 152.90/153.46
% 152.90/153.46 % ------ Resolution Options
% 152.90/153.46
% 152.90/153.46 % --resolution_flag true
% 152.90/153.46 % --res_lit_sel kbo_max
% 152.90/153.46 % --res_to_prop_solver none
% 152.90/153.46 % --res_prop_simpl_new false
% 152.90/153.46 % --res_prop_simpl_given false
% 152.90/153.46 % --res_passive_queue_type priority_queues
% 152.90/153.46 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 152.90/153.46 % --res_passive_queues_freq [15;5]
% 152.90/153.46 % --res_forward_subs full
% 152.90/153.46 % --res_backward_subs full
% 152.90/153.46 % --res_forward_subs_resolution true
% 152.90/153.46 % --res_backward_subs_resolution true
% 152.90/153.46 % --res_orphan_elimination false
% 152.90/153.46 % --res_time_limit 1000.
% 152.90/153.46 % --res_out_proof true
% 152.90/153.46 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_6581ac.s
% 152.90/153.46 % --modulo true
% 152.90/153.46
% 152.90/153.46 % ------ Combination Options
% 152.90/153.46
% 152.90/153.46 % --comb_res_mult 1000
% 152.90/153.46 % --comb_inst_mult 300
% 152.90/153.46 % ------
% 152.90/153.46
% 152.90/153.46 % ------ Parsing...% successful
% 152.90/153.46
% 152.90/153.46 % ------ 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 %
% 152.90/153.46
% 152.90/153.46 % ------ Proving...
% 152.90/153.46 % ------ Problem Properties
% 152.90/153.46
% 152.90/153.46 %
% 152.90/153.46 % EPR false
% 152.90/153.46 % Horn false
% 152.90/153.46 % Has equality true
% 152.90/153.46
% 152.90/153.46 % % ------ Input Options Time Limit: Unbounded
% 152.90/153.46
% 152.90/153.46
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 Compiling...
% 152.90/153.46 Loading plugin: done.
% 152.90/153.46 % % ------ Current options:
% 152.90/153.46
% 152.90/153.46 % ------ Input Options
% 152.90/153.46
% 152.90/153.46 % --out_options all
% 152.90/153.46 % --tptp_safe_out true
% 152.90/153.46 % --problem_path ""
% 152.90/153.46 % --include_path ""
% 152.90/153.46 % --clausifier .//eprover
% 152.90/153.46 % --clausifier_options --tstp-format
% 152.90/153.46 % --stdin false
% 152.90/153.46 % --dbg_backtrace false
% 152.90/153.46 % --dbg_dump_prop_clauses false
% 152.90/153.46 % --dbg_dump_prop_clauses_file -
% 152.90/153.46 % --dbg_out_stat false
% 152.90/153.46
% 152.90/153.46 % ------ General Options
% 152.90/153.46
% 152.90/153.46 % --fof false
% 152.90/153.46 % --time_out_real 150.
% 152.90/153.46 % --time_out_prep_mult 0.2
% 152.90/153.46 % --time_out_virtual -1.
% 152.90/153.46 % --schedule none
% 152.90/153.46 % --ground_splitting input
% 152.90/153.46 % --splitting_nvd 16
% 152.90/153.46 % --non_eq_to_eq false
% 152.90/153.46 % --prep_gs_sim true
% 152.90/153.46 % --prep_unflatten false
% 152.90/153.46 % --prep_res_sim true
% 152.90/153.46 % --prep_upred true
% 152.90/153.46 % --res_sim_input true
% 152.90/153.46 % --clause_weak_htbl true
% 152.90/153.46 % --gc_record_bc_elim false
% 152.90/153.46 % --symbol_type_check false
% 152.90/153.46 % --clausify_out false
% 152.90/153.46 % --large_theory_mode false
% 152.90/153.46 % --prep_sem_filter none
% 152.90/153.46 % --prep_sem_filter_out false
% 152.90/153.46 % --preprocessed_out false
% 152.90/153.46 % --sub_typing false
% 152.90/153.46 % --brand_transform false
% 152.90/153.46 % --pure_diseq_elim true
% 152.90/153.46 % --min_unsat_core false
% 152.90/153.46 % --pred_elim true
% 152.90/153.46 % --add_important_lit false
% 152.90/153.46 % --soft_assumptions false
% 152.90/153.46 % --reset_solvers false
% 152.90/153.46 % --bc_imp_inh []
% 152.90/153.46 % --conj_cone_tolerance 1.5
% 152.90/153.46 % --prolific_symb_bound 500
% 152.90/153.46 % --lt_threshold 2000
% 152.90/153.46
% 152.90/153.46 % ------ SAT Options
% 152.90/153.46
% 152.90/153.46 % --sat_mode false
% 152.90/153.46 % --sat_fm_restart_options ""
% 152.90/153.46 % --sat_gr_def false
% 152.90/153.46 % --sat_epr_types true
% 152.90/153.46 % --sat_non_cyclic_types false
% 152.90/153.46 % --sat_finite_models false
% 152.90/153.46 % --sat_fm_lemmas false
% 152.90/153.46 % --sat_fm_prep false
% 152.90/153.46 % --sat_fm_uc_incr true
% 152.90/153.46 % --sat_out_model small
% 152.90/153.46 % --sat_out_clauses false
% 152.90/153.46
% 152.90/153.46 % ------ QBF Options
% 152.90/153.46
% 152.90/153.46 % --qbf_mode false
% 152.90/153.46 % --qbf_elim_univ true
% 152.90/153.46 % --qbf_sk_in true
% 152.90/153.46 % --qbf_pred_elim true
% 152.90/153.46 % --qbf_split 32
% 152.90/153.46
% 152.90/153.46 % ------ BMC1 Options
% 152.90/153.46
% 152.90/153.46 % --bmc1_incremental false
% 152.90/153.46 % --bmc1_axioms reachable_all
% 152.90/153.46 % --bmc1_min_bound 0
% 152.90/153.46 % --bmc1_max_bound -1
% 152.90/153.46 % --bmc1_max_bound_default -1
% 152.90/153.46 % --bmc1_symbol_reachability true
% 152.90/153.46 % --bmc1_property_lemmas false
% 152.90/153.46 % --bmc1_k_induction false
% 152.90/153.46 % --bmc1_non_equiv_states false
% 152.90/153.46 % --bmc1_deadlock false
% 152.90/153.46 % --bmc1_ucm false
% 152.90/153.46 % --bmc1_add_unsat_core none
% 152.90/153.46 % --bmc1_unsat_core_children false
% 152.90/153.46 % --bmc1_unsat_core_extrapolate_axioms false
% 152.90/153.46 % --bmc1_out_stat full
% 152.90/153.46 % --bmc1_ground_init false
% 152.90/153.46 % --bmc1_pre_inst_next_state false
% 152.90/153.46 % --bmc1_pre_inst_state false
% 152.90/153.46 % --bmc1_pre_inst_reach_state false
% 152.90/153.46 % --bmc1_out_unsat_core false
% 152.90/153.46 % --bmc1_aig_witness_out false
% 152.90/153.46 % --bmc1_verbose false
% 152.90/153.46 % --bmc1_dump_clauses_tptp false
% 152.90/153.46 % --bmc1_dump_unsat_core_tptp false
% 152.90/153.46 % --bmc1_dump_file -
% 152.90/153.46 % --bmc1_ucm_expand_uc_limit 128
% 152.90/153.46 % --bmc1_ucm_n_expand_iterations 6
% 152.90/153.46 % --bmc1_ucm_extend_mode 1
% 152.90/153.46 % --bmc1_ucm_init_mode 2
% 152.90/153.46 % --bmc1_ucm_cone_mode none
% 152.90/153.46 % --bmc1_ucm_reduced_relation_type 0
% 152.90/153.46 % --bmc1_ucm_relax_model 4
% 152.90/153.46 % --bmc1_ucm_full_tr_after_sat true
% 152.90/153.46 % --bmc1_ucm_expand_neg_assumptions false
% 152.90/153.46 % --bmc1_ucm_layered_model none
% 152.90/153.46 % --bmc1_ucm_max_lemma_size 10
% 152.90/153.46
% 152.90/153.46 % ------ AIG Options
% 152.90/153.46
% 152.90/153.46 % --aig_mode false
% 152.90/153.46
% 152.90/153.46 % ------ Instantiation Options
% 152.90/153.46
% 152.90/153.46 % --instantiation_flag true
% 152.90/153.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 152.90/153.46 % --inst_solver_per_active 750
% 152.90/153.46 % --inst_solver_calls_frac 0.5
% 152.90/153.46 % --inst_passive_queue_type priority_queues
% 152.90/153.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 152.90/153.46 % --inst_passive_queues_freq [25;2]
% 152.90/153.46 % --inst_dismatching true
% 152.90/153.46 % --inst_eager_unprocessed_to_passive true
% 152.90/153.46 % --inst_prop_sim_given true
% 152.90/153.46 % --inst_prop_sim_new false
% 152.90/153.46 % --inst_orphan_elimination true
% 152.90/153.46 % --inst_learning_loop_flag true
% 152.90/153.46 % --inst_learning_start 3000
% 152.90/153.46 % --inst_learning_factor 2
% 152.90/153.46 % --inst_start_prop_sim_after_learn 3
% 152.90/153.46 % --inst_sel_renew solver
% 152.90/153.46 % --inst_lit_activity_flag true
% 152.90/153.46 % --inst_out_proof true
% 152.90/153.46
% 152.90/153.46 % ------ Resolution Options
% 152.90/153.46
% 152.90/153.46 % --resolution_flag true
% 152.90/153.46 % --res_lit_sel kbo_max
% 152.90/153.46 % --res_to_prop_solver none
% 152.90/153.46 % --res_prop_simpl_new false
% 152.90/153.46 % --res_prop_simpl_given false
% 152.90/153.46 % --res_passive_queue_type priority_queues
% 152.90/153.46 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 152.90/153.46 % --res_passive_queues_freq [15;5]
% 152.90/153.46 % --res_forward_subs full
% 152.90/153.46 % --res_backward_subs full
% 152.90/153.46 % --res_forward_subs_resolution true
% 152.90/153.46 % --res_backward_subs_resolution true
% 152.90/153.46 % --res_orphan_elimination false
% 152.90/153.46 % --res_time_limit 1000.
% 152.90/153.46 % --res_out_proof true
% 152.90/153.46 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_6581ac.s
% 152.90/153.46 % --modulo true
% 152.90/153.46
% 152.90/153.46 % ------ Combination Options
% 152.90/153.46
% 152.90/153.46 % --comb_res_mult 1000
% 152.90/153.46 % --comb_inst_mult 300
% 152.90/153.46 % ------
% 152.90/153.46
% 152.90/153.46
% 152.90/153.46
% 152.90/153.46 % ------ Proving...
% 152.90/153.46 %
% 152.90/153.46
% 152.90/153.46
% 152.90/153.46 % Resolution empty clause
% 152.90/153.46
% 152.90/153.46 % ------ Statistics
% 152.90/153.46
% 152.90/153.46 % ------ General
% 152.90/153.46
% 152.90/153.46 % num_of_input_clauses: 971
% 152.90/153.46 % num_of_input_neg_conjectures: 1
% 152.90/153.46 % num_of_splits: 0
% 152.90/153.46 % num_of_split_atoms: 0
% 152.90/153.46 % num_of_sem_filtered_clauses: 0
% 152.90/153.46 % num_of_subtypes: 0
% 152.90/153.46 % monotx_restored_types: 0
% 152.90/153.46 % sat_num_of_epr_types: 0
% 152.90/153.46 % sat_num_of_non_cyclic_types: 0
% 152.90/153.46 % sat_guarded_non_collapsed_types: 0
% 152.90/153.46 % is_epr: 0
% 152.90/153.46 % is_horn: 0
% 152.90/153.46 % has_eq: 1
% 152.90/153.46 % num_pure_diseq_elim: 0
% 152.90/153.46 % simp_replaced_by: 0
% 152.90/153.46 % res_preprocessed: 2
% 152.90/153.46 % prep_upred: 0
% 152.90/153.46 % prep_unflattend: 0
% 152.90/153.46 % pred_elim_cands: 0
% 152.90/153.46 % pred_elim: 0
% 152.90/153.46 % pred_elim_cl: 0
% 152.90/153.46 % pred_elim_cycles: 0
% 152.90/153.46 % forced_gc_time: 0
% 152.90/153.46 % gc_basic_clause_elim: 0
% 152.90/153.46 % parsing_time: 0.027
% 152.90/153.46 % sem_filter_time: 0.
% 152.90/153.46 % pred_elim_time: 0.
% 152.90/153.46 % out_proof_time: 0.001
% 152.90/153.46 % monotx_time: 0.
% 152.90/153.46 % subtype_inf_time: 0.
% 152.90/153.46 % unif_index_cands_time: 0.
% 152.90/153.46 % unif_index_add_time: 0.
% 152.90/153.46 % total_time: 2.842
% 152.90/153.46 % num_of_symbols: 124
% 152.90/153.46 % num_of_terms: 3090
% 152.90/153.46
% 152.90/153.46 % ------ Propositional Solver
% 152.90/153.46
% 152.90/153.46 % prop_solver_calls: 1
% 152.90/153.46 % prop_fast_solver_calls: 3
% 152.90/153.46 % prop_num_of_clauses: 962
% 152.90/153.46 % prop_preprocess_simplified: 2848
% 152.90/153.46 % prop_fo_subsumed: 0
% 152.90/153.46 % prop_solver_time: 0.
% 152.90/153.46 % prop_fast_solver_time: 0.
% 152.90/153.46 % prop_unsat_core_time: 0.
% 152.90/153.46
% 152.90/153.46 % ------ QBF
% 152.90/153.46
% 152.90/153.46 % qbf_q_res: 0
% 152.90/153.46 % qbf_num_tautologies: 0
% 152.90/153.46 % qbf_prep_cycles: 0
% 152.90/153.47
% 152.90/153.47 % ------ BMC1
% 152.90/153.47
% 152.90/153.47 % bmc1_current_bound: -1
% 152.90/153.47 % bmc1_last_solved_bound: -1
% 152.90/153.47 % bmc1_unsat_core_size: -1
% 152.90/153.47 % bmc1_unsat_core_parents_size: -1
% 152.90/153.47 % bmc1_merge_next_fun: 0
% 152.90/153.47 % bmc1_unsat_core_clauses_time: 0.
% 152.90/153.47
% 152.90/153.47 % ------ Instantiation
% 152.90/153.47
% 152.90/153.47 % inst_num_of_clauses: 834
% 152.90/153.47 % inst_num_in_passive: 0
% 152.90/153.47 % inst_num_in_active: 0
% 152.90/153.47 % inst_num_in_unprocessed: 971
% 152.90/153.47 % inst_num_of_loops: 0
% 152.90/153.47 % inst_num_of_learning_restarts: 0
% 152.90/153.47 % inst_num_moves_active_passive: 0
% 152.90/153.47 % inst_lit_activity: 0
% 152.90/153.47 % inst_lit_activity_moves: 0
% 152.90/153.47 % inst_num_tautologies: 0
% 152.90/153.47 % inst_num_prop_implied: 0
% 152.90/153.47 % inst_num_existing_simplified: 0
% 152.90/153.47 % inst_num_eq_res_simplified: 0
% 152.90/153.47 % inst_num_child_elim: 0
% 152.90/153.47 % inst_num_of_dismatching_blockings: 0
% 152.90/153.47 % inst_num_of_non_proper_insts: 0
% 152.90/153.47 % inst_num_of_duplicates: 0
% 152.90/153.47 % inst_inst_num_from_inst_to_res: 0
% 152.90/153.47 % inst_dismatching_checking_time: 0.
% 152.90/153.47
% 152.90/153.47 % ------ Resolution
% 152.90/153.47
% 152.90/153.47 % res_num_of_clauses: 880
% 152.90/153.47 % res_num_in_passive: 1
% 152.90/153.47 % res_num_in_active: 387
% 152.90/153.47 % res_num_of_loops: 3
% 152.90/153.47 % res_forward_subset_subsumed: 505
% 152.90/153.47 % res_backward_subset_subsumed: 0
% 152.90/153.47 % res_forward_subsumed: 0
% 152.90/153.47 % res_backward_subsumed: 0
% 152.90/153.47 % res_forward_subsumption_resolution: 1
% 152.90/153.47 % res_backward_subsumption_resolution: 0
% 152.90/153.47 % res_clause_to_clause_subsumption: 1
% 152.90/153.47 % res_orphan_elimination: 0
% 152.90/153.47 % res_tautology_del: 0
% 152.90/153.47 % res_num_eq_res_simplified: 0
% 152.90/153.47 % res_num_sel_changes: 0
% 152.90/153.47 % res_moves_from_active_to_pass: 0
% 152.90/153.47
% 152.90/153.47 % Status Unsatisfiable
% 152.90/153.47 % SZS status Unsatisfiable
% 152.90/153.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------