TSTP Solution File: SCT169^2 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT169^2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:12:16 EDT 2023
% Result : Theorem 159.65s 160.01s
% Output : Proof 159.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.20 % Problem : SCT169^2 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.22 % Command : do_cvc5 %s %d
% 0.21/0.42 % Computer : n020.cluster.edu
% 0.21/0.42 % Model : x86_64 x86_64
% 0.21/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.42 % Memory : 8042.1875MB
% 0.21/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.27/0.42 % CPULimit : 300
% 0.27/0.42 % WCLimit : 300
% 0.27/0.42 % DateTime : Thu Aug 24 15:31:00 EDT 2023
% 0.27/0.43 % CPUTime :
% 0.27/0.63 %----Proving TH0
% 0.27/0.64 %------------------------------------------------------------------------------
% 0.27/0.64 % File : SCT169^2 : TPTP v8.1.2. Released v5.3.0.
% 0.27/0.64 % Domain : Social Choice Theory
% 0.27/0.64 % Problem : Arrow's Impossibility Theorem line 29, 500 axioms selected
% 0.27/0.64 % Version : Especial.
% 0.27/0.64 % English :
% 0.27/0.64
% 0.27/0.64 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.27/0.64 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.27/0.64 % Source : [Bla11]
% 0.27/0.64 % Names : arrow_500_thf_l29 [Bla11]
% 0.27/0.64
% 0.27/0.64 % Status : Theorem
% 0.27/0.64 % Rating : 0.92 v8.1.0, 0.91 v7.5.0, 1.00 v5.3.0
% 0.27/0.64 % Syntax : Number of formulae : 813 ( 283 unt; 109 typ; 0 def)
% 0.27/0.64 % Number of atoms : 1376 ( 806 equ; 2 cnn)
% 0.27/0.64 % Maximal formula atoms : 6 ( 1 avg)
% 0.27/0.64 % Number of connectives : 4739 ( 229 ~; 31 |; 88 &;3800 @)
% 0.27/0.64 % ( 161 <=>; 430 =>; 0 <=; 0 <~>)
% 0.27/0.64 % Maximal formula depth : 17 ( 5 avg)
% 0.27/0.64 % Number of types : 9 ( 8 usr)
% 0.27/0.64 % Number of type conns : 358 ( 358 >; 0 *; 0 +; 0 <<)
% 0.27/0.64 % Number of symbols : 105 ( 101 usr; 14 con; 0-3 aty)
% 0.27/0.64 % Number of variables : 1547 ( 2 ^;1492 !; 53 ?;1547 :)
% 0.27/0.64 % SPC : TH0_THM_EQU_NAR
% 0.27/0.64
% 0.27/0.64 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.27/0.64 % 2011-08-09 19:13:13
% 0.27/0.64 %------------------------------------------------------------------------------
% 0.27/0.64 %----Should-be-implicit typings (8)
% 0.27/0.64 thf(ty_ty_tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 arrow_475358991le_alt: $tType ).
% 0.27/0.64
% 0.27/0.64 thf(ty_ty_tc__Int__Oint,type,
% 0.27/0.64 int: $tType ).
% 0.27/0.64
% 0.27/0.64 thf(ty_ty_tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_J,type,
% 0.27/0.64 list_A2115238852le_alt: $tType ).
% 0.27/0.64
% 0.27/0.64 thf(ty_ty_tc__List__Olist_Itc__Int__Oint_J,type,
% 0.27/0.64 list_int: $tType ).
% 0.27/0.64
% 0.27/0.64 thf(ty_ty_tc__List__Olist_Itc__Nat__Onat_J,type,
% 0.27/0.64 list_nat: $tType ).
% 0.27/0.64
% 0.27/0.64 thf(ty_ty_tc__Nat__Onat,type,
% 0.27/0.64 nat: $tType ).
% 0.27/0.64
% 0.27/0.64 thf(ty_ty_tc__Option__Ooption_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_J,type,
% 0.27/0.64 option514678660le_alt: $tType ).
% 0.27/0.64
% 0.27/0.64 thf(ty_ty_tc__Option__Ooption_Itc__Nat__Onat_J,type,
% 0.27/0.64 option_nat: $tType ).
% 0.27/0.64
% 0.27/0.64 %----Explicit typings (101)
% 0.27/0.64 thf(sy_c_Ex1,type,
% 0.27/0.64 ex1: ( nat > $o ) > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Ex2,type,
% 0.27/0.64 ex2: ( arrow_475358991le_alt > $o ) > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.27/0.64 minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint,type,
% 0.27/0.64 minus_minus_int: int > int > int ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.27/0.64 minus_minus_nat: nat > nat > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Groups_Oone__class_Oone_000tc__Int__Oint,type,
% 0.27/0.64 one_one_int: int ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
% 0.27/0.64 one_one_nat: nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,type,
% 0.27/0.64 plus_plus_int: int > int > int ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.27/0.64 plus_plus_nat: nat > nat > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,type,
% 0.27/0.64 zero_zero_int: int ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
% 0.27/0.64 zero_zero_nat: nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_HOL_Oequal__class_Oequal_000tc__List__Olist_Itc__Arrow____Order____Mirabell,type,
% 0.27/0.64 equal_484611810le_alt: list_A2115238852le_alt > list_A2115238852le_alt > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_HOL_Oequal__class_Oequal_000tc__List__Olist_Itc__Nat__Onat_J,type,
% 0.27/0.64 equal_equal_list_nat: list_nat > list_nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint,type,
% 0.27/0.64 number_number_of_int: int > int ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat,type,
% 0.27/0.64 number_number_of_nat: int > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Int_Oring__1__class_OInts_000tc__Int__Oint,type,
% 0.27/0.64 ring_1_Ints_int: int > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_OListMem_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 listMe78047147le_alt: arrow_475358991le_alt > list_A2115238852le_alt > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Oappend_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 append179082452le_alt: list_A2115238852le_alt > list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Oappend_000tc__Nat__Onat,type,
% 0.27/0.64 append_nat: list_nat > list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 butlas274947851le_alt: list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Obutlast_000tc__Nat__Onat,type,
% 0.27/0.64 butlast_nat: list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 distin236324274le_alt: list_A2115238852le_alt > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Odistinct_000tc__Nat__Onat,type,
% 0.27/0.64 distinct_nat: list_nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 dropWh1316781920le_alt: ( arrow_475358991le_alt > $o ) > list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_OdropWhile_000tc__Nat__Onat,type,
% 0.27/0.64 dropWhile_nat: ( nat > $o ) > list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Odrop_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 drop_A1346709759le_alt: nat > list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Odrop_000tc__Nat__Onat,type,
% 0.27/0.64 drop_nat: nat > list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Ofoldr_000tc__Int__Oint_000tc__Int__Oint,type,
% 0.27/0.64 foldr_int_int: ( int > int > int ) > list_int > int > int ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Ofoldr_000tc__Nat__Onat_000tc__Nat__Onat,type,
% 0.27/0.64 foldr_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 hd_Arr1965683346le_alt: list_A2115238852le_alt > arrow_475358991le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Ohd_000tc__Nat__Onat,type,
% 0.27/0.64 hd_nat: list_nat > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 insert2120566741le_alt: arrow_475358991le_alt > list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Oinsert_000tc__Nat__Onat,type,
% 0.27/0.64 insert_nat: nat > list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 last_A1217315288le_alt: list_A2115238852le_alt > arrow_475358991le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olast_000tc__Nat__Onat,type,
% 0.27/0.64 last_nat: list_nat > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olinorder__class_Osorted_000tc__Int__Oint,type,
% 0.27/0.64 linorder_sorted_int: list_int > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olinorder__class_Osorted_000tc__Nat__Onat,type,
% 0.27/0.64 linorder_sorted_nat: list_nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_000tc__Nat__Onat,type,
% 0.27/0.64 linord810813188et_nat: ( nat > $o ) > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 cons_A228743023le_alt: arrow_475358991le_alt > list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist_OCons_000tc__Nat__Onat,type,
% 0.27/0.64 cons_nat: nat > list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 nil_Ar1286194111le_alt: list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist_ONil_000tc__Int__Oint,type,
% 0.27/0.64 nil_int: list_int ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist_ONil_000tc__Nat__Onat,type,
% 0.27/0.64 nil_nat: list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist_Olist__size_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa,type,
% 0.27/0.64 list_s250295873le_alt: ( arrow_475358991le_alt > nat ) > list_A2115238852le_alt > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist_Olist__size_000tc__Nat__Onat,type,
% 0.27/0.64 list_size_nat: ( nat > nat ) > list_nat > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist__ex1_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 list_e239244930le_alt: ( arrow_475358991le_alt > $o ) > list_A2115238852le_alt > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist__ex1_000tc__Nat__Onat,type,
% 0.27/0.64 list_ex1_nat: ( nat > $o ) > list_nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist__ex_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 list_e1252802557le_alt: ( arrow_475358991le_alt > $o ) > list_A2115238852le_alt > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist__ex_000tc__Nat__Onat,type,
% 0.27/0.64 list_ex_nat: ( nat > $o ) > list_nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist__update_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 list_u62477863le_alt: list_A2115238852le_alt > nat > arrow_475358991le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olist__update_000tc__Nat__Onat,type,
% 0.27/0.64 list_update_nat: list_nat > nat > nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olistrelp_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 listre1213162009le_alt: ( arrow_475358991le_alt > arrow_475358991le_alt > $o ) > list_A2115238852le_alt > list_A2115238852le_alt > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Olistrelp_000tc__Nat__Onat,type,
% 0.27/0.64 listrelp_nat: ( nat > nat > $o ) > list_nat > list_nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Omap__filter_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_00,type,
% 0.27/0.64 map_fi312151301lt_nat: ( arrow_475358991le_alt > option_nat ) > list_A2115238852le_alt > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Omap__filter_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____lc,type,
% 0.27/0.64 map_fi1462697295le_alt: ( nat > option514678660le_alt ) > list_nat > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Omaps_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000tc__Ar,type,
% 0.27/0.64 maps_A409156225le_alt: ( arrow_475358991le_alt > list_A2115238852le_alt ) > list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Omaps_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000tc__Na,type,
% 0.27/0.64 maps_A2124894076lt_nat: ( arrow_475358991le_alt > list_nat ) > list_A2115238852le_alt > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Omaps_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____lcilvlkkz,type,
% 0.27/0.64 maps_n1127956422le_alt: ( nat > list_A2115238852le_alt ) > list_nat > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Omember_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 member1504968148le_alt: list_A2115238852le_alt > arrow_475358991le_alt > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Omember_000tc__Nat__Onat,type,
% 0.27/0.64 member_nat_1: list_nat > nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Onth_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 nth_Ar125878976le_alt: list_A2115238852le_alt > nat > arrow_475358991le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Onth_000tc__Int__Oint,type,
% 0.27/0.64 nth_int: list_int > nat > int ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Onth_000tc__Nat__Onat,type,
% 0.27/0.64 nth_nat: list_nat > nat > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Onull_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 null_A1520965063le_alt: list_A2115238852le_alt > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Onull_000tc__Nat__Onat,type,
% 0.27/0.64 null_nat: list_nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Oreplicate_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 replic1511538809le_alt: nat > arrow_475358991le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Oreplicate_000tc__Nat__Onat,type,
% 0.27/0.64 replicate_nat: nat > nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 rev_Ar1106406943le_alt: list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Orev_000tc__Int__Oint,type,
% 0.27/0.64 rev_int: list_int > list_int ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Orev_000tc__Nat__Onat,type,
% 0.27/0.64 rev_nat: list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Orotate1_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 rotate335349260le_alt: list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Orotate1_000tc__Nat__Onat,type,
% 0.27/0.64 rotate1_nat: list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Osplice_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 splice1520898450le_alt: list_A2115238852le_alt > list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Osplice_000tc__Nat__Onat,type,
% 0.27/0.64 splice_nat: list_nat > list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Osublist_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 sublis2047953604le_alt: list_A2115238852le_alt > ( nat > $o ) > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Osublist_000tc__Nat__Onat,type,
% 0.27/0.64 sublist_nat: list_nat > ( nat > $o ) > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 takeWh1696291512le_alt: ( arrow_475358991le_alt > $o ) > list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_OtakeWhile_000tc__Nat__Onat,type,
% 0.27/0.64 takeWhile_nat: ( nat > $o ) > list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Otake_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 take_A614047655le_alt: nat > list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt,type,
% 0.27/0.64 tl_Arr465451158le_alt: list_A2115238852le_alt > list_A2115238852le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_List_Otl_000tc__Nat__Onat,type,
% 0.27/0.64 tl_nat: list_nat > list_nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Nat_OSuc,type,
% 0.27/0.64 suc: nat > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
% 0.27/0.64 size_s1858781230le_alt: list_A2115238852le_alt > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Nat__Onat_J,type,
% 0.27/0.64 size_size_list_nat: list_nat > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.27/0.64 bot_bot_int_o: int > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.27/0.64 bot_bot_nat_o: nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.27/0.64 bot_bot_o: $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Obot__class_Obot_000tc__Nat__Onat,type,
% 0.27/0.64 bot_bot_nat: nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.27/0.64 ord_less_int_o: ( int > $o ) > ( int > $o ) > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.27/0.64 ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Oord__class_Oless_000_Eo,type,
% 0.27/0.64 ord_less_o: $o > $o > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint,type,
% 0.27/0.64 ord_less_int: int > int > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.27/0.64 ord_less_nat: nat > nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Oord__class_Omax_000tc__Int__Oint,type,
% 0.27/0.64 ord_max_int: int > int > int ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Orderings_Oord__class_Omax_000tc__Nat__Onat,type,
% 0.27/0.64 ord_max_nat: nat > nat > nat ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_Set_OCollect_000tc__Nat__Onat,type,
% 0.27/0.64 collect_nat: ( nat > $o ) > nat > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O,type,
% 0.27/0.64 fequal781288069le_alt: list_A2115238852le_alt > list_A2115238852le_alt > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_member_000tc__Int__Oint,type,
% 0.27/0.64 member_int: int > ( int > $o ) > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_c_member_000tc__Nat__Onat,type,
% 0.27/0.64 member_nat: nat > ( nat > $o ) > $o ).
% 0.27/0.64
% 0.27/0.64 thf(sy_v_a,type,
% 0.27/0.64 a: arrow_475358991le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(sy_v_b,type,
% 0.27/0.64 b: arrow_475358991le_alt ).
% 0.27/0.64
% 0.27/0.64 %----Relevant facts (700)
% 0.27/0.64 thf(fact_0_alt3,axiom,
% 0.27/0.64 ? [A_90: arrow_475358991le_alt,B_48: arrow_475358991le_alt,C: arrow_475358991le_alt] : ( distin236324274le_alt @ ( cons_A228743023le_alt @ A_90 @ ( cons_A228743023le_alt @ B_48 @ ( cons_A228743023le_alt @ C @ nil_Ar1286194111le_alt ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_1_distinct_Osimps_I1_J,axiom,
% 0.27/0.64 distin236324274le_alt @ nil_Ar1286194111le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(fact_2_distinct_Osimps_I1_J,axiom,
% 0.27/0.64 distinct_nat @ nil_nat ).
% 0.27/0.64
% 0.27/0.64 thf(fact_3_list_Osimps_I2_J,axiom,
% 0.27/0.64 ! [A_92: arrow_475358991le_alt,List_6: list_A2115238852le_alt] :
% 0.27/0.64 ( nil_Ar1286194111le_alt
% 0.27/0.64 != ( cons_A228743023le_alt @ A_92 @ List_6 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_4_list_Osimps_I2_J,axiom,
% 0.27/0.64 ! [A_92: nat,List_6: list_nat] :
% 0.27/0.64 ( nil_nat
% 0.27/0.64 != ( cons_nat @ A_92 @ List_6 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_5_list_Osimps_I3_J,axiom,
% 0.27/0.64 ! [A_91: arrow_475358991le_alt,List_5: list_A2115238852le_alt] :
% 0.27/0.64 ( ( cons_A228743023le_alt @ A_91 @ List_5 )
% 0.27/0.64 != nil_Ar1286194111le_alt ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_6_list_Osimps_I3_J,axiom,
% 0.27/0.64 ! [A_91: nat,List_5: list_nat] :
% 0.27/0.64 ( ( cons_nat @ A_91 @ List_5 )
% 0.27/0.64 != nil_nat ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_7_neq__Nil__conv,axiom,
% 0.27/0.64 ! [Xs_183: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_183 != nil_Ar1286194111le_alt )
% 0.27/0.64 <=> ? [Y_3: arrow_475358991le_alt,Ys_5: list_A2115238852le_alt] :
% 0.27/0.64 ( Xs_183
% 0.27/0.64 = ( cons_A228743023le_alt @ Y_3 @ Ys_5 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_8_neq__Nil__conv,axiom,
% 0.27/0.64 ! [Xs_183: list_nat] :
% 0.27/0.64 ( ( Xs_183 != nil_nat )
% 0.27/0.64 <=> ? [Y_3: nat,Ys_5: list_nat] :
% 0.27/0.64 ( Xs_183
% 0.27/0.64 = ( cons_nat @ Y_3 @ Ys_5 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_9_list_Oexhaust,axiom,
% 0.27/0.64 ! [Y_44: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Y_44 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ~ ! [A_90: arrow_475358991le_alt,List_4: list_A2115238852le_alt] :
% 0.27/0.64 ( Y_44
% 0.27/0.64 != ( cons_A228743023le_alt @ A_90 @ List_4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_10_list_Oexhaust,axiom,
% 0.27/0.64 ! [Y_44: list_nat] :
% 0.27/0.64 ( ( Y_44 != nil_nat )
% 0.27/0.64 => ~ ! [A_90: nat,List_4: list_nat] :
% 0.27/0.64 ( Y_44
% 0.27/0.64 != ( cons_nat @ A_90 @ List_4 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_11_not__Cons__self,axiom,
% 0.27/0.64 ! [Xs_182: list_A2115238852le_alt,X_115: arrow_475358991le_alt] :
% 0.27/0.64 ( Xs_182
% 0.27/0.64 != ( cons_A228743023le_alt @ X_115 @ Xs_182 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_12_not__Cons__self2,axiom,
% 0.27/0.64 ! [X_114: arrow_475358991le_alt,Xs_181: list_A2115238852le_alt] :
% 0.27/0.64 ( ( cons_A228743023le_alt @ X_114 @ Xs_181 )
% 0.27/0.64 != Xs_181 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_13_list_Oinject,axiom,
% 0.27/0.64 ! [A_89: arrow_475358991le_alt,List_3: list_A2115238852le_alt,A_88: arrow_475358991le_alt,List_2: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( cons_A228743023le_alt @ A_89 @ List_3 )
% 0.27/0.64 = ( cons_A228743023le_alt @ A_88 @ List_2 ) )
% 0.27/0.64 <=> ( ( A_89 = A_88 )
% 0.27/0.64 & ( List_3 = List_2 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_14_splice_Osimps_I2_J,axiom,
% 0.27/0.64 ! [V_4: arrow_475358991le_alt,Va: list_A2115238852le_alt] :
% 0.27/0.64 ( ( splice1520898450le_alt @ ( cons_A228743023le_alt @ V_4 @ Va ) @ nil_Ar1286194111le_alt )
% 0.27/0.64 = ( cons_A228743023le_alt @ V_4 @ Va ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_15_splice_Osimps_I2_J,axiom,
% 0.27/0.64 ! [V_4: nat,Va: list_nat] :
% 0.27/0.64 ( ( splice_nat @ ( cons_nat @ V_4 @ Va ) @ nil_nat )
% 0.27/0.64 = ( cons_nat @ V_4 @ Va ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_16_insert__Nil,axiom,
% 0.27/0.64 ! [X_113: arrow_475358991le_alt] :
% 0.27/0.64 ( ( insert2120566741le_alt @ X_113 @ nil_Ar1286194111le_alt )
% 0.27/0.64 = ( cons_A228743023le_alt @ X_113 @ nil_Ar1286194111le_alt ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_17_insert__Nil,axiom,
% 0.27/0.64 ! [X_113: nat] :
% 0.27/0.64 ( ( insert_nat @ X_113 @ nil_nat )
% 0.27/0.64 = ( cons_nat @ X_113 @ nil_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_18_list__nonempty__induct,axiom,
% 0.27/0.64 ! [P_33: list_A2115238852le_alt > $o,Xs_180: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_180 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ! [X_1: arrow_475358991le_alt] : ( P_33 @ ( cons_A228743023le_alt @ X_1 @ nil_Ar1286194111le_alt ) )
% 0.27/0.64 => ( ! [X_1: arrow_475358991le_alt,Xs_54: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_54 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( P_33 @ Xs_54 )
% 0.27/0.64 => ( P_33 @ ( cons_A228743023le_alt @ X_1 @ Xs_54 ) ) ) )
% 0.27/0.64 => ( P_33 @ Xs_180 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_19_list__nonempty__induct,axiom,
% 0.27/0.64 ! [P_33: list_nat > $o,Xs_180: list_nat] :
% 0.27/0.64 ( ( Xs_180 != nil_nat )
% 0.27/0.64 => ( ! [X_1: nat] : ( P_33 @ ( cons_nat @ X_1 @ nil_nat ) )
% 0.27/0.64 => ( ! [X_1: nat,Xs_54: list_nat] :
% 0.27/0.64 ( ( Xs_54 != nil_nat )
% 0.27/0.64 => ( ( P_33 @ Xs_54 )
% 0.27/0.64 => ( P_33 @ ( cons_nat @ X_1 @ Xs_54 ) ) ) )
% 0.27/0.64 => ( P_33 @ Xs_180 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_20_distinct__butlast,axiom,
% 0.27/0.64 ! [Xs_179: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_179 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( distin236324274le_alt @ Xs_179 )
% 0.27/0.64 => ( distin236324274le_alt @ ( butlas274947851le_alt @ Xs_179 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_21_distinct__butlast,axiom,
% 0.27/0.64 ! [Xs_179: list_nat] :
% 0.27/0.64 ( ( Xs_179 != nil_nat )
% 0.27/0.64 => ( ( distinct_nat @ Xs_179 )
% 0.27/0.64 => ( distinct_nat @ ( butlast_nat @ Xs_179 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_22_butlast_Osimps_I1_J,axiom,
% 0.27/0.64 ( ( butlas274947851le_alt @ nil_Ar1286194111le_alt )
% 0.27/0.64 = nil_Ar1286194111le_alt ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_23_butlast_Osimps_I1_J,axiom,
% 0.27/0.64 ( ( butlast_nat @ nil_nat )
% 0.27/0.64 = nil_nat ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_24_distinct__insert,axiom,
% 0.27/0.64 ! [X_112: arrow_475358991le_alt,Xs_178: list_A2115238852le_alt] :
% 0.27/0.64 ( ( distin236324274le_alt @ Xs_178 )
% 0.27/0.64 => ( distin236324274le_alt @ ( insert2120566741le_alt @ X_112 @ Xs_178 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_25_splice_Osimps_I3_J,axiom,
% 0.27/0.64 ! [X_111: arrow_475358991le_alt,Xs_177: list_A2115238852le_alt,Y_43: arrow_475358991le_alt,Ys_54: list_A2115238852le_alt] :
% 0.27/0.64 ( ( splice1520898450le_alt @ ( cons_A228743023le_alt @ X_111 @ Xs_177 ) @ ( cons_A228743023le_alt @ Y_43 @ Ys_54 ) )
% 0.27/0.64 = ( cons_A228743023le_alt @ X_111 @ ( cons_A228743023le_alt @ Y_43 @ ( splice1520898450le_alt @ Xs_177 @ Ys_54 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_26_splice__Nil2,axiom,
% 0.27/0.64 ! [Xs_176: list_A2115238852le_alt] :
% 0.27/0.64 ( ( splice1520898450le_alt @ Xs_176 @ nil_Ar1286194111le_alt )
% 0.27/0.64 = Xs_176 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_27_splice__Nil2,axiom,
% 0.27/0.64 ! [Xs_176: list_nat] :
% 0.27/0.64 ( ( splice_nat @ Xs_176 @ nil_nat )
% 0.27/0.64 = Xs_176 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_28_splice_Osimps_I1_J,axiom,
% 0.27/0.64 ! [Ys_53: list_A2115238852le_alt] :
% 0.27/0.64 ( ( splice1520898450le_alt @ nil_Ar1286194111le_alt @ Ys_53 )
% 0.27/0.64 = Ys_53 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_29_splice_Osimps_I1_J,axiom,
% 0.27/0.64 ! [Ys_53: list_nat] :
% 0.27/0.64 ( ( splice_nat @ nil_nat @ Ys_53 )
% 0.27/0.64 = Ys_53 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_30_butlast_Osimps_I2_J,axiom,
% 0.27/0.64 ! [X_110: arrow_475358991le_alt,Xs_175: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( Xs_175 = nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( butlas274947851le_alt @ ( cons_A228743023le_alt @ X_110 @ Xs_175 ) )
% 0.27/0.64 = nil_Ar1286194111le_alt ) )
% 0.27/0.64 & ( ( Xs_175 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( butlas274947851le_alt @ ( cons_A228743023le_alt @ X_110 @ Xs_175 ) )
% 0.27/0.64 = ( cons_A228743023le_alt @ X_110 @ ( butlas274947851le_alt @ Xs_175 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_31_butlast_Osimps_I2_J,axiom,
% 0.27/0.64 ! [X_110: nat,Xs_175: list_nat] :
% 0.27/0.64 ( ( ( Xs_175 = nil_nat )
% 0.27/0.64 => ( ( butlast_nat @ ( cons_nat @ X_110 @ Xs_175 ) )
% 0.27/0.64 = nil_nat ) )
% 0.27/0.64 & ( ( Xs_175 != nil_nat )
% 0.27/0.64 => ( ( butlast_nat @ ( cons_nat @ X_110 @ Xs_175 ) )
% 0.27/0.64 = ( cons_nat @ X_110 @ ( butlast_nat @ Xs_175 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_32_eq__Nil__null,axiom,
% 0.27/0.64 ! [Xs_174: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_174 = nil_Ar1286194111le_alt )
% 0.27/0.64 <=> ( null_A1520965063le_alt @ Xs_174 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_33_eq__Nil__null,axiom,
% 0.27/0.64 ! [Xs_174: list_nat] :
% 0.27/0.64 ( ( Xs_174 = nil_nat )
% 0.27/0.64 <=> ( null_nat @ Xs_174 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_34_List_Onull__def,axiom,
% 0.27/0.64 ! [Xs_173: list_A2115238852le_alt] :
% 0.27/0.64 ( ( null_A1520965063le_alt @ Xs_173 )
% 0.27/0.64 <=> ( Xs_173 = nil_Ar1286194111le_alt ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_35_List_Onull__def,axiom,
% 0.27/0.64 ! [Xs_173: list_nat] :
% 0.27/0.64 ( ( null_nat @ Xs_173 )
% 0.27/0.64 <=> ( Xs_173 = nil_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_36_null__rec_I2_J,axiom,
% 0.27/0.64 null_A1520965063le_alt @ nil_Ar1286194111le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(fact_37_null__rec_I2_J,axiom,
% 0.27/0.64 null_nat @ nil_nat ).
% 0.27/0.64
% 0.27/0.64 thf(fact_38_null__rec_I1_J,axiom,
% 0.27/0.64 ! [X_109: arrow_475358991le_alt,Xs_172: list_A2115238852le_alt] :
% 0.27/0.64 ~ ( null_A1520965063le_alt @ ( cons_A228743023le_alt @ X_109 @ Xs_172 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_39_butlast__snoc,axiom,
% 0.27/0.64 ! [Xs_171: list_A2115238852le_alt,X_108: arrow_475358991le_alt] :
% 0.27/0.64 ( ( butlas274947851le_alt @ ( append179082452le_alt @ Xs_171 @ ( cons_A228743023le_alt @ X_108 @ nil_Ar1286194111le_alt ) ) )
% 0.27/0.64 = Xs_171 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_40_butlast__snoc,axiom,
% 0.27/0.64 ! [Xs_171: list_nat,X_108: nat] :
% 0.27/0.64 ( ( butlast_nat @ ( append_nat @ Xs_171 @ ( cons_nat @ X_108 @ nil_nat ) ) )
% 0.27/0.64 = Xs_171 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_41_maps__simps_I2_J,axiom,
% 0.27/0.64 ! [F_7: nat > list_A2115238852le_alt] :
% 0.27/0.64 ( ( maps_n1127956422le_alt @ F_7 @ nil_nat )
% 0.27/0.64 = nil_Ar1286194111le_alt ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_42_maps__simps_I2_J,axiom,
% 0.27/0.64 ! [F_7: arrow_475358991le_alt > list_nat] :
% 0.27/0.64 ( ( maps_A2124894076lt_nat @ F_7 @ nil_Ar1286194111le_alt )
% 0.27/0.64 = nil_nat ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_43_maps__simps_I2_J,axiom,
% 0.27/0.64 ! [F_7: arrow_475358991le_alt > list_A2115238852le_alt] :
% 0.27/0.64 ( ( maps_A409156225le_alt @ F_7 @ nil_Ar1286194111le_alt )
% 0.27/0.64 = nil_Ar1286194111le_alt ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_44_sorted__single,axiom,
% 0.27/0.64 ! [X_107: nat] : ( linorder_sorted_nat @ ( cons_nat @ X_107 @ nil_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_45_sorted_ONil,axiom,
% 0.27/0.64 linorder_sorted_nat @ nil_nat ).
% 0.27/0.64
% 0.27/0.64 thf(fact_46_append__assoc,axiom,
% 0.27/0.64 ! [Xs_170: list_A2115238852le_alt,Ys_52: list_A2115238852le_alt,Zs_9: list_A2115238852le_alt] :
% 0.27/0.64 ( ( append179082452le_alt @ ( append179082452le_alt @ Xs_170 @ Ys_52 ) @ Zs_9 )
% 0.27/0.64 = ( append179082452le_alt @ Xs_170 @ ( append179082452le_alt @ Ys_52 @ Zs_9 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_47_append__eq__append__conv2,axiom,
% 0.27/0.64 ! [Xs_169: list_A2115238852le_alt,Ys_51: list_A2115238852le_alt,Zs_8: list_A2115238852le_alt,Ts: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( append179082452le_alt @ Xs_169 @ Ys_51 )
% 0.27/0.64 = ( append179082452le_alt @ Zs_8 @ Ts ) )
% 0.27/0.64 <=> ? [Us_1: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( Xs_169
% 0.27/0.64 = ( append179082452le_alt @ Zs_8 @ Us_1 ) )
% 0.27/0.64 & ( ( append179082452le_alt @ Us_1 @ Ys_51 )
% 0.27/0.64 = Ts ) )
% 0.27/0.64 | ( ( ( append179082452le_alt @ Xs_169 @ Us_1 )
% 0.27/0.64 = Zs_8 )
% 0.27/0.64 & ( Ys_51
% 0.27/0.64 = ( append179082452le_alt @ Us_1 @ Ts ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_48_same__append__eq,axiom,
% 0.27/0.64 ! [Xs_168: list_A2115238852le_alt,Ys_50: list_A2115238852le_alt,Zs_7: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( append179082452le_alt @ Xs_168 @ Ys_50 )
% 0.27/0.64 = ( append179082452le_alt @ Xs_168 @ Zs_7 ) )
% 0.27/0.64 <=> ( Ys_50 = Zs_7 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_49_append__same__eq,axiom,
% 0.27/0.64 ! [Ys_49: list_A2115238852le_alt,Xs_167: list_A2115238852le_alt,Zs_6: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( append179082452le_alt @ Ys_49 @ Xs_167 )
% 0.27/0.64 = ( append179082452le_alt @ Zs_6 @ Xs_167 ) )
% 0.27/0.64 <=> ( Ys_49 = Zs_6 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_50_append__eq__appendI,axiom,
% 0.27/0.64 ! [Ys_48: list_A2115238852le_alt,Us: list_A2115238852le_alt,Xs_166: list_A2115238852le_alt,Xs1_1: list_A2115238852le_alt,Zs_5: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( append179082452le_alt @ Xs_166 @ Xs1_1 )
% 0.27/0.64 = Zs_5 )
% 0.27/0.64 => ( ( Ys_48
% 0.27/0.64 = ( append179082452le_alt @ Xs1_1 @ Us ) )
% 0.27/0.64 => ( ( append179082452le_alt @ Xs_166 @ Ys_48 )
% 0.27/0.64 = ( append179082452le_alt @ Zs_5 @ Us ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_51_maps__simps_I1_J,axiom,
% 0.27/0.64 ! [F_6: arrow_475358991le_alt > list_A2115238852le_alt,X_106: arrow_475358991le_alt,Xs_165: list_A2115238852le_alt] :
% 0.27/0.64 ( ( maps_A409156225le_alt @ F_6 @ ( cons_A228743023le_alt @ X_106 @ Xs_165 ) )
% 0.27/0.64 = ( append179082452le_alt @ ( F_6 @ X_106 ) @ ( maps_A409156225le_alt @ F_6 @ Xs_165 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_52_append__Cons,axiom,
% 0.27/0.64 ! [X_105: arrow_475358991le_alt,Xs_164: list_A2115238852le_alt,Ys_47: list_A2115238852le_alt] :
% 0.27/0.64 ( ( append179082452le_alt @ ( cons_A228743023le_alt @ X_105 @ Xs_164 ) @ Ys_47 )
% 0.27/0.64 = ( cons_A228743023le_alt @ X_105 @ ( append179082452le_alt @ Xs_164 @ Ys_47 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_53_Cons__eq__appendI,axiom,
% 0.27/0.64 ! [Xs_163: list_A2115238852le_alt,Zs_4: list_A2115238852le_alt,X_104: arrow_475358991le_alt,Xs1: list_A2115238852le_alt,Ys_46: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( cons_A228743023le_alt @ X_104 @ Xs1 )
% 0.27/0.64 = Ys_46 )
% 0.27/0.64 => ( ( Xs_163
% 0.27/0.64 = ( append179082452le_alt @ Xs1 @ Zs_4 ) )
% 0.27/0.64 => ( ( cons_A228743023le_alt @ X_104 @ Xs_163 )
% 0.27/0.64 = ( append179082452le_alt @ Ys_46 @ Zs_4 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_54_append__Nil,axiom,
% 0.27/0.64 ! [Ys_45: list_A2115238852le_alt] :
% 0.27/0.64 ( ( append179082452le_alt @ nil_Ar1286194111le_alt @ Ys_45 )
% 0.27/0.64 = Ys_45 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_55_append__Nil,axiom,
% 0.27/0.64 ! [Ys_45: list_nat] :
% 0.27/0.64 ( ( append_nat @ nil_nat @ Ys_45 )
% 0.27/0.64 = Ys_45 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_56_Nil__is__append__conv,axiom,
% 0.27/0.64 ! [Xs_162: list_A2115238852le_alt,Ys_44: list_A2115238852le_alt] :
% 0.27/0.64 ( ( nil_Ar1286194111le_alt
% 0.27/0.64 = ( append179082452le_alt @ Xs_162 @ Ys_44 ) )
% 0.27/0.64 <=> ( ( Xs_162 = nil_Ar1286194111le_alt )
% 0.27/0.64 & ( Ys_44 = nil_Ar1286194111le_alt ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_57_Nil__is__append__conv,axiom,
% 0.27/0.64 ! [Xs_162: list_nat,Ys_44: list_nat] :
% 0.27/0.64 ( ( nil_nat
% 0.27/0.64 = ( append_nat @ Xs_162 @ Ys_44 ) )
% 0.27/0.64 <=> ( ( Xs_162 = nil_nat )
% 0.27/0.64 & ( Ys_44 = nil_nat ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_58_append__Nil2,axiom,
% 0.27/0.64 ! [Xs_161: list_A2115238852le_alt] :
% 0.27/0.64 ( ( append179082452le_alt @ Xs_161 @ nil_Ar1286194111le_alt )
% 0.27/0.64 = Xs_161 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_59_append__Nil2,axiom,
% 0.27/0.64 ! [Xs_161: list_nat] :
% 0.27/0.64 ( ( append_nat @ Xs_161 @ nil_nat )
% 0.27/0.64 = Xs_161 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_60_self__append__conv,axiom,
% 0.27/0.64 ! [Xs_160: list_A2115238852le_alt,Ys_43: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_160
% 0.27/0.64 = ( append179082452le_alt @ Xs_160 @ Ys_43 ) )
% 0.27/0.64 <=> ( Ys_43 = nil_Ar1286194111le_alt ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_61_self__append__conv,axiom,
% 0.27/0.64 ! [Xs_160: list_nat,Ys_43: list_nat] :
% 0.27/0.64 ( ( Xs_160
% 0.27/0.64 = ( append_nat @ Xs_160 @ Ys_43 ) )
% 0.27/0.64 <=> ( Ys_43 = nil_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_62_self__append__conv2,axiom,
% 0.27/0.64 ! [Ys_42: list_A2115238852le_alt,Xs_159: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Ys_42
% 0.27/0.64 = ( append179082452le_alt @ Xs_159 @ Ys_42 ) )
% 0.27/0.64 <=> ( Xs_159 = nil_Ar1286194111le_alt ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_63_self__append__conv2,axiom,
% 0.27/0.64 ! [Ys_42: list_nat,Xs_159: list_nat] :
% 0.27/0.64 ( ( Ys_42
% 0.27/0.64 = ( append_nat @ Xs_159 @ Ys_42 ) )
% 0.27/0.64 <=> ( Xs_159 = nil_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_64_append__is__Nil__conv,axiom,
% 0.27/0.64 ! [Xs_158: list_A2115238852le_alt,Ys_41: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( append179082452le_alt @ Xs_158 @ Ys_41 )
% 0.27/0.64 = nil_Ar1286194111le_alt )
% 0.27/0.64 <=> ( ( Xs_158 = nil_Ar1286194111le_alt )
% 0.27/0.64 & ( Ys_41 = nil_Ar1286194111le_alt ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_65_append__is__Nil__conv,axiom,
% 0.27/0.64 ! [Xs_158: list_nat,Ys_41: list_nat] :
% 0.27/0.64 ( ( ( append_nat @ Xs_158 @ Ys_41 )
% 0.27/0.64 = nil_nat )
% 0.27/0.64 <=> ( ( Xs_158 = nil_nat )
% 0.27/0.64 & ( Ys_41 = nil_nat ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_66_append__self__conv,axiom,
% 0.27/0.64 ! [Xs_157: list_A2115238852le_alt,Ys_40: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( append179082452le_alt @ Xs_157 @ Ys_40 )
% 0.27/0.64 = Xs_157 )
% 0.27/0.64 <=> ( Ys_40 = nil_Ar1286194111le_alt ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_67_append__self__conv,axiom,
% 0.27/0.64 ! [Xs_157: list_nat,Ys_40: list_nat] :
% 0.27/0.64 ( ( ( append_nat @ Xs_157 @ Ys_40 )
% 0.27/0.64 = Xs_157 )
% 0.27/0.64 <=> ( Ys_40 = nil_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_68_append__self__conv2,axiom,
% 0.27/0.64 ! [Xs_156: list_A2115238852le_alt,Ys_39: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( append179082452le_alt @ Xs_156 @ Ys_39 )
% 0.27/0.64 = Ys_39 )
% 0.27/0.64 <=> ( Xs_156 = nil_Ar1286194111le_alt ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_69_append__self__conv2,axiom,
% 0.27/0.64 ! [Xs_156: list_nat,Ys_39: list_nat] :
% 0.27/0.64 ( ( ( append_nat @ Xs_156 @ Ys_39 )
% 0.27/0.64 = Ys_39 )
% 0.27/0.64 <=> ( Xs_156 = nil_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_70_eq__Nil__appendI,axiom,
% 0.27/0.64 ! [Xs_155: list_A2115238852le_alt,Ys_38: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_155 = Ys_38 )
% 0.27/0.64 => ( Xs_155
% 0.27/0.64 = ( append179082452le_alt @ nil_Ar1286194111le_alt @ Ys_38 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_71_eq__Nil__appendI,axiom,
% 0.27/0.64 ! [Xs_155: list_nat,Ys_38: list_nat] :
% 0.27/0.64 ( ( Xs_155 = Ys_38 )
% 0.27/0.64 => ( Xs_155
% 0.27/0.64 = ( append_nat @ nil_nat @ Ys_38 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_72_append__eq__Cons__conv,axiom,
% 0.27/0.64 ! [Ys_37: list_A2115238852le_alt,Zs_3: list_A2115238852le_alt,X_103: arrow_475358991le_alt,Xs_154: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( append179082452le_alt @ Ys_37 @ Zs_3 )
% 0.27/0.64 = ( cons_A228743023le_alt @ X_103 @ Xs_154 ) )
% 0.27/0.64 <=> ( ( ( Ys_37 = nil_Ar1286194111le_alt )
% 0.27/0.64 & ( Zs_3
% 0.27/0.64 = ( cons_A228743023le_alt @ X_103 @ Xs_154 ) ) )
% 0.27/0.64 | ? [Ys_36: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Ys_37
% 0.27/0.64 = ( cons_A228743023le_alt @ X_103 @ Ys_36 ) )
% 0.27/0.64 & ( ( append179082452le_alt @ Ys_36 @ Zs_3 )
% 0.27/0.64 = Xs_154 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_73_append__eq__Cons__conv,axiom,
% 0.27/0.64 ! [Ys_37: list_nat,Zs_3: list_nat,X_103: nat,Xs_154: list_nat] :
% 0.27/0.64 ( ( ( append_nat @ Ys_37 @ Zs_3 )
% 0.27/0.64 = ( cons_nat @ X_103 @ Xs_154 ) )
% 0.27/0.64 <=> ( ( ( Ys_37 = nil_nat )
% 0.27/0.64 & ( Zs_3
% 0.27/0.64 = ( cons_nat @ X_103 @ Xs_154 ) ) )
% 0.27/0.64 | ? [Ys_36: list_nat] :
% 0.27/0.64 ( ( Ys_37
% 0.27/0.64 = ( cons_nat @ X_103 @ Ys_36 ) )
% 0.27/0.64 & ( ( append_nat @ Ys_36 @ Zs_3 )
% 0.27/0.64 = Xs_154 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_74_Cons__eq__append__conv,axiom,
% 0.27/0.64 ! [X_102: arrow_475358991le_alt,Xs_153: list_A2115238852le_alt,Ys_35: list_A2115238852le_alt,Zs_2: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( cons_A228743023le_alt @ X_102 @ Xs_153 )
% 0.27/0.64 = ( append179082452le_alt @ Ys_35 @ Zs_2 ) )
% 0.27/0.64 <=> ( ( ( Ys_35 = nil_Ar1286194111le_alt )
% 0.27/0.64 & ( ( cons_A228743023le_alt @ X_102 @ Xs_153 )
% 0.27/0.64 = Zs_2 ) )
% 0.27/0.64 | ? [Ys_36: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( cons_A228743023le_alt @ X_102 @ Ys_36 )
% 0.27/0.64 = Ys_35 )
% 0.27/0.64 & ( Xs_153
% 0.27/0.64 = ( append179082452le_alt @ Ys_36 @ Zs_2 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_75_Cons__eq__append__conv,axiom,
% 0.27/0.64 ! [X_102: nat,Xs_153: list_nat,Ys_35: list_nat,Zs_2: list_nat] :
% 0.27/0.64 ( ( ( cons_nat @ X_102 @ Xs_153 )
% 0.27/0.64 = ( append_nat @ Ys_35 @ Zs_2 ) )
% 0.27/0.64 <=> ( ( ( Ys_35 = nil_nat )
% 0.27/0.64 & ( ( cons_nat @ X_102 @ Xs_153 )
% 0.27/0.64 = Zs_2 ) )
% 0.27/0.64 | ? [Ys_36: list_nat] :
% 0.27/0.64 ( ( ( cons_nat @ X_102 @ Ys_36 )
% 0.27/0.64 = Ys_35 )
% 0.27/0.64 & ( Xs_153
% 0.27/0.64 = ( append_nat @ Ys_36 @ Zs_2 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_76_append1__eq__conv,axiom,
% 0.27/0.64 ! [Xs_152: list_A2115238852le_alt,X_101: arrow_475358991le_alt,Ys_34: list_A2115238852le_alt,Y_42: arrow_475358991le_alt] :
% 0.27/0.64 ( ( ( append179082452le_alt @ Xs_152 @ ( cons_A228743023le_alt @ X_101 @ nil_Ar1286194111le_alt ) )
% 0.27/0.64 = ( append179082452le_alt @ Ys_34 @ ( cons_A228743023le_alt @ Y_42 @ nil_Ar1286194111le_alt ) ) )
% 0.27/0.64 <=> ( ( Xs_152 = Ys_34 )
% 0.27/0.64 & ( X_101 = Y_42 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_77_append1__eq__conv,axiom,
% 0.27/0.64 ! [Xs_152: list_nat,X_101: nat,Ys_34: list_nat,Y_42: nat] :
% 0.27/0.64 ( ( ( append_nat @ Xs_152 @ ( cons_nat @ X_101 @ nil_nat ) )
% 0.27/0.64 = ( append_nat @ Ys_34 @ ( cons_nat @ Y_42 @ nil_nat ) ) )
% 0.27/0.64 <=> ( ( Xs_152 = Ys_34 )
% 0.27/0.64 & ( X_101 = Y_42 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_78_butlast__append,axiom,
% 0.27/0.64 ! [Xs_151: list_A2115238852le_alt,Ys_33: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( Ys_33 = nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( butlas274947851le_alt @ ( append179082452le_alt @ Xs_151 @ Ys_33 ) )
% 0.27/0.64 = ( butlas274947851le_alt @ Xs_151 ) ) )
% 0.27/0.64 & ( ( Ys_33 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( butlas274947851le_alt @ ( append179082452le_alt @ Xs_151 @ Ys_33 ) )
% 0.27/0.64 = ( append179082452le_alt @ Xs_151 @ ( butlas274947851le_alt @ Ys_33 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_79_butlast__append,axiom,
% 0.27/0.64 ! [Xs_151: list_nat,Ys_33: list_nat] :
% 0.27/0.64 ( ( ( Ys_33 = nil_nat )
% 0.27/0.64 => ( ( butlast_nat @ ( append_nat @ Xs_151 @ Ys_33 ) )
% 0.27/0.64 = ( butlast_nat @ Xs_151 ) ) )
% 0.27/0.64 & ( ( Ys_33 != nil_nat )
% 0.27/0.64 => ( ( butlast_nat @ ( append_nat @ Xs_151 @ Ys_33 ) )
% 0.27/0.64 = ( append_nat @ Xs_151 @ ( butlast_nat @ Ys_33 ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_80_sorted__butlast,axiom,
% 0.27/0.64 ! [Xs_150: list_nat] :
% 0.27/0.64 ( ( Xs_150 != nil_nat )
% 0.27/0.64 => ( ( linorder_sorted_nat @ Xs_150 )
% 0.27/0.64 => ( linorder_sorted_nat @ ( butlast_nat @ Xs_150 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_81_rev__induct,axiom,
% 0.27/0.64 ! [Xs_149: list_A2115238852le_alt,P_32: list_A2115238852le_alt > $o] :
% 0.27/0.64 ( ( P_32 @ nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ! [X_1: arrow_475358991le_alt,Xs_54: list_A2115238852le_alt] :
% 0.27/0.64 ( ( P_32 @ Xs_54 )
% 0.27/0.64 => ( P_32 @ ( append179082452le_alt @ Xs_54 @ ( cons_A228743023le_alt @ X_1 @ nil_Ar1286194111le_alt ) ) ) )
% 0.27/0.64 => ( P_32 @ Xs_149 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_82_rev__induct,axiom,
% 0.27/0.64 ! [Xs_149: list_nat,P_32: list_nat > $o] :
% 0.27/0.64 ( ( P_32 @ nil_nat )
% 0.27/0.64 => ( ! [X_1: nat,Xs_54: list_nat] :
% 0.27/0.64 ( ( P_32 @ Xs_54 )
% 0.27/0.64 => ( P_32 @ ( append_nat @ Xs_54 @ ( cons_nat @ X_1 @ nil_nat ) ) ) )
% 0.27/0.64 => ( P_32 @ Xs_149 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_83_rev__cases,axiom,
% 0.27/0.64 ! [Xs_148: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_148 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ~ ! [Ys_5: list_A2115238852le_alt,Y_3: arrow_475358991le_alt] :
% 0.27/0.64 ( Xs_148
% 0.27/0.64 != ( append179082452le_alt @ Ys_5 @ ( cons_A228743023le_alt @ Y_3 @ nil_Ar1286194111le_alt ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_84_rev__cases,axiom,
% 0.27/0.64 ! [Xs_148: list_nat] :
% 0.27/0.64 ( ( Xs_148 != nil_nat )
% 0.27/0.64 => ~ ! [Ys_5: list_nat,Y_3: nat] :
% 0.27/0.64 ( Xs_148
% 0.27/0.64 != ( append_nat @ Ys_5 @ ( cons_nat @ Y_3 @ nil_nat ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_85_equal__Nil__null,axiom,
% 0.27/0.64 ! [Xs_147: list_A2115238852le_alt] :
% 0.27/0.64 ( ( equal_484611810le_alt @ Xs_147 @ nil_Ar1286194111le_alt )
% 0.27/0.64 <=> ( null_A1520965063le_alt @ Xs_147 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_86_equal__Nil__null,axiom,
% 0.27/0.64 ! [Xs_147: list_nat] :
% 0.27/0.64 ( ( equal_equal_list_nat @ Xs_147 @ nil_nat )
% 0.27/0.64 <=> ( null_nat @ Xs_147 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_87_snoc__eq__iff__butlast,axiom,
% 0.27/0.64 ! [Xs_146: list_A2115238852le_alt,X_100: arrow_475358991le_alt,Ys_32: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( append179082452le_alt @ Xs_146 @ ( cons_A228743023le_alt @ X_100 @ nil_Ar1286194111le_alt ) )
% 0.27/0.64 = Ys_32 )
% 0.27/0.64 <=> ( ( Ys_32 != nil_Ar1286194111le_alt )
% 0.27/0.64 & ( ( butlas274947851le_alt @ Ys_32 )
% 0.27/0.64 = Xs_146 )
% 0.27/0.64 & ( ( last_A1217315288le_alt @ Ys_32 )
% 0.27/0.64 = X_100 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_88_snoc__eq__iff__butlast,axiom,
% 0.27/0.64 ! [Xs_146: list_nat,X_100: nat,Ys_32: list_nat] :
% 0.27/0.64 ( ( ( append_nat @ Xs_146 @ ( cons_nat @ X_100 @ nil_nat ) )
% 0.27/0.64 = Ys_32 )
% 0.27/0.64 <=> ( ( Ys_32 != nil_nat )
% 0.27/0.64 & ( ( butlast_nat @ Ys_32 )
% 0.27/0.64 = Xs_146 )
% 0.27/0.64 & ( ( last_nat @ Ys_32 )
% 0.27/0.64 = X_100 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_89_append__butlast__last__id,axiom,
% 0.27/0.64 ! [Xs_145: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_145 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( append179082452le_alt @ ( butlas274947851le_alt @ Xs_145 ) @ ( cons_A228743023le_alt @ ( last_A1217315288le_alt @ Xs_145 ) @ nil_Ar1286194111le_alt ) )
% 0.27/0.64 = Xs_145 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_90_append__butlast__last__id,axiom,
% 0.27/0.64 ! [Xs_145: list_nat] :
% 0.27/0.64 ( ( Xs_145 != nil_nat )
% 0.27/0.64 => ( ( append_nat @ ( butlast_nat @ Xs_145 ) @ ( cons_nat @ ( last_nat @ Xs_145 ) @ nil_nat ) )
% 0.27/0.64 = Xs_145 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_91_rotate__simps,axiom,
% 0.27/0.64 ! [X_99: arrow_475358991le_alt,Xs_144: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( rotate1_nat @ nil_nat )
% 0.27/0.64 = nil_nat )
% 0.27/0.64 & ( ( rotate335349260le_alt @ ( cons_A228743023le_alt @ X_99 @ Xs_144 ) )
% 0.27/0.64 = ( append179082452le_alt @ Xs_144 @ ( cons_A228743023le_alt @ X_99 @ nil_Ar1286194111le_alt ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_92_rotate__simps,axiom,
% 0.27/0.64 ! [X_99: arrow_475358991le_alt,Xs_144: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( rotate335349260le_alt @ nil_Ar1286194111le_alt )
% 0.27/0.64 = nil_Ar1286194111le_alt )
% 0.27/0.64 & ( ( rotate335349260le_alt @ ( cons_A228743023le_alt @ X_99 @ Xs_144 ) )
% 0.27/0.64 = ( append179082452le_alt @ Xs_144 @ ( cons_A228743023le_alt @ X_99 @ nil_Ar1286194111le_alt ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_93_rotate__simps,axiom,
% 0.27/0.64 ! [X_99: nat,Xs_144: list_nat] :
% 0.27/0.64 ( ( ( rotate335349260le_alt @ nil_Ar1286194111le_alt )
% 0.27/0.64 = nil_Ar1286194111le_alt )
% 0.27/0.64 & ( ( rotate1_nat @ ( cons_nat @ X_99 @ Xs_144 ) )
% 0.27/0.64 = ( append_nat @ Xs_144 @ ( cons_nat @ X_99 @ nil_nat ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_94_last__snoc,axiom,
% 0.27/0.64 ! [Xs_143: list_A2115238852le_alt,X_98: arrow_475358991le_alt] :
% 0.27/0.64 ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_143 @ ( cons_A228743023le_alt @ X_98 @ nil_Ar1286194111le_alt ) ) )
% 0.27/0.64 = X_98 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_95_last__snoc,axiom,
% 0.27/0.64 ! [Xs_143: list_nat,X_98: nat] :
% 0.27/0.64 ( ( last_nat @ ( append_nat @ Xs_143 @ ( cons_nat @ X_98 @ nil_nat ) ) )
% 0.27/0.64 = X_98 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_96_not__distinct__decomp,axiom,
% 0.27/0.64 ! [Ws: list_A2115238852le_alt] :
% 0.27/0.64 ( ~ ( distin236324274le_alt @ Ws )
% 0.27/0.64 => ? [Xs_54: list_A2115238852le_alt,Ys_5: list_A2115238852le_alt,Zs_1: list_A2115238852le_alt,Y_3: arrow_475358991le_alt] :
% 0.27/0.64 ( Ws
% 0.27/0.64 = ( append179082452le_alt @ Xs_54 @ ( append179082452le_alt @ ( cons_A228743023le_alt @ Y_3 @ nil_Ar1286194111le_alt ) @ ( append179082452le_alt @ Ys_5 @ ( append179082452le_alt @ ( cons_A228743023le_alt @ Y_3 @ nil_Ar1286194111le_alt ) @ Zs_1 ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_97_not__distinct__decomp,axiom,
% 0.27/0.64 ! [Ws: list_nat] :
% 0.27/0.64 ( ~ ( distinct_nat @ Ws )
% 0.27/0.64 => ? [Xs_54: list_nat,Ys_5: list_nat,Zs_1: list_nat,Y_3: nat] :
% 0.27/0.64 ( Ws
% 0.27/0.64 = ( append_nat @ Xs_54 @ ( append_nat @ ( cons_nat @ Y_3 @ nil_nat ) @ ( append_nat @ Ys_5 @ ( append_nat @ ( cons_nat @ Y_3 @ nil_nat ) @ Zs_1 ) ) ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_98_replicate__append__same,axiom,
% 0.27/0.64 ! [I_28: nat,X_97: arrow_475358991le_alt] :
% 0.27/0.64 ( ( append179082452le_alt @ ( replic1511538809le_alt @ I_28 @ X_97 ) @ ( cons_A228743023le_alt @ X_97 @ nil_Ar1286194111le_alt ) )
% 0.27/0.64 = ( cons_A228743023le_alt @ X_97 @ ( replic1511538809le_alt @ I_28 @ X_97 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_99_replicate__append__same,axiom,
% 0.27/0.64 ! [I_28: nat,X_97: nat] :
% 0.27/0.64 ( ( append_nat @ ( replicate_nat @ I_28 @ X_97 ) @ ( cons_nat @ X_97 @ nil_nat ) )
% 0.27/0.64 = ( cons_nat @ X_97 @ ( replicate_nat @ I_28 @ X_97 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_100_rev_Osimps_I2_J,axiom,
% 0.27/0.64 ! [X_96: arrow_475358991le_alt,Xs_142: list_A2115238852le_alt] :
% 0.27/0.64 ( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X_96 @ Xs_142 ) )
% 0.27/0.64 = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ Xs_142 ) @ ( cons_A228743023le_alt @ X_96 @ nil_Ar1286194111le_alt ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_101_rev_Osimps_I2_J,axiom,
% 0.27/0.64 ! [X_96: nat,Xs_142: list_nat] :
% 0.27/0.64 ( ( rev_nat @ ( cons_nat @ X_96 @ Xs_142 ) )
% 0.27/0.64 = ( append_nat @ ( rev_nat @ Xs_142 ) @ ( cons_nat @ X_96 @ nil_nat ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_102_rev__is__rev__conv,axiom,
% 0.27/0.64 ! [Xs_141: list_nat,Ys_31: list_nat] :
% 0.27/0.64 ( ( ( rev_nat @ Xs_141 )
% 0.27/0.64 = ( rev_nat @ Ys_31 ) )
% 0.27/0.64 <=> ( Xs_141 = Ys_31 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_103_rev__is__rev__conv,axiom,
% 0.27/0.64 ! [Xs_141: list_A2115238852le_alt,Ys_31: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( rev_Ar1106406943le_alt @ Xs_141 )
% 0.27/0.64 = ( rev_Ar1106406943le_alt @ Ys_31 ) )
% 0.27/0.64 <=> ( Xs_141 = Ys_31 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_104_rev__swap,axiom,
% 0.27/0.64 ! [Xs_140: list_nat,Ys_30: list_nat] :
% 0.27/0.64 ( ( ( rev_nat @ Xs_140 )
% 0.27/0.64 = Ys_30 )
% 0.27/0.64 <=> ( Xs_140
% 0.27/0.64 = ( rev_nat @ Ys_30 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_105_rev__swap,axiom,
% 0.27/0.64 ! [Xs_140: list_A2115238852le_alt,Ys_30: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( rev_Ar1106406943le_alt @ Xs_140 )
% 0.27/0.64 = Ys_30 )
% 0.27/0.64 <=> ( Xs_140
% 0.27/0.64 = ( rev_Ar1106406943le_alt @ Ys_30 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_106_rev__replicate,axiom,
% 0.27/0.64 ! [N_53: nat,X_95: nat] :
% 0.27/0.64 ( ( rev_nat @ ( replicate_nat @ N_53 @ X_95 ) )
% 0.27/0.64 = ( replicate_nat @ N_53 @ X_95 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_107_rev__replicate,axiom,
% 0.27/0.64 ! [N_53: nat,X_95: arrow_475358991le_alt] :
% 0.27/0.64 ( ( rev_Ar1106406943le_alt @ ( replic1511538809le_alt @ N_53 @ X_95 ) )
% 0.27/0.64 = ( replic1511538809le_alt @ N_53 @ X_95 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_108_rev__rev__ident,axiom,
% 0.27/0.64 ! [Xs_139: list_nat] :
% 0.27/0.64 ( ( rev_nat @ ( rev_nat @ Xs_139 ) )
% 0.27/0.64 = Xs_139 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_109_rev__rev__ident,axiom,
% 0.27/0.64 ! [Xs_139: list_A2115238852le_alt] :
% 0.27/0.64 ( ( rev_Ar1106406943le_alt @ ( rev_Ar1106406943le_alt @ Xs_139 ) )
% 0.27/0.64 = Xs_139 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_110_equal__list__def,axiom,
% 0.27/0.64 ! [X_94: list_A2115238852le_alt,Y_41: list_A2115238852le_alt] :
% 0.27/0.64 ( ( equal_484611810le_alt @ X_94 @ Y_41 )
% 0.27/0.64 <=> ( X_94 = Y_41 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_111_rev__is__Nil__conv,axiom,
% 0.27/0.64 ! [Xs_138: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( rev_Ar1106406943le_alt @ Xs_138 )
% 0.27/0.64 = nil_Ar1286194111le_alt )
% 0.27/0.64 <=> ( Xs_138 = nil_Ar1286194111le_alt ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_112_rev__is__Nil__conv,axiom,
% 0.27/0.64 ! [Xs_138: list_nat] :
% 0.27/0.64 ( ( ( rev_nat @ Xs_138 )
% 0.27/0.64 = nil_nat )
% 0.27/0.64 <=> ( Xs_138 = nil_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_113_Nil__is__rev__conv,axiom,
% 0.27/0.64 ! [Xs_137: list_A2115238852le_alt] :
% 0.27/0.64 ( ( nil_Ar1286194111le_alt
% 0.27/0.64 = ( rev_Ar1106406943le_alt @ Xs_137 ) )
% 0.27/0.64 <=> ( Xs_137 = nil_Ar1286194111le_alt ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_114_Nil__is__rev__conv,axiom,
% 0.27/0.64 ! [Xs_137: list_nat] :
% 0.27/0.64 ( ( nil_nat
% 0.27/0.64 = ( rev_nat @ Xs_137 ) )
% 0.27/0.64 <=> ( Xs_137 = nil_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_115_rev_Osimps_I1_J,axiom,
% 0.27/0.64 ( ( rev_Ar1106406943le_alt @ nil_Ar1286194111le_alt )
% 0.27/0.64 = nil_Ar1286194111le_alt ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_116_rev_Osimps_I1_J,axiom,
% 0.27/0.64 ( ( rev_nat @ nil_nat )
% 0.27/0.64 = nil_nat ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_117_rev__append,axiom,
% 0.27/0.64 ! [Xs_136: list_nat,Ys_29: list_nat] :
% 0.27/0.64 ( ( rev_nat @ ( append_nat @ Xs_136 @ Ys_29 ) )
% 0.27/0.64 = ( append_nat @ ( rev_nat @ Ys_29 ) @ ( rev_nat @ Xs_136 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_118_rev__append,axiom,
% 0.27/0.64 ! [Xs_136: list_A2115238852le_alt,Ys_29: list_A2115238852le_alt] :
% 0.27/0.64 ( ( rev_Ar1106406943le_alt @ ( append179082452le_alt @ Xs_136 @ Ys_29 ) )
% 0.27/0.64 = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ Ys_29 ) @ ( rev_Ar1106406943le_alt @ Xs_136 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_119_distinct__rev,axiom,
% 0.27/0.64 ! [Xs_135: list_A2115238852le_alt] :
% 0.27/0.64 ( ( distin236324274le_alt @ ( rev_Ar1106406943le_alt @ Xs_135 ) )
% 0.27/0.64 <=> ( distin236324274le_alt @ Xs_135 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_120_distinct__rev,axiom,
% 0.27/0.64 ! [Xs_135: list_nat] :
% 0.27/0.64 ( ( distinct_nat @ ( rev_nat @ Xs_135 ) )
% 0.27/0.64 <=> ( distinct_nat @ Xs_135 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_121_append__replicate__commute,axiom,
% 0.27/0.64 ! [N_52: nat,X_93: arrow_475358991le_alt,K_8: nat] :
% 0.27/0.64 ( ( append179082452le_alt @ ( replic1511538809le_alt @ N_52 @ X_93 ) @ ( replic1511538809le_alt @ K_8 @ X_93 ) )
% 0.27/0.64 = ( append179082452le_alt @ ( replic1511538809le_alt @ K_8 @ X_93 ) @ ( replic1511538809le_alt @ N_52 @ X_93 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_122_rotate1__is__Nil__conv,axiom,
% 0.27/0.64 ! [Xs_134: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( rotate335349260le_alt @ Xs_134 )
% 0.27/0.64 = nil_Ar1286194111le_alt )
% 0.27/0.64 <=> ( Xs_134 = nil_Ar1286194111le_alt ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_123_rotate1__is__Nil__conv,axiom,
% 0.27/0.64 ! [Xs_134: list_nat] :
% 0.27/0.64 ( ( ( rotate1_nat @ Xs_134 )
% 0.27/0.64 = nil_nat )
% 0.27/0.64 <=> ( Xs_134 = nil_nat ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_124_mem__def,axiom,
% 0.27/0.64 ! [X_92: nat,A_87: nat > $o] :
% 0.27/0.64 ( ( member_nat @ X_92 @ A_87 )
% 0.27/0.64 <=> ( A_87 @ X_92 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_125_mem__def,axiom,
% 0.27/0.64 ! [X_92: int,A_87: int > $o] :
% 0.27/0.64 ( ( member_int @ X_92 @ A_87 )
% 0.27/0.64 <=> ( A_87 @ X_92 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_126_Collect__def,axiom,
% 0.27/0.64 ! [P_31: nat > $o] :
% 0.27/0.64 ( ( collect_nat @ P_31 )
% 0.27/0.64 = P_31 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_127_distinct1__rotate,axiom,
% 0.27/0.64 ! [Xs_133: list_A2115238852le_alt] :
% 0.27/0.64 ( ( distin236324274le_alt @ ( rotate335349260le_alt @ Xs_133 ) )
% 0.27/0.64 <=> ( distin236324274le_alt @ Xs_133 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_128_singleton__rev__conv,axiom,
% 0.27/0.64 ! [X_91: arrow_475358991le_alt,Xs_132: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( cons_A228743023le_alt @ X_91 @ nil_Ar1286194111le_alt )
% 0.27/0.64 = ( rev_Ar1106406943le_alt @ Xs_132 ) )
% 0.27/0.64 <=> ( Xs_132
% 0.27/0.64 = ( cons_A228743023le_alt @ X_91 @ nil_Ar1286194111le_alt ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_129_singleton__rev__conv,axiom,
% 0.27/0.64 ! [X_91: nat,Xs_132: list_nat] :
% 0.27/0.64 ( ( ( cons_nat @ X_91 @ nil_nat )
% 0.27/0.64 = ( rev_nat @ Xs_132 ) )
% 0.27/0.64 <=> ( Xs_132
% 0.27/0.64 = ( cons_nat @ X_91 @ nil_nat ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_130_rev__singleton__conv,axiom,
% 0.27/0.64 ! [Xs_131: list_A2115238852le_alt,X_90: arrow_475358991le_alt] :
% 0.27/0.64 ( ( ( rev_Ar1106406943le_alt @ Xs_131 )
% 0.27/0.64 = ( cons_A228743023le_alt @ X_90 @ nil_Ar1286194111le_alt ) )
% 0.27/0.64 <=> ( Xs_131
% 0.27/0.64 = ( cons_A228743023le_alt @ X_90 @ nil_Ar1286194111le_alt ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_131_rev__singleton__conv,axiom,
% 0.27/0.64 ! [Xs_131: list_nat,X_90: nat] :
% 0.27/0.64 ( ( ( rev_nat @ Xs_131 )
% 0.27/0.64 = ( cons_nat @ X_90 @ nil_nat ) )
% 0.27/0.64 <=> ( Xs_131
% 0.27/0.64 = ( cons_nat @ X_90 @ nil_nat ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_132_replicate__app__Cons__same,axiom,
% 0.27/0.64 ! [N_51: nat,X_89: arrow_475358991le_alt,Xs_130: list_A2115238852le_alt] :
% 0.27/0.64 ( ( append179082452le_alt @ ( replic1511538809le_alt @ N_51 @ X_89 ) @ ( cons_A228743023le_alt @ X_89 @ Xs_130 ) )
% 0.27/0.64 = ( cons_A228743023le_alt @ X_89 @ ( append179082452le_alt @ ( replic1511538809le_alt @ N_51 @ X_89 ) @ Xs_130 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_133_last__ConsL,axiom,
% 0.27/0.64 ! [X_88: arrow_475358991le_alt,Xs_129: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_129 = nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X_88 @ Xs_129 ) )
% 0.27/0.64 = X_88 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_134_last__ConsL,axiom,
% 0.27/0.64 ! [X_88: nat,Xs_129: list_nat] :
% 0.27/0.64 ( ( Xs_129 = nil_nat )
% 0.27/0.64 => ( ( last_nat @ ( cons_nat @ X_88 @ Xs_129 ) )
% 0.27/0.64 = X_88 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_135_last__ConsR,axiom,
% 0.27/0.64 ! [X_87: arrow_475358991le_alt,Xs_128: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_128 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X_87 @ Xs_128 ) )
% 0.27/0.64 = ( last_A1217315288le_alt @ Xs_128 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_136_last__ConsR,axiom,
% 0.27/0.64 ! [X_87: nat,Xs_128: list_nat] :
% 0.27/0.64 ( ( Xs_128 != nil_nat )
% 0.27/0.64 => ( ( last_nat @ ( cons_nat @ X_87 @ Xs_128 ) )
% 0.27/0.64 = ( last_nat @ Xs_128 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_137_last_Osimps,axiom,
% 0.27/0.64 ! [X_86: arrow_475358991le_alt,Xs_127: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( Xs_127 = nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X_86 @ Xs_127 ) )
% 0.27/0.64 = X_86 ) )
% 0.27/0.64 & ( ( Xs_127 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( last_A1217315288le_alt @ ( cons_A228743023le_alt @ X_86 @ Xs_127 ) )
% 0.27/0.64 = ( last_A1217315288le_alt @ Xs_127 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_138_last_Osimps,axiom,
% 0.27/0.64 ! [X_86: nat,Xs_127: list_nat] :
% 0.27/0.64 ( ( ( Xs_127 = nil_nat )
% 0.27/0.64 => ( ( last_nat @ ( cons_nat @ X_86 @ Xs_127 ) )
% 0.27/0.64 = X_86 ) )
% 0.27/0.64 & ( ( Xs_127 != nil_nat )
% 0.27/0.64 => ( ( last_nat @ ( cons_nat @ X_86 @ Xs_127 ) )
% 0.27/0.64 = ( last_nat @ Xs_127 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_139_last__append,axiom,
% 0.27/0.64 ! [Xs_126: list_A2115238852le_alt,Ys_28: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( Ys_28 = nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_126 @ Ys_28 ) )
% 0.27/0.64 = ( last_A1217315288le_alt @ Xs_126 ) ) )
% 0.27/0.64 & ( ( Ys_28 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_126 @ Ys_28 ) )
% 0.27/0.64 = ( last_A1217315288le_alt @ Ys_28 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_140_last__append,axiom,
% 0.27/0.64 ! [Xs_126: list_nat,Ys_28: list_nat] :
% 0.27/0.64 ( ( ( Ys_28 = nil_nat )
% 0.27/0.64 => ( ( last_nat @ ( append_nat @ Xs_126 @ Ys_28 ) )
% 0.27/0.64 = ( last_nat @ Xs_126 ) ) )
% 0.27/0.64 & ( ( Ys_28 != nil_nat )
% 0.27/0.64 => ( ( last_nat @ ( append_nat @ Xs_126 @ Ys_28 ) )
% 0.27/0.64 = ( last_nat @ Ys_28 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_141_last__appendR,axiom,
% 0.27/0.64 ! [Xs_125: list_A2115238852le_alt,Ys_27: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Ys_27 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_125 @ Ys_27 ) )
% 0.27/0.64 = ( last_A1217315288le_alt @ Ys_27 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_142_last__appendR,axiom,
% 0.27/0.64 ! [Xs_125: list_nat,Ys_27: list_nat] :
% 0.27/0.64 ( ( Ys_27 != nil_nat )
% 0.27/0.64 => ( ( last_nat @ ( append_nat @ Xs_125 @ Ys_27 ) )
% 0.27/0.64 = ( last_nat @ Ys_27 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_143_last__appendL,axiom,
% 0.27/0.64 ! [Xs_124: list_A2115238852le_alt,Ys_26: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Ys_26 = nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_124 @ Ys_26 ) )
% 0.27/0.64 = ( last_A1217315288le_alt @ Xs_124 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_144_last__appendL,axiom,
% 0.27/0.64 ! [Xs_124: list_nat,Ys_26: list_nat] :
% 0.27/0.64 ( ( Ys_26 = nil_nat )
% 0.27/0.64 => ( ( last_nat @ ( append_nat @ Xs_124 @ Ys_26 ) )
% 0.27/0.64 = ( last_nat @ Xs_124 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_145_rev__eq__Cons__iff,axiom,
% 0.27/0.64 ! [Xs_123: list_A2115238852le_alt,Y_40: arrow_475358991le_alt,Ys_25: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( rev_Ar1106406943le_alt @ Xs_123 )
% 0.27/0.64 = ( cons_A228743023le_alt @ Y_40 @ Ys_25 ) )
% 0.27/0.64 <=> ( Xs_123
% 0.27/0.64 = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ Ys_25 ) @ ( cons_A228743023le_alt @ Y_40 @ nil_Ar1286194111le_alt ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_146_rev__eq__Cons__iff,axiom,
% 0.27/0.64 ! [Xs_123: list_nat,Y_40: nat,Ys_25: list_nat] :
% 0.27/0.64 ( ( ( rev_nat @ Xs_123 )
% 0.27/0.64 = ( cons_nat @ Y_40 @ Ys_25 ) )
% 0.27/0.64 <=> ( Xs_123
% 0.27/0.64 = ( append_nat @ ( rev_nat @ Ys_25 ) @ ( cons_nat @ Y_40 @ nil_nat ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_147_last__rev,axiom,
% 0.27/0.64 ! [Xs_122: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_122 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( last_A1217315288le_alt @ ( rev_Ar1106406943le_alt @ Xs_122 ) )
% 0.27/0.64 = ( hd_Arr1965683346le_alt @ Xs_122 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_148_last__rev,axiom,
% 0.27/0.64 ! [Xs_122: list_nat] :
% 0.27/0.64 ( ( Xs_122 != nil_nat )
% 0.27/0.64 => ( ( last_nat @ ( rev_nat @ Xs_122 ) )
% 0.27/0.64 = ( hd_nat @ Xs_122 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_149_hd__rev,axiom,
% 0.27/0.64 ! [Xs_121: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_121 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( hd_Arr1965683346le_alt @ ( rev_Ar1106406943le_alt @ Xs_121 ) )
% 0.27/0.64 = ( last_A1217315288le_alt @ Xs_121 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_150_hd__rev,axiom,
% 0.27/0.64 ! [Xs_121: list_nat] :
% 0.27/0.64 ( ( Xs_121 != nil_nat )
% 0.27/0.64 => ( ( hd_nat @ ( rev_nat @ Xs_121 ) )
% 0.27/0.64 = ( last_nat @ Xs_121 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_151_equal,axiom,
% 0.27/0.64 equal_484611810le_alt = fequal781288069le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(fact_152_equal__refl,axiom,
% 0.27/0.64 ! [X_85: list_A2115238852le_alt] : ( equal_484611810le_alt @ X_85 @ X_85 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_153_equal__eq,axiom,
% 0.27/0.64 ! [X_84: list_A2115238852le_alt,Y_39: list_A2115238852le_alt] :
% 0.27/0.64 ( ( equal_484611810le_alt @ X_84 @ Y_39 )
% 0.27/0.64 <=> ( X_84 = Y_39 ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_154_eq__equal,axiom,
% 0.27/0.64 fequal781288069le_alt = equal_484611810le_alt ).
% 0.27/0.64
% 0.27/0.64 thf(fact_155_hd__append,axiom,
% 0.27/0.64 ! [Ys_24: list_A2115238852le_alt,Xs_120: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( Xs_120 = nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( hd_Arr1965683346le_alt @ ( append179082452le_alt @ Xs_120 @ Ys_24 ) )
% 0.27/0.64 = ( hd_Arr1965683346le_alt @ Ys_24 ) ) )
% 0.27/0.64 & ( ( Xs_120 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( hd_Arr1965683346le_alt @ ( append179082452le_alt @ Xs_120 @ Ys_24 ) )
% 0.27/0.64 = ( hd_Arr1965683346le_alt @ Xs_120 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_156_hd__append,axiom,
% 0.27/0.64 ! [Ys_24: list_nat,Xs_120: list_nat] :
% 0.27/0.64 ( ( ( Xs_120 = nil_nat )
% 0.27/0.64 => ( ( hd_nat @ ( append_nat @ Xs_120 @ Ys_24 ) )
% 0.27/0.64 = ( hd_nat @ Ys_24 ) ) )
% 0.27/0.64 & ( ( Xs_120 != nil_nat )
% 0.27/0.64 => ( ( hd_nat @ ( append_nat @ Xs_120 @ Ys_24 ) )
% 0.27/0.64 = ( hd_nat @ Xs_120 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_157_hd__append2,axiom,
% 0.27/0.64 ! [Ys_23: list_A2115238852le_alt,Xs_119: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_119 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( hd_Arr1965683346le_alt @ ( append179082452le_alt @ Xs_119 @ Ys_23 ) )
% 0.27/0.64 = ( hd_Arr1965683346le_alt @ Xs_119 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_158_hd__append2,axiom,
% 0.27/0.64 ! [Ys_23: list_nat,Xs_119: list_nat] :
% 0.27/0.64 ( ( Xs_119 != nil_nat )
% 0.27/0.64 => ( ( hd_nat @ ( append_nat @ Xs_119 @ Ys_23 ) )
% 0.27/0.64 = ( hd_nat @ Xs_119 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_159_rotate1__hd__tl,axiom,
% 0.27/0.64 ! [Xs_118: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_118 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( rotate335349260le_alt @ Xs_118 )
% 0.27/0.64 = ( append179082452le_alt @ ( tl_Arr465451158le_alt @ Xs_118 ) @ ( cons_A228743023le_alt @ ( hd_Arr1965683346le_alt @ Xs_118 ) @ nil_Ar1286194111le_alt ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_160_rotate1__hd__tl,axiom,
% 0.27/0.64 ! [Xs_118: list_nat] :
% 0.27/0.64 ( ( Xs_118 != nil_nat )
% 0.27/0.64 => ( ( rotate1_nat @ Xs_118 )
% 0.27/0.64 = ( append_nat @ ( tl_nat @ Xs_118 ) @ ( cons_nat @ ( hd_nat @ Xs_118 ) @ nil_nat ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_161_tl_Osimps_I2_J,axiom,
% 0.27/0.64 ! [X_83: arrow_475358991le_alt,Xs_117: list_A2115238852le_alt] :
% 0.27/0.64 ( ( tl_Arr465451158le_alt @ ( cons_A228743023le_alt @ X_83 @ Xs_117 ) )
% 0.27/0.64 = Xs_117 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_162_tl_Osimps_I1_J,axiom,
% 0.27/0.64 ( ( tl_Arr465451158le_alt @ nil_Ar1286194111le_alt )
% 0.27/0.64 = nil_Ar1286194111le_alt ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_163_tl_Osimps_I1_J,axiom,
% 0.27/0.64 ( ( tl_nat @ nil_nat )
% 0.27/0.64 = nil_nat ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_164_hd_Osimps,axiom,
% 0.27/0.64 ! [X_82: arrow_475358991le_alt,Xs_116: list_A2115238852le_alt] :
% 0.27/0.64 ( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X_82 @ Xs_116 ) )
% 0.27/0.64 = X_82 ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_165_distinct__tl,axiom,
% 0.27/0.64 ! [Xs_115: list_A2115238852le_alt] :
% 0.27/0.64 ( ( distin236324274le_alt @ Xs_115 )
% 0.27/0.64 => ( distin236324274le_alt @ ( tl_Arr465451158le_alt @ Xs_115 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_166_sorted__tl,axiom,
% 0.27/0.64 ! [Xs_114: list_nat] :
% 0.27/0.64 ( ( linorder_sorted_nat @ Xs_114 )
% 0.27/0.64 => ( linorder_sorted_nat @ ( tl_nat @ Xs_114 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_167_tl__append2,axiom,
% 0.27/0.64 ! [Ys_22: list_A2115238852le_alt,Xs_113: list_A2115238852le_alt] :
% 0.27/0.64 ( ( Xs_113 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ( ( tl_Arr465451158le_alt @ ( append179082452le_alt @ Xs_113 @ Ys_22 ) )
% 0.27/0.64 = ( append179082452le_alt @ ( tl_Arr465451158le_alt @ Xs_113 ) @ Ys_22 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_168_tl__append2,axiom,
% 0.27/0.64 ! [Ys_22: list_nat,Xs_113: list_nat] :
% 0.27/0.64 ( ( Xs_113 != nil_nat )
% 0.27/0.64 => ( ( tl_nat @ ( append_nat @ Xs_113 @ Ys_22 ) )
% 0.27/0.64 = ( append_nat @ ( tl_nat @ Xs_113 ) @ Ys_22 ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_169_hd__dropWhile,axiom,
% 0.27/0.64 ! [P_30: arrow_475358991le_alt > $o,Xs_112: list_A2115238852le_alt] :
% 0.27/0.64 ( ( ( dropWh1316781920le_alt @ P_30 @ Xs_112 )
% 0.27/0.64 != nil_Ar1286194111le_alt )
% 0.27/0.64 => ~ ( P_30 @ ( hd_Arr1965683346le_alt @ ( dropWh1316781920le_alt @ P_30 @ Xs_112 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_170_hd__dropWhile,axiom,
% 0.27/0.64 ! [P_30: nat > $o,Xs_112: list_nat] :
% 0.27/0.64 ( ( ( dropWhile_nat @ P_30 @ Xs_112 )
% 0.27/0.64 != nil_nat )
% 0.27/0.64 => ~ ( P_30 @ ( hd_nat @ ( dropWhile_nat @ P_30 @ Xs_112 ) ) ) ) ).
% 0.27/0.64
% 0.27/0.64 thf(fact_171_member__rec_I2_J,axiom,
% 0.27/0.64 ! [Y_38: arrow_475358991le_alt] :
% 0.27/0.65 ~ ( member1504968148le_alt @ nil_Ar1286194111le_alt @ Y_38 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_172_member__rec_I2_J,axiom,
% 0.27/0.65 ! [Y_38: nat] :
% 0.27/0.65 ~ ( member_nat_1 @ nil_nat @ Y_38 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_173_list__ex1__simps_I1_J,axiom,
% 0.27/0.65 ! [P_29: arrow_475358991le_alt > $o] :
% 0.27/0.65 ~ ( list_e239244930le_alt @ P_29 @ nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_174_list__ex1__simps_I1_J,axiom,
% 0.27/0.65 ! [P_29: nat > $o] :
% 0.27/0.65 ~ ( list_ex1_nat @ P_29 @ nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_175_elem,axiom,
% 0.27/0.65 ! [X_81: arrow_475358991le_alt,Xs_111: list_A2115238852le_alt] : ( listMe78047147le_alt @ X_81 @ ( cons_A228743023le_alt @ X_81 @ Xs_111 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_176_member__rec_I1_J,axiom,
% 0.27/0.65 ! [X_80: arrow_475358991le_alt,Xs_110: list_A2115238852le_alt,Y_37: arrow_475358991le_alt] :
% 0.27/0.65 ( ( member1504968148le_alt @ ( cons_A228743023le_alt @ X_80 @ Xs_110 ) @ Y_37 )
% 0.27/0.65 <=> ( ( X_80 = Y_37 )
% 0.27/0.65 | ( member1504968148le_alt @ Xs_110 @ Y_37 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_177_insert,axiom,
% 0.27/0.65 ! [Y_36: arrow_475358991le_alt,X_79: arrow_475358991le_alt,Xs_109: list_A2115238852le_alt] :
% 0.27/0.65 ( ( listMe78047147le_alt @ X_79 @ Xs_109 )
% 0.27/0.65 => ( listMe78047147le_alt @ X_79 @ ( cons_A228743023le_alt @ Y_36 @ Xs_109 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_178_hd__replicate,axiom,
% 0.27/0.65 ! [X_78: arrow_475358991le_alt,N_50: nat] :
% 0.27/0.65 ( ( N_50 != zero_zero_nat )
% 0.27/0.65 => ( ( hd_Arr1965683346le_alt @ ( replic1511538809le_alt @ N_50 @ X_78 ) )
% 0.27/0.65 = X_78 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_179_last__replicate,axiom,
% 0.27/0.65 ! [X_77: arrow_475358991le_alt,N_49: nat] :
% 0.27/0.65 ( ( N_49 != zero_zero_nat )
% 0.27/0.65 => ( ( last_A1217315288le_alt @ ( replic1511538809le_alt @ N_49 @ X_77 ) )
% 0.27/0.65 = X_77 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_180_replicate__eq__replicate,axiom,
% 0.27/0.65 ! [M_5: nat,X_76: arrow_475358991le_alt,N_48: nat,Y_35: arrow_475358991le_alt] :
% 0.27/0.65 ( ( ( replic1511538809le_alt @ M_5 @ X_76 )
% 0.27/0.65 = ( replic1511538809le_alt @ N_48 @ Y_35 ) )
% 0.27/0.65 <=> ( ( M_5 = N_48 )
% 0.27/0.65 & ( ( M_5 != zero_zero_nat )
% 0.27/0.65 => ( X_76 = Y_35 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_181_dropWhile_Osimps_I2_J,axiom,
% 0.27/0.65 ! [Xs_108: list_A2115238852le_alt,P_28: arrow_475358991le_alt > $o,X_75: arrow_475358991le_alt] :
% 0.27/0.65 ( ( ( P_28 @ X_75 )
% 0.27/0.65 => ( ( dropWh1316781920le_alt @ P_28 @ ( cons_A228743023le_alt @ X_75 @ Xs_108 ) )
% 0.27/0.65 = ( dropWh1316781920le_alt @ P_28 @ Xs_108 ) ) )
% 0.27/0.65 & ( ~ ( P_28 @ X_75 )
% 0.27/0.65 => ( ( dropWh1316781920le_alt @ P_28 @ ( cons_A228743023le_alt @ X_75 @ Xs_108 ) )
% 0.27/0.65 = ( cons_A228743023le_alt @ X_75 @ Xs_108 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_182_dropWhile_Osimps_I1_J,axiom,
% 0.27/0.65 ! [P_27: arrow_475358991le_alt > $o] :
% 0.27/0.65 ( ( dropWh1316781920le_alt @ P_27 @ nil_Ar1286194111le_alt )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_183_dropWhile_Osimps_I1_J,axiom,
% 0.27/0.65 ! [P_27: nat > $o] :
% 0.27/0.65 ( ( dropWhile_nat @ P_27 @ nil_nat )
% 0.27/0.65 = nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_184_distinct__dropWhile,axiom,
% 0.27/0.65 ! [P_26: arrow_475358991le_alt > $o,Xs_107: list_A2115238852le_alt] :
% 0.27/0.65 ( ( distin236324274le_alt @ Xs_107 )
% 0.27/0.65 => ( distin236324274le_alt @ ( dropWh1316781920le_alt @ P_26 @ Xs_107 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_185_sorted__dropWhile,axiom,
% 0.27/0.65 ! [P_25: nat > $o,Xs_106: list_nat] :
% 0.27/0.65 ( ( linorder_sorted_nat @ Xs_106 )
% 0.27/0.65 => ( linorder_sorted_nat @ ( dropWhile_nat @ P_25 @ Xs_106 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_186_replicate__0,axiom,
% 0.27/0.65 ! [X_74: arrow_475358991le_alt] :
% 0.27/0.65 ( ( replic1511538809le_alt @ zero_zero_nat @ X_74 )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_187_replicate__0,axiom,
% 0.27/0.65 ! [X_74: nat] :
% 0.27/0.65 ( ( replicate_nat @ zero_zero_nat @ X_74 )
% 0.27/0.65 = nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_188_empty__replicate,axiom,
% 0.27/0.65 ! [N_47: nat,X_73: arrow_475358991le_alt] :
% 0.27/0.65 ( ( nil_Ar1286194111le_alt
% 0.27/0.65 = ( replic1511538809le_alt @ N_47 @ X_73 ) )
% 0.27/0.65 <=> ( N_47 = zero_zero_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_189_empty__replicate,axiom,
% 0.27/0.65 ! [N_47: nat,X_73: nat] :
% 0.27/0.65 ( ( nil_nat
% 0.27/0.65 = ( replicate_nat @ N_47 @ X_73 ) )
% 0.27/0.65 <=> ( N_47 = zero_zero_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_190_replicate__empty,axiom,
% 0.27/0.65 ! [N_46: nat,X_72: arrow_475358991le_alt] :
% 0.27/0.65 ( ( ( replic1511538809le_alt @ N_46 @ X_72 )
% 0.27/0.65 = nil_Ar1286194111le_alt )
% 0.27/0.65 <=> ( N_46 = zero_zero_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_191_replicate__empty,axiom,
% 0.27/0.65 ! [N_46: nat,X_72: nat] :
% 0.27/0.65 ( ( ( replicate_nat @ N_46 @ X_72 )
% 0.27/0.65 = nil_nat )
% 0.27/0.65 <=> ( N_46 = zero_zero_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_192_sublist__singleton,axiom,
% 0.27/0.65 ! [X_71: arrow_475358991le_alt,A_86: nat > $o] :
% 0.27/0.65 ( ( ( member_nat @ zero_zero_nat @ A_86 )
% 0.27/0.65 => ( ( sublis2047953604le_alt @ ( cons_A228743023le_alt @ X_71 @ nil_Ar1286194111le_alt ) @ A_86 )
% 0.27/0.65 = ( cons_A228743023le_alt @ X_71 @ nil_Ar1286194111le_alt ) ) )
% 0.27/0.65 & ( ~ ( member_nat @ zero_zero_nat @ A_86 )
% 0.27/0.65 => ( ( sublis2047953604le_alt @ ( cons_A228743023le_alt @ X_71 @ nil_Ar1286194111le_alt ) @ A_86 )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_193_sublist__singleton,axiom,
% 0.27/0.65 ! [X_71: nat,A_86: nat > $o] :
% 0.27/0.65 ( ( ( member_nat @ zero_zero_nat @ A_86 )
% 0.27/0.65 => ( ( sublist_nat @ ( cons_nat @ X_71 @ nil_nat ) @ A_86 )
% 0.27/0.65 = ( cons_nat @ X_71 @ nil_nat ) ) )
% 0.27/0.65 & ( ~ ( member_nat @ zero_zero_nat @ A_86 )
% 0.27/0.65 => ( ( sublist_nat @ ( cons_nat @ X_71 @ nil_nat ) @ A_86 )
% 0.27/0.65 = nil_nat ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_194_dropWhile__eq__Cons__conv,axiom,
% 0.27/0.65 ! [P_24: arrow_475358991le_alt > $o,Xs_105: list_A2115238852le_alt,Y_34: arrow_475358991le_alt,Ys_21: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( dropWh1316781920le_alt @ P_24 @ Xs_105 )
% 0.27/0.65 = ( cons_A228743023le_alt @ Y_34 @ Ys_21 ) )
% 0.27/0.65 <=> ( ( Xs_105
% 0.27/0.65 = ( append179082452le_alt @ ( takeWh1696291512le_alt @ P_24 @ Xs_105 ) @ ( cons_A228743023le_alt @ Y_34 @ Ys_21 ) ) )
% 0.27/0.65 & ~ ( P_24 @ Y_34 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_195_list_Osize_I1_J,axiom,
% 0.27/0.65 ! [Fa_1: arrow_475358991le_alt > nat] :
% 0.27/0.65 ( ( list_s250295873le_alt @ Fa_1 @ nil_Ar1286194111le_alt )
% 0.27/0.65 = zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_196_list_Osize_I1_J,axiom,
% 0.27/0.65 ! [Fa_1: nat > nat] :
% 0.27/0.65 ( ( list_size_nat @ Fa_1 @ nil_nat )
% 0.27/0.65 = zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_197_ListMem_Osimps,axiom,
% 0.27/0.65 ! [A1_1: arrow_475358991le_alt,A2_1: list_A2115238852le_alt] :
% 0.27/0.65 ( ( listMe78047147le_alt @ A1_1 @ A2_1 )
% 0.27/0.65 <=> ( ? [X_1: arrow_475358991le_alt,Xs_54: list_A2115238852le_alt] :
% 0.27/0.65 ( ( A1_1 = X_1 )
% 0.27/0.65 & ( A2_1
% 0.27/0.65 = ( cons_A228743023le_alt @ X_1 @ Xs_54 ) ) )
% 0.27/0.65 | ? [X_1: arrow_475358991le_alt,Xs_54: list_A2115238852le_alt,Y_3: arrow_475358991le_alt] :
% 0.27/0.65 ( ( A1_1 = X_1 )
% 0.27/0.65 & ( A2_1
% 0.27/0.65 = ( cons_A228743023le_alt @ Y_3 @ Xs_54 ) )
% 0.27/0.65 & ( listMe78047147le_alt @ X_1 @ Xs_54 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_198_zero__reorient,axiom,
% 0.27/0.65 ! [X_70: int] :
% 0.27/0.65 ( ( zero_zero_int = X_70 )
% 0.27/0.65 <=> ( X_70 = zero_zero_int ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_199_zero__reorient,axiom,
% 0.27/0.65 ! [X_70: nat] :
% 0.27/0.65 ( ( zero_zero_nat = X_70 )
% 0.27/0.65 <=> ( X_70 = zero_zero_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_200_hd__conv__nth,axiom,
% 0.27/0.65 ! [Xs_104: list_nat] :
% 0.27/0.65 ( ( Xs_104 != nil_nat )
% 0.27/0.65 => ( ( hd_nat @ Xs_104 )
% 0.27/0.65 = ( nth_nat @ Xs_104 @ zero_zero_nat ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_201_hd__conv__nth,axiom,
% 0.27/0.65 ! [Xs_104: list_A2115238852le_alt] :
% 0.27/0.65 ( ( Xs_104 != nil_Ar1286194111le_alt )
% 0.27/0.65 => ( ( hd_Arr1965683346le_alt @ Xs_104 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Xs_104 @ zero_zero_nat ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_202_takeWhile_Osimps_I1_J,axiom,
% 0.27/0.65 ! [P_23: nat > $o] :
% 0.27/0.65 ( ( takeWhile_nat @ P_23 @ nil_nat )
% 0.27/0.65 = nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_203_takeWhile_Osimps_I1_J,axiom,
% 0.27/0.65 ! [P_23: arrow_475358991le_alt > $o] :
% 0.27/0.65 ( ( takeWh1696291512le_alt @ P_23 @ nil_Ar1286194111le_alt )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_204_distinct__takeWhile,axiom,
% 0.27/0.65 ! [P_22: arrow_475358991le_alt > $o,Xs_103: list_A2115238852le_alt] :
% 0.27/0.65 ( ( distin236324274le_alt @ Xs_103 )
% 0.27/0.65 => ( distin236324274le_alt @ ( takeWh1696291512le_alt @ P_22 @ Xs_103 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_205_sorted__takeWhile,axiom,
% 0.27/0.65 ! [P_21: nat > $o,Xs_102: list_nat] :
% 0.27/0.65 ( ( linorder_sorted_nat @ Xs_102 )
% 0.27/0.65 => ( linorder_sorted_nat @ ( takeWhile_nat @ P_21 @ Xs_102 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_206_sublist__nil,axiom,
% 0.27/0.65 ! [A_85: nat > $o] :
% 0.27/0.65 ( ( sublist_nat @ nil_nat @ A_85 )
% 0.27/0.65 = nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_207_sublist__nil,axiom,
% 0.27/0.65 ! [A_85: nat > $o] :
% 0.27/0.65 ( ( sublis2047953604le_alt @ nil_Ar1286194111le_alt @ A_85 )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_208_distinct__sublistI,axiom,
% 0.27/0.65 ! [I_27: nat > $o,Xs_101: list_A2115238852le_alt] :
% 0.27/0.65 ( ( distin236324274le_alt @ Xs_101 )
% 0.27/0.65 => ( distin236324274le_alt @ ( sublis2047953604le_alt @ Xs_101 @ I_27 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_209_nth__Cons__0,axiom,
% 0.27/0.65 ! [X_69: nat,Xs_100: list_nat] :
% 0.27/0.65 ( ( nth_nat @ ( cons_nat @ X_69 @ Xs_100 ) @ zero_zero_nat )
% 0.27/0.65 = X_69 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_210_nth__Cons__0,axiom,
% 0.27/0.65 ! [X_69: arrow_475358991le_alt,Xs_100: list_A2115238852le_alt] :
% 0.27/0.65 ( ( nth_Ar125878976le_alt @ ( cons_A228743023le_alt @ X_69 @ Xs_100 ) @ zero_zero_nat )
% 0.27/0.65 = X_69 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_211_takeWhile_Osimps_I2_J,axiom,
% 0.27/0.65 ! [Xs_99: list_nat,P_20: nat > $o,X_68: nat] :
% 0.27/0.65 ( ( ( P_20 @ X_68 )
% 0.27/0.65 => ( ( takeWhile_nat @ P_20 @ ( cons_nat @ X_68 @ Xs_99 ) )
% 0.27/0.65 = ( cons_nat @ X_68 @ ( takeWhile_nat @ P_20 @ Xs_99 ) ) ) )
% 0.27/0.65 & ( ~ ( P_20 @ X_68 )
% 0.27/0.65 => ( ( takeWhile_nat @ P_20 @ ( cons_nat @ X_68 @ Xs_99 ) )
% 0.27/0.65 = nil_nat ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_212_takeWhile_Osimps_I2_J,axiom,
% 0.27/0.65 ! [Xs_99: list_A2115238852le_alt,P_20: arrow_475358991le_alt > $o,X_68: arrow_475358991le_alt] :
% 0.27/0.65 ( ( ( P_20 @ X_68 )
% 0.27/0.65 => ( ( takeWh1696291512le_alt @ P_20 @ ( cons_A228743023le_alt @ X_68 @ Xs_99 ) )
% 0.27/0.65 = ( cons_A228743023le_alt @ X_68 @ ( takeWh1696291512le_alt @ P_20 @ Xs_99 ) ) ) )
% 0.27/0.65 & ( ~ ( P_20 @ X_68 )
% 0.27/0.65 => ( ( takeWh1696291512le_alt @ P_20 @ ( cons_A228743023le_alt @ X_68 @ Xs_99 ) )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_213_takeWhile__tail,axiom,
% 0.27/0.65 ! [Xs_98: list_A2115238852le_alt,L_1: list_A2115238852le_alt,P_19: arrow_475358991le_alt > $o,X_67: arrow_475358991le_alt] :
% 0.27/0.65 ( ~ ( P_19 @ X_67 )
% 0.27/0.65 => ( ( takeWh1696291512le_alt @ P_19 @ ( append179082452le_alt @ Xs_98 @ ( cons_A228743023le_alt @ X_67 @ L_1 ) ) )
% 0.27/0.65 = ( takeWh1696291512le_alt @ P_19 @ Xs_98 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_214_takeWhile__dropWhile__id,axiom,
% 0.27/0.65 ! [P_18: arrow_475358991le_alt > $o,Xs_97: list_A2115238852le_alt] :
% 0.27/0.65 ( ( append179082452le_alt @ ( takeWh1696291512le_alt @ P_18 @ Xs_97 ) @ ( dropWh1316781920le_alt @ P_18 @ Xs_97 ) )
% 0.27/0.65 = Xs_97 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_215_nth__append__length,axiom,
% 0.27/0.65 ! [Xs_96: list_nat,X_66: nat,Ys_20: list_nat] :
% 0.27/0.65 ( ( nth_nat @ ( append_nat @ Xs_96 @ ( cons_nat @ X_66 @ Ys_20 ) ) @ ( size_size_list_nat @ Xs_96 ) )
% 0.27/0.65 = X_66 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_216_nth__append__length,axiom,
% 0.27/0.65 ! [Xs_96: list_A2115238852le_alt,X_66: arrow_475358991le_alt,Ys_20: list_A2115238852le_alt] :
% 0.27/0.65 ( ( nth_Ar125878976le_alt @ ( append179082452le_alt @ Xs_96 @ ( cons_A228743023le_alt @ X_66 @ Ys_20 ) ) @ ( size_s1858781230le_alt @ Xs_96 ) )
% 0.27/0.65 = X_66 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_217_foldr__max__sorted,axiom,
% 0.27/0.65 ! [Y_33: int,Xs_95: list_int] :
% 0.27/0.65 ( ( linorder_sorted_int @ ( rev_int @ Xs_95 ) )
% 0.27/0.65 => ( ( ( Xs_95 = nil_int )
% 0.27/0.65 => ( ( foldr_int_int @ ord_max_int @ Xs_95 @ Y_33 )
% 0.27/0.65 = Y_33 ) )
% 0.27/0.65 & ( ( Xs_95 != nil_int )
% 0.27/0.65 => ( ( foldr_int_int @ ord_max_int @ Xs_95 @ Y_33 )
% 0.27/0.65 = ( ord_max_int @ ( nth_int @ Xs_95 @ zero_zero_nat ) @ Y_33 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_218_foldr__max__sorted,axiom,
% 0.27/0.65 ! [Y_33: nat,Xs_95: list_nat] :
% 0.27/0.65 ( ( linorder_sorted_nat @ ( rev_nat @ Xs_95 ) )
% 0.27/0.65 => ( ( ( Xs_95 = nil_nat )
% 0.27/0.65 => ( ( foldr_nat_nat @ ord_max_nat @ Xs_95 @ Y_33 )
% 0.27/0.65 = Y_33 ) )
% 0.27/0.65 & ( ( Xs_95 != nil_nat )
% 0.27/0.65 => ( ( foldr_nat_nat @ ord_max_nat @ Xs_95 @ Y_33 )
% 0.27/0.65 = ( ord_max_nat @ ( nth_nat @ Xs_95 @ zero_zero_nat ) @ Y_33 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_219_list__induct2_H,axiom,
% 0.27/0.65 ! [Xs_94: list_A2115238852le_alt,Ys_19: list_nat,P_17: list_A2115238852le_alt > list_nat > $o] :
% 0.27/0.65 ( ( P_17 @ nil_Ar1286194111le_alt @ nil_nat )
% 0.27/0.65 => ( ! [X_1: arrow_475358991le_alt,Xs_54: list_A2115238852le_alt] : ( P_17 @ ( cons_A228743023le_alt @ X_1 @ Xs_54 ) @ nil_nat )
% 0.27/0.65 => ( ! [Y_3: nat,Ys_5: list_nat] : ( P_17 @ nil_Ar1286194111le_alt @ ( cons_nat @ Y_3 @ Ys_5 ) )
% 0.27/0.65 => ( ! [X_1: arrow_475358991le_alt,Xs_54: list_A2115238852le_alt,Y_3: nat,Ys_5: list_nat] :
% 0.27/0.65 ( ( P_17 @ Xs_54 @ Ys_5 )
% 0.27/0.65 => ( P_17 @ ( cons_A228743023le_alt @ X_1 @ Xs_54 ) @ ( cons_nat @ Y_3 @ Ys_5 ) ) )
% 0.27/0.65 => ( P_17 @ Xs_94 @ Ys_19 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_220_list__induct2_H,axiom,
% 0.27/0.65 ! [Xs_94: list_nat,Ys_19: list_A2115238852le_alt,P_17: list_nat > list_A2115238852le_alt > $o] :
% 0.27/0.65 ( ( P_17 @ nil_nat @ nil_Ar1286194111le_alt )
% 0.27/0.65 => ( ! [X_1: nat,Xs_54: list_nat] : ( P_17 @ ( cons_nat @ X_1 @ Xs_54 ) @ nil_Ar1286194111le_alt )
% 0.27/0.65 => ( ! [Y_3: arrow_475358991le_alt,Ys_5: list_A2115238852le_alt] : ( P_17 @ nil_nat @ ( cons_A228743023le_alt @ Y_3 @ Ys_5 ) )
% 0.27/0.65 => ( ! [X_1: nat,Xs_54: list_nat,Y_3: arrow_475358991le_alt,Ys_5: list_A2115238852le_alt] :
% 0.27/0.65 ( ( P_17 @ Xs_54 @ Ys_5 )
% 0.27/0.65 => ( P_17 @ ( cons_nat @ X_1 @ Xs_54 ) @ ( cons_A228743023le_alt @ Y_3 @ Ys_5 ) ) )
% 0.27/0.65 => ( P_17 @ Xs_94 @ Ys_19 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_221_map__filter__simps_I2_J,axiom,
% 0.27/0.65 ! [F_5: arrow_475358991le_alt > option_nat] :
% 0.27/0.65 ( ( map_fi312151301lt_nat @ F_5 @ nil_Ar1286194111le_alt )
% 0.27/0.65 = nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_222_map__filter__simps_I2_J,axiom,
% 0.27/0.65 ! [F_5: nat > option514678660le_alt] :
% 0.27/0.65 ( ( map_fi1462697295le_alt @ F_5 @ nil_nat )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_223_listrelp_ONil,axiom,
% 0.27/0.65 ! [R_2: nat > nat > $o] : ( listrelp_nat @ R_2 @ nil_nat @ nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_224_listrelp_ONil,axiom,
% 0.27/0.65 ! [R_2: arrow_475358991le_alt > arrow_475358991le_alt > $o] : ( listre1213162009le_alt @ R_2 @ nil_Ar1286194111le_alt @ nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_225_listrelp_OCons,axiom,
% 0.27/0.65 ! [Xs_93: list_A2115238852le_alt,Ys_18: list_A2115238852le_alt,R_1: arrow_475358991le_alt > arrow_475358991le_alt > $o,X_65: arrow_475358991le_alt,Y_32: arrow_475358991le_alt] :
% 0.27/0.65 ( ( R_1 @ X_65 @ Y_32 )
% 0.27/0.65 => ( ( listre1213162009le_alt @ R_1 @ Xs_93 @ Ys_18 )
% 0.27/0.65 => ( listre1213162009le_alt @ R_1 @ ( cons_A228743023le_alt @ X_65 @ Xs_93 ) @ ( cons_A228743023le_alt @ Y_32 @ Ys_18 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_226_sublist__empty,axiom,
% 0.27/0.65 ! [Xs_92: list_nat] :
% 0.27/0.65 ( ( sublist_nat @ Xs_92 @ bot_bot_nat_o )
% 0.27/0.65 = nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_227_sublist__empty,axiom,
% 0.27/0.65 ! [Xs_92: list_A2115238852le_alt] :
% 0.27/0.65 ( ( sublis2047953604le_alt @ Xs_92 @ bot_bot_nat_o )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_228_neq__if__length__neq,axiom,
% 0.27/0.65 ! [Xs_91: list_A2115238852le_alt,Ys_17: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( size_s1858781230le_alt @ Xs_91 )
% 0.27/0.65 != ( size_s1858781230le_alt @ Ys_17 ) )
% 0.27/0.65 => ( Xs_91 != Ys_17 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_229_length__rev,axiom,
% 0.27/0.65 ! [Xs_90: list_nat] :
% 0.27/0.65 ( ( size_size_list_nat @ ( rev_nat @ Xs_90 ) )
% 0.27/0.65 = ( size_size_list_nat @ Xs_90 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_230_length__rev,axiom,
% 0.27/0.65 ! [Xs_90: list_A2115238852le_alt] :
% 0.27/0.65 ( ( size_s1858781230le_alt @ ( rev_Ar1106406943le_alt @ Xs_90 ) )
% 0.27/0.65 = ( size_s1858781230le_alt @ Xs_90 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_231_length__replicate,axiom,
% 0.27/0.65 ! [N_45: nat,X_64: arrow_475358991le_alt] :
% 0.27/0.65 ( ( size_s1858781230le_alt @ ( replic1511538809le_alt @ N_45 @ X_64 ) )
% 0.27/0.65 = N_45 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_232_length__rotate1,axiom,
% 0.27/0.65 ! [Xs_89: list_A2115238852le_alt] :
% 0.27/0.65 ( ( size_s1858781230le_alt @ ( rotate335349260le_alt @ Xs_89 ) )
% 0.27/0.65 = ( size_s1858781230le_alt @ Xs_89 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_233_foldr_Osimps_I2_J,axiom,
% 0.27/0.65 ! [F_4: nat > nat > nat,X_63: nat,Xs_88: list_nat,A_84: nat] :
% 0.27/0.65 ( ( foldr_nat_nat @ F_4 @ ( cons_nat @ X_63 @ Xs_88 ) @ A_84 )
% 0.27/0.65 = ( F_4 @ X_63 @ ( foldr_nat_nat @ F_4 @ Xs_88 @ A_84 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_234_foldr_Osimps_I1_J,axiom,
% 0.27/0.65 ! [F_3: nat > nat > nat,A_83: nat] :
% 0.27/0.65 ( ( foldr_nat_nat @ F_3 @ nil_nat @ A_83 )
% 0.27/0.65 = A_83 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_235_foldr__append,axiom,
% 0.27/0.65 ! [F_2: nat > nat > nat,Xs_87: list_nat,Ys_16: list_nat,A_82: nat] :
% 0.27/0.65 ( ( foldr_nat_nat @ F_2 @ ( append_nat @ Xs_87 @ Ys_16 ) @ A_82 )
% 0.27/0.65 = ( foldr_nat_nat @ F_2 @ Xs_87 @ ( foldr_nat_nat @ F_2 @ Ys_16 @ A_82 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_236_length__0__conv,axiom,
% 0.27/0.65 ! [Xs_86: list_nat] :
% 0.27/0.65 ( ( ( size_size_list_nat @ Xs_86 )
% 0.27/0.65 = zero_zero_nat )
% 0.27/0.65 <=> ( Xs_86 = nil_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_237_length__0__conv,axiom,
% 0.27/0.65 ! [Xs_86: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( size_s1858781230le_alt @ Xs_86 )
% 0.27/0.65 = zero_zero_nat )
% 0.27/0.65 <=> ( Xs_86 = nil_Ar1286194111le_alt ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_238_list_Osize_I3_J,axiom,
% 0.27/0.65 ( ( size_size_list_nat @ nil_nat )
% 0.27/0.65 = zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_239_list_Osize_I3_J,axiom,
% 0.27/0.65 ( ( size_s1858781230le_alt @ nil_Ar1286194111le_alt )
% 0.27/0.65 = zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_240_list__induct2,axiom,
% 0.27/0.65 ! [P_16: list_A2115238852le_alt > list_nat > $o,Xs_85: list_A2115238852le_alt,Ys_15: list_nat] :
% 0.27/0.65 ( ( ( size_s1858781230le_alt @ Xs_85 )
% 0.27/0.65 = ( size_size_list_nat @ Ys_15 ) )
% 0.27/0.65 => ( ( P_16 @ nil_Ar1286194111le_alt @ nil_nat )
% 0.27/0.65 => ( ! [X_1: arrow_475358991le_alt,Xs_54: list_A2115238852le_alt,Y_3: nat,Ys_5: list_nat] :
% 0.27/0.65 ( ( ( size_s1858781230le_alt @ Xs_54 )
% 0.27/0.65 = ( size_size_list_nat @ Ys_5 ) )
% 0.27/0.65 => ( ( P_16 @ Xs_54 @ Ys_5 )
% 0.27/0.65 => ( P_16 @ ( cons_A228743023le_alt @ X_1 @ Xs_54 ) @ ( cons_nat @ Y_3 @ Ys_5 ) ) ) )
% 0.27/0.65 => ( P_16 @ Xs_85 @ Ys_15 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_241_list__induct2,axiom,
% 0.27/0.65 ! [P_16: list_nat > list_A2115238852le_alt > $o,Xs_85: list_nat,Ys_15: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( size_size_list_nat @ Xs_85 )
% 0.27/0.65 = ( size_s1858781230le_alt @ Ys_15 ) )
% 0.27/0.65 => ( ( P_16 @ nil_nat @ nil_Ar1286194111le_alt )
% 0.27/0.65 => ( ! [X_1: nat,Xs_54: list_nat,Y_3: arrow_475358991le_alt,Ys_5: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( size_size_list_nat @ Xs_54 )
% 0.27/0.65 = ( size_s1858781230le_alt @ Ys_5 ) )
% 0.27/0.65 => ( ( P_16 @ Xs_54 @ Ys_5 )
% 0.27/0.65 => ( P_16 @ ( cons_nat @ X_1 @ Xs_54 ) @ ( cons_A228743023le_alt @ Y_3 @ Ys_5 ) ) ) )
% 0.27/0.65 => ( P_16 @ Xs_85 @ Ys_15 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_242_list__induct2,axiom,
% 0.27/0.65 ! [P_16: list_A2115238852le_alt > list_A2115238852le_alt > $o,Xs_85: list_A2115238852le_alt,Ys_15: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( size_s1858781230le_alt @ Xs_85 )
% 0.27/0.65 = ( size_s1858781230le_alt @ Ys_15 ) )
% 0.27/0.65 => ( ( P_16 @ nil_Ar1286194111le_alt @ nil_Ar1286194111le_alt )
% 0.27/0.65 => ( ! [X_1: arrow_475358991le_alt,Xs_54: list_A2115238852le_alt,Y_3: arrow_475358991le_alt,Ys_5: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( size_s1858781230le_alt @ Xs_54 )
% 0.27/0.65 = ( size_s1858781230le_alt @ Ys_5 ) )
% 0.27/0.65 => ( ( P_16 @ Xs_54 @ Ys_5 )
% 0.27/0.65 => ( P_16 @ ( cons_A228743023le_alt @ X_1 @ Xs_54 ) @ ( cons_A228743023le_alt @ Y_3 @ Ys_5 ) ) ) )
% 0.27/0.65 => ( P_16 @ Xs_85 @ Ys_15 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_243_emptyE,axiom,
% 0.27/0.65 ! [A_81: int] :
% 0.27/0.65 ~ ( member_int @ A_81 @ bot_bot_int_o ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_244_emptyE,axiom,
% 0.27/0.65 ! [A_81: nat] :
% 0.27/0.65 ~ ( member_nat @ A_81 @ bot_bot_nat_o ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_245_bot__fun__def,axiom,
% 0.27/0.65 ! [X_1: nat] :
% 0.27/0.65 ( ( bot_bot_nat_o @ X_1 )
% 0.27/0.65 <=> bot_bot_o ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_246_bot__apply,axiom,
% 0.27/0.65 ! [X_62: nat] :
% 0.27/0.65 ( ( bot_bot_nat_o @ X_62 )
% 0.27/0.65 <=> bot_bot_o ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_247_Ex__list__of__length,axiom,
% 0.27/0.65 ! [N_44: nat] :
% 0.27/0.65 ? [Xs_54: list_A2115238852le_alt] :
% 0.27/0.65 ( ( size_s1858781230le_alt @ Xs_54 )
% 0.27/0.65 = N_44 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_248_listrelp_Osimps,axiom,
% 0.27/0.65 ! [R: nat > nat > $o,A1: list_nat,A2: list_nat] :
% 0.27/0.65 ( ( listrelp_nat @ R @ A1 @ A2 )
% 0.27/0.65 <=> ( ( ( A1 = nil_nat )
% 0.27/0.65 & ( A2 = nil_nat ) )
% 0.27/0.65 | ? [X_1: nat,Y_3: nat,Xs_54: list_nat,Ys_5: list_nat] :
% 0.27/0.65 ( ( A1
% 0.27/0.65 = ( cons_nat @ X_1 @ Xs_54 ) )
% 0.27/0.65 & ( A2
% 0.27/0.65 = ( cons_nat @ Y_3 @ Ys_5 ) )
% 0.27/0.65 & ( R @ X_1 @ Y_3 )
% 0.27/0.65 & ( listrelp_nat @ R @ Xs_54 @ Ys_5 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_249_listrelp_Osimps,axiom,
% 0.27/0.65 ! [R: arrow_475358991le_alt > arrow_475358991le_alt > $o,A1: list_A2115238852le_alt,A2: list_A2115238852le_alt] :
% 0.27/0.65 ( ( listre1213162009le_alt @ R @ A1 @ A2 )
% 0.27/0.65 <=> ( ( ( A1 = nil_Ar1286194111le_alt )
% 0.27/0.65 & ( A2 = nil_Ar1286194111le_alt ) )
% 0.27/0.65 | ? [X_1: arrow_475358991le_alt,Y_3: arrow_475358991le_alt,Xs_54: list_A2115238852le_alt,Ys_5: list_A2115238852le_alt] :
% 0.27/0.65 ( ( A1
% 0.27/0.65 = ( cons_A228743023le_alt @ X_1 @ Xs_54 ) )
% 0.27/0.65 & ( A2
% 0.27/0.65 = ( cons_A228743023le_alt @ Y_3 @ Ys_5 ) )
% 0.27/0.65 & ( R @ X_1 @ Y_3 )
% 0.27/0.65 & ( listre1213162009le_alt @ R @ Xs_54 @ Ys_5 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_250_equals0D,axiom,
% 0.27/0.65 ! [A_80: int,A_79: int > $o] :
% 0.27/0.65 ( ( A_79 = bot_bot_int_o )
% 0.27/0.65 => ~ ( member_int @ A_80 @ A_79 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_251_equals0D,axiom,
% 0.27/0.65 ! [A_80: nat,A_79: nat > $o] :
% 0.27/0.65 ( ( A_79 = bot_bot_nat_o )
% 0.27/0.65 => ~ ( member_nat @ A_80 @ A_79 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_252_Collect__empty__eq,axiom,
% 0.27/0.65 ! [P_15: nat > $o] :
% 0.27/0.65 ( ( ( collect_nat @ P_15 )
% 0.27/0.65 = bot_bot_nat_o )
% 0.27/0.65 <=> ! [X_1: nat] :
% 0.27/0.65 ~ ( P_15 @ X_1 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_253_empty__iff,axiom,
% 0.27/0.65 ! [C_36: int] :
% 0.27/0.65 ~ ( member_int @ C_36 @ bot_bot_int_o ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_254_empty__iff,axiom,
% 0.27/0.65 ! [C_36: nat] :
% 0.27/0.65 ~ ( member_nat @ C_36 @ bot_bot_nat_o ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_255_empty__Collect__eq,axiom,
% 0.27/0.65 ! [P_14: nat > $o] :
% 0.27/0.65 ( ( bot_bot_nat_o
% 0.27/0.65 = ( collect_nat @ P_14 ) )
% 0.27/0.65 <=> ! [X_1: nat] :
% 0.27/0.65 ~ ( P_14 @ X_1 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_256_ex__in__conv,axiom,
% 0.27/0.65 ! [A_78: int > $o] :
% 0.27/0.65 ( ? [X_1: int] : ( member_int @ X_1 @ A_78 )
% 0.27/0.65 <=> ( A_78 != bot_bot_int_o ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_257_ex__in__conv,axiom,
% 0.27/0.65 ! [A_78: nat > $o] :
% 0.27/0.65 ( ? [X_1: nat] : ( member_nat @ X_1 @ A_78 )
% 0.27/0.65 <=> ( A_78 != bot_bot_nat_o ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_258_all__not__in__conv,axiom,
% 0.27/0.65 ! [A_77: int > $o] :
% 0.27/0.65 ( ! [X_1: int] :
% 0.27/0.65 ~ ( member_int @ X_1 @ A_77 )
% 0.27/0.65 <=> ( A_77 = bot_bot_int_o ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_259_all__not__in__conv,axiom,
% 0.27/0.65 ! [A_77: nat > $o] :
% 0.27/0.65 ( ! [X_1: nat] :
% 0.27/0.65 ~ ( member_nat @ X_1 @ A_77 )
% 0.27/0.65 <=> ( A_77 = bot_bot_nat_o ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_260_empty__def,axiom,
% 0.27/0.65 ( bot_bot_nat_o
% 0.27/0.65 = ( collect_nat
% 0.27/0.65 @ ^ [X_1: nat] : $false ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_261_equals0I,axiom,
% 0.27/0.65 ! [A_76: int > $o] :
% 0.27/0.65 ( ! [Y_3: int] :
% 0.27/0.65 ~ ( member_int @ Y_3 @ A_76 )
% 0.27/0.65 => ( A_76 = bot_bot_int_o ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_262_equals0I,axiom,
% 0.27/0.65 ! [A_76: nat > $o] :
% 0.27/0.65 ( ! [Y_3: nat] :
% 0.27/0.65 ~ ( member_nat @ Y_3 @ A_76 )
% 0.27/0.65 => ( A_76 = bot_bot_nat_o ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_263_sorted__list__of__set__empty,axiom,
% 0.27/0.65 ( ( linord810813188et_nat @ bot_bot_nat_o )
% 0.27/0.65 = nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_264_min__max_Osup__assoc,axiom,
% 0.27/0.65 ! [X_61: int,Y_31: int,Z_8: int] :
% 0.27/0.65 ( ( ord_max_int @ ( ord_max_int @ X_61 @ Y_31 ) @ Z_8 )
% 0.27/0.65 = ( ord_max_int @ X_61 @ ( ord_max_int @ Y_31 @ Z_8 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_265_min__max_Osup__assoc,axiom,
% 0.27/0.65 ! [X_61: nat,Y_31: nat,Z_8: nat] :
% 0.27/0.65 ( ( ord_max_nat @ ( ord_max_nat @ X_61 @ Y_31 ) @ Z_8 )
% 0.27/0.65 = ( ord_max_nat @ X_61 @ ( ord_max_nat @ Y_31 @ Z_8 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_266_min__max_Osup_Oassoc,axiom,
% 0.27/0.65 ! [A_75: int,B_47: int,C_35: int] :
% 0.27/0.65 ( ( ord_max_int @ ( ord_max_int @ A_75 @ B_47 ) @ C_35 )
% 0.27/0.65 = ( ord_max_int @ A_75 @ ( ord_max_int @ B_47 @ C_35 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_267_min__max_Osup_Oassoc,axiom,
% 0.27/0.65 ! [A_75: nat,B_47: nat,C_35: nat] :
% 0.27/0.65 ( ( ord_max_nat @ ( ord_max_nat @ A_75 @ B_47 ) @ C_35 )
% 0.27/0.65 = ( ord_max_nat @ A_75 @ ( ord_max_nat @ B_47 @ C_35 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_268_min__max_Osup__left__commute,axiom,
% 0.27/0.65 ! [X_60: int,Y_30: int,Z_7: int] :
% 0.27/0.65 ( ( ord_max_int @ X_60 @ ( ord_max_int @ Y_30 @ Z_7 ) )
% 0.27/0.65 = ( ord_max_int @ Y_30 @ ( ord_max_int @ X_60 @ Z_7 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_269_min__max_Osup__left__commute,axiom,
% 0.27/0.65 ! [X_60: nat,Y_30: nat,Z_7: nat] :
% 0.27/0.65 ( ( ord_max_nat @ X_60 @ ( ord_max_nat @ Y_30 @ Z_7 ) )
% 0.27/0.65 = ( ord_max_nat @ Y_30 @ ( ord_max_nat @ X_60 @ Z_7 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_270_min__max_Osup_Oleft__commute,axiom,
% 0.27/0.65 ! [B_46: int,A_74: int,C_34: int] :
% 0.27/0.65 ( ( ord_max_int @ B_46 @ ( ord_max_int @ A_74 @ C_34 ) )
% 0.27/0.65 = ( ord_max_int @ A_74 @ ( ord_max_int @ B_46 @ C_34 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_271_min__max_Osup_Oleft__commute,axiom,
% 0.27/0.65 ! [B_46: nat,A_74: nat,C_34: nat] :
% 0.27/0.65 ( ( ord_max_nat @ B_46 @ ( ord_max_nat @ A_74 @ C_34 ) )
% 0.27/0.65 = ( ord_max_nat @ A_74 @ ( ord_max_nat @ B_46 @ C_34 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_272_min__max_Osup_Oidem,axiom,
% 0.27/0.65 ! [A_73: int] :
% 0.27/0.65 ( ( ord_max_int @ A_73 @ A_73 )
% 0.27/0.65 = A_73 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_273_min__max_Osup_Oidem,axiom,
% 0.27/0.65 ! [A_73: nat] :
% 0.27/0.65 ( ( ord_max_nat @ A_73 @ A_73 )
% 0.27/0.65 = A_73 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_274_min__max_Osup_Ocommute,axiom,
% 0.27/0.65 ! [A_72: int,B_45: int] :
% 0.27/0.65 ( ( ord_max_int @ A_72 @ B_45 )
% 0.27/0.65 = ( ord_max_int @ B_45 @ A_72 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_275_min__max_Osup_Ocommute,axiom,
% 0.27/0.65 ! [A_72: nat,B_45: nat] :
% 0.27/0.65 ( ( ord_max_nat @ A_72 @ B_45 )
% 0.27/0.65 = ( ord_max_nat @ B_45 @ A_72 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_276_min__max_Osup__commute,axiom,
% 0.27/0.65 ! [X_59: int,Y_29: int] :
% 0.27/0.65 ( ( ord_max_int @ X_59 @ Y_29 )
% 0.27/0.65 = ( ord_max_int @ Y_29 @ X_59 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_277_min__max_Osup__commute,axiom,
% 0.27/0.65 ! [X_59: nat,Y_29: nat] :
% 0.27/0.65 ( ( ord_max_nat @ X_59 @ Y_29 )
% 0.27/0.65 = ( ord_max_nat @ Y_29 @ X_59 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_278_min__max_Osup_Oleft__idem,axiom,
% 0.27/0.65 ! [A_71: int,B_44: int] :
% 0.27/0.65 ( ( ord_max_int @ A_71 @ ( ord_max_int @ A_71 @ B_44 ) )
% 0.27/0.65 = ( ord_max_int @ A_71 @ B_44 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_279_min__max_Osup_Oleft__idem,axiom,
% 0.27/0.65 ! [A_71: nat,B_44: nat] :
% 0.27/0.65 ( ( ord_max_nat @ A_71 @ ( ord_max_nat @ A_71 @ B_44 ) )
% 0.27/0.65 = ( ord_max_nat @ A_71 @ B_44 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_280_min__max_Osup__left__idem,axiom,
% 0.27/0.65 ! [X_58: int,Y_28: int] :
% 0.27/0.65 ( ( ord_max_int @ X_58 @ ( ord_max_int @ X_58 @ Y_28 ) )
% 0.27/0.65 = ( ord_max_int @ X_58 @ Y_28 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_281_min__max_Osup__left__idem,axiom,
% 0.27/0.65 ! [X_58: nat,Y_28: nat] :
% 0.27/0.65 ( ( ord_max_nat @ X_58 @ ( ord_max_nat @ X_58 @ Y_28 ) )
% 0.27/0.65 = ( ord_max_nat @ X_58 @ Y_28 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_282_Max_Oidem,axiom,
% 0.27/0.65 ! [X_57: int] :
% 0.27/0.65 ( ( ord_max_int @ X_57 @ X_57 )
% 0.27/0.65 = X_57 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_283_Max_Oidem,axiom,
% 0.27/0.65 ! [X_57: nat] :
% 0.27/0.65 ( ( ord_max_nat @ X_57 @ X_57 )
% 0.27/0.65 = X_57 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_284_dropWhile__eq__drop,axiom,
% 0.27/0.65 ! [P_13: arrow_475358991le_alt > $o,Xs_84: list_A2115238852le_alt] :
% 0.27/0.65 ( ( dropWh1316781920le_alt @ P_13 @ Xs_84 )
% 0.27/0.65 = ( drop_A1346709759le_alt @ ( size_s1858781230le_alt @ ( takeWh1696291512le_alt @ P_13 @ Xs_84 ) ) @ Xs_84 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_285_nth__length__takeWhile,axiom,
% 0.27/0.65 ! [P_12: nat > $o,Xs_83: list_nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( size_size_list_nat @ ( takeWhile_nat @ P_12 @ Xs_83 ) ) @ ( size_size_list_nat @ Xs_83 ) )
% 0.27/0.65 => ~ ( P_12 @ ( nth_nat @ Xs_83 @ ( size_size_list_nat @ ( takeWhile_nat @ P_12 @ Xs_83 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_286_nth__length__takeWhile,axiom,
% 0.27/0.65 ! [P_12: arrow_475358991le_alt > $o,Xs_83: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ ( size_s1858781230le_alt @ ( takeWh1696291512le_alt @ P_12 @ Xs_83 ) ) @ ( size_s1858781230le_alt @ Xs_83 ) )
% 0.27/0.65 => ~ ( P_12 @ ( nth_Ar125878976le_alt @ Xs_83 @ ( size_s1858781230le_alt @ ( takeWh1696291512le_alt @ P_12 @ Xs_83 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_287_takeWhile__nth,axiom,
% 0.27/0.65 ! [J_7: nat,P_11: nat > $o,Xs_82: list_nat] :
% 0.27/0.65 ( ( ord_less_nat @ J_7 @ ( size_size_list_nat @ ( takeWhile_nat @ P_11 @ Xs_82 ) ) )
% 0.27/0.65 => ( ( nth_nat @ ( takeWhile_nat @ P_11 @ Xs_82 ) @ J_7 )
% 0.27/0.65 = ( nth_nat @ Xs_82 @ J_7 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_288_takeWhile__nth,axiom,
% 0.27/0.65 ! [J_7: nat,P_11: arrow_475358991le_alt > $o,Xs_82: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ J_7 @ ( size_s1858781230le_alt @ ( takeWh1696291512le_alt @ P_11 @ Xs_82 ) ) )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ ( takeWh1696291512le_alt @ P_11 @ Xs_82 ) @ J_7 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Xs_82 @ J_7 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_289_list__update__length,axiom,
% 0.27/0.65 ! [Xs_81: list_A2115238852le_alt,X_56: arrow_475358991le_alt,Ys_14: list_A2115238852le_alt,Y_27: arrow_475358991le_alt] :
% 0.27/0.65 ( ( list_u62477863le_alt @ ( append179082452le_alt @ Xs_81 @ ( cons_A228743023le_alt @ X_56 @ Ys_14 ) ) @ ( size_s1858781230le_alt @ Xs_81 ) @ Y_27 )
% 0.27/0.65 = ( append179082452le_alt @ Xs_81 @ ( cons_A228743023le_alt @ Y_27 @ Ys_14 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_290_max__0L,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( ord_max_nat @ zero_zero_nat @ N_5 )
% 0.27/0.65 = N_5 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_291_less__zeroE,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ~ ( ord_less_nat @ N_5 @ zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_292_list__update__overwrite,axiom,
% 0.27/0.65 ! [Xs_80: list_A2115238852le_alt,I_26: nat,X_55: arrow_475358991le_alt,Y_26: arrow_475358991le_alt] :
% 0.27/0.65 ( ( list_u62477863le_alt @ ( list_u62477863le_alt @ Xs_80 @ I_26 @ X_55 ) @ I_26 @ Y_26 )
% 0.27/0.65 = ( list_u62477863le_alt @ Xs_80 @ I_26 @ Y_26 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_293_list__update__swap,axiom,
% 0.27/0.65 ! [Xs_79: list_A2115238852le_alt,X_54: arrow_475358991le_alt,X_53: arrow_475358991le_alt,I_25: nat,I_24: nat] :
% 0.27/0.65 ( ( I_25 != I_24 )
% 0.27/0.65 => ( ( list_u62477863le_alt @ ( list_u62477863le_alt @ Xs_79 @ I_25 @ X_54 ) @ I_24 @ X_53 )
% 0.27/0.65 = ( list_u62477863le_alt @ ( list_u62477863le_alt @ Xs_79 @ I_24 @ X_53 ) @ I_25 @ X_54 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_294_nat__less__cases,axiom,
% 0.27/0.65 ! [P: nat > nat > $o,M: nat,N_5: nat] :
% 0.27/0.65 ( ( ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 => ( P @ N_5 @ M ) )
% 0.27/0.65 => ( ( ( M = N_5 )
% 0.27/0.65 => ( P @ N_5 @ M ) )
% 0.27/0.65 => ( ( ( ord_less_nat @ N_5 @ M )
% 0.27/0.65 => ( P @ N_5 @ M ) )
% 0.27/0.65 => ( P @ N_5 @ M ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_295_less__not__refl3,axiom,
% 0.27/0.65 ! [S: nat,T: nat] :
% 0.27/0.65 ( ( ord_less_nat @ S @ T )
% 0.27/0.65 => ( S != T ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_296_less__not__refl2,axiom,
% 0.27/0.65 ! [N_5: nat,M: nat] :
% 0.27/0.65 ( ( ord_less_nat @ N_5 @ M )
% 0.27/0.65 => ( M != N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_297_less__irrefl__nat,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ~ ( ord_less_nat @ N_5 @ N_5 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_298_linorder__neqE__nat,axiom,
% 0.27/0.65 ! [X: nat,Y: nat] :
% 0.27/0.65 ( ( X != Y )
% 0.27/0.65 => ( ~ ( ord_less_nat @ X @ Y )
% 0.27/0.65 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_299_nat__neq__iff,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( M != N_5 )
% 0.27/0.65 <=> ( ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 | ( ord_less_nat @ N_5 @ M ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_300_less__not__refl,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ~ ( ord_less_nat @ N_5 @ N_5 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_301_gr0I,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( N_5 != zero_zero_nat )
% 0.27/0.65 => ( ord_less_nat @ zero_zero_nat @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_302_gr__implies__not0,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 => ( N_5 != zero_zero_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_303_less__nat__zero__code,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ~ ( ord_less_nat @ N_5 @ zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_304_neq0__conv,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( N_5 != zero_zero_nat )
% 0.27/0.65 <=> ( ord_less_nat @ zero_zero_nat @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_305_not__less0,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ~ ( ord_less_nat @ N_5 @ zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_306_order__less__irrefl,axiom,
% 0.27/0.65 ! [X_52: int] :
% 0.27/0.65 ~ ( ord_less_int @ X_52 @ X_52 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_307_order__less__irrefl,axiom,
% 0.27/0.65 ! [X_52: nat > $o] :
% 0.27/0.65 ~ ( ord_less_nat_o @ X_52 @ X_52 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_308_order__less__irrefl,axiom,
% 0.27/0.65 ! [X_52: nat] :
% 0.27/0.65 ~ ( ord_less_nat @ X_52 @ X_52 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_309_linorder__neq__iff,axiom,
% 0.27/0.65 ! [X_51: int,Y_25: int] :
% 0.27/0.65 ( ( X_51 != Y_25 )
% 0.27/0.65 <=> ( ( ord_less_int @ X_51 @ Y_25 )
% 0.27/0.65 | ( ord_less_int @ Y_25 @ X_51 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_310_linorder__neq__iff,axiom,
% 0.27/0.65 ! [X_51: nat,Y_25: nat] :
% 0.27/0.65 ( ( X_51 != Y_25 )
% 0.27/0.65 <=> ( ( ord_less_nat @ X_51 @ Y_25 )
% 0.27/0.65 | ( ord_less_nat @ Y_25 @ X_51 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_311_not__less__iff__gr__or__eq,axiom,
% 0.27/0.65 ! [X_50: int,Y_24: int] :
% 0.27/0.65 ( ~ ( ord_less_int @ X_50 @ Y_24 )
% 0.27/0.65 <=> ( ( ord_less_int @ Y_24 @ X_50 )
% 0.27/0.65 | ( X_50 = Y_24 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_312_not__less__iff__gr__or__eq,axiom,
% 0.27/0.65 ! [X_50: nat,Y_24: nat] :
% 0.27/0.65 ( ~ ( ord_less_nat @ X_50 @ Y_24 )
% 0.27/0.65 <=> ( ( ord_less_nat @ Y_24 @ X_50 )
% 0.27/0.65 | ( X_50 = Y_24 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_313_linorder__less__linear,axiom,
% 0.27/0.65 ! [X_49: int,Y_23: int] :
% 0.27/0.65 ( ( ord_less_int @ X_49 @ Y_23 )
% 0.27/0.65 | ( X_49 = Y_23 )
% 0.27/0.65 | ( ord_less_int @ Y_23 @ X_49 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_314_linorder__less__linear,axiom,
% 0.27/0.65 ! [X_49: nat,Y_23: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_49 @ Y_23 )
% 0.27/0.65 | ( X_49 = Y_23 )
% 0.27/0.65 | ( ord_less_nat @ Y_23 @ X_49 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_315_linorder__antisym__conv3,axiom,
% 0.27/0.65 ! [Y_22: int,X_48: int] :
% 0.27/0.65 ( ~ ( ord_less_int @ Y_22 @ X_48 )
% 0.27/0.65 => ( ~ ( ord_less_int @ X_48 @ Y_22 )
% 0.27/0.65 <=> ( X_48 = Y_22 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_316_linorder__antisym__conv3,axiom,
% 0.27/0.65 ! [Y_22: nat,X_48: nat] :
% 0.27/0.65 ( ~ ( ord_less_nat @ Y_22 @ X_48 )
% 0.27/0.65 => ( ~ ( ord_less_nat @ X_48 @ Y_22 )
% 0.27/0.65 <=> ( X_48 = Y_22 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_317_linorder__neqE,axiom,
% 0.27/0.65 ! [X_47: int,Y_21: int] :
% 0.27/0.65 ( ( X_47 != Y_21 )
% 0.27/0.65 => ( ~ ( ord_less_int @ X_47 @ Y_21 )
% 0.27/0.65 => ( ord_less_int @ Y_21 @ X_47 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_318_linorder__neqE,axiom,
% 0.27/0.65 ! [X_47: nat,Y_21: nat] :
% 0.27/0.65 ( ( X_47 != Y_21 )
% 0.27/0.65 => ( ~ ( ord_less_nat @ X_47 @ Y_21 )
% 0.27/0.65 => ( ord_less_nat @ Y_21 @ X_47 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_319_less__imp__neq,axiom,
% 0.27/0.65 ! [X_46: int,Y_20: int] :
% 0.27/0.65 ( ( ord_less_int @ X_46 @ Y_20 )
% 0.27/0.65 => ( X_46 != Y_20 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_320_less__imp__neq,axiom,
% 0.27/0.65 ! [X_46: nat > $o,Y_20: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ X_46 @ Y_20 )
% 0.27/0.65 => ( X_46 != Y_20 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_321_less__imp__neq,axiom,
% 0.27/0.65 ! [X_46: nat,Y_20: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_46 @ Y_20 )
% 0.27/0.65 => ( X_46 != Y_20 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_322_order__less__not__sym,axiom,
% 0.27/0.65 ! [X_45: int,Y_19: int] :
% 0.27/0.65 ( ( ord_less_int @ X_45 @ Y_19 )
% 0.27/0.65 => ~ ( ord_less_int @ Y_19 @ X_45 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_323_order__less__not__sym,axiom,
% 0.27/0.65 ! [X_45: nat > $o,Y_19: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ X_45 @ Y_19 )
% 0.27/0.65 => ~ ( ord_less_nat_o @ Y_19 @ X_45 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_324_order__less__not__sym,axiom,
% 0.27/0.65 ! [X_45: nat,Y_19: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_45 @ Y_19 )
% 0.27/0.65 => ~ ( ord_less_nat @ Y_19 @ X_45 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_325_order__less__imp__not__less,axiom,
% 0.27/0.65 ! [X_44: int,Y_18: int] :
% 0.27/0.65 ( ( ord_less_int @ X_44 @ Y_18 )
% 0.27/0.65 => ~ ( ord_less_int @ Y_18 @ X_44 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_326_order__less__imp__not__less,axiom,
% 0.27/0.65 ! [X_44: nat > $o,Y_18: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ X_44 @ Y_18 )
% 0.27/0.65 => ~ ( ord_less_nat_o @ Y_18 @ X_44 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_327_order__less__imp__not__less,axiom,
% 0.27/0.65 ! [X_44: nat,Y_18: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_44 @ Y_18 )
% 0.27/0.65 => ~ ( ord_less_nat @ Y_18 @ X_44 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_328_order__less__imp__not__eq,axiom,
% 0.27/0.65 ! [X_43: int,Y_17: int] :
% 0.27/0.65 ( ( ord_less_int @ X_43 @ Y_17 )
% 0.27/0.65 => ( X_43 != Y_17 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_329_order__less__imp__not__eq,axiom,
% 0.27/0.65 ! [X_43: nat > $o,Y_17: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ X_43 @ Y_17 )
% 0.27/0.65 => ( X_43 != Y_17 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_330_order__less__imp__not__eq,axiom,
% 0.27/0.65 ! [X_43: nat,Y_17: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_43 @ Y_17 )
% 0.27/0.65 => ( X_43 != Y_17 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_331_order__less__imp__not__eq2,axiom,
% 0.27/0.65 ! [X_42: int,Y_16: int] :
% 0.27/0.65 ( ( ord_less_int @ X_42 @ Y_16 )
% 0.27/0.65 => ( Y_16 != X_42 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_332_order__less__imp__not__eq2,axiom,
% 0.27/0.65 ! [X_42: nat > $o,Y_16: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ X_42 @ Y_16 )
% 0.27/0.65 => ( Y_16 != X_42 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_333_order__less__imp__not__eq2,axiom,
% 0.27/0.65 ! [X_42: nat,Y_16: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_42 @ Y_16 )
% 0.27/0.65 => ( Y_16 != X_42 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_334_order__less__imp__triv,axiom,
% 0.27/0.65 ! [P_10: $o,X_41: int,Y_15: int] :
% 0.27/0.65 ( ( ord_less_int @ X_41 @ Y_15 )
% 0.27/0.65 => ( ( ord_less_int @ Y_15 @ X_41 )
% 0.27/0.65 => P_10 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_335_order__less__imp__triv,axiom,
% 0.27/0.65 ! [P_10: $o,X_41: nat > $o,Y_15: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ X_41 @ Y_15 )
% 0.27/0.65 => ( ( ord_less_nat_o @ Y_15 @ X_41 )
% 0.27/0.65 => P_10 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_336_order__less__imp__triv,axiom,
% 0.27/0.65 ! [P_10: $o,X_41: nat,Y_15: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_41 @ Y_15 )
% 0.27/0.65 => ( ( ord_less_nat @ Y_15 @ X_41 )
% 0.27/0.65 => P_10 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_337_order__less__asym_H,axiom,
% 0.27/0.65 ! [A_70: int,B_43: int] :
% 0.27/0.65 ( ( ord_less_int @ A_70 @ B_43 )
% 0.27/0.65 => ~ ( ord_less_int @ B_43 @ A_70 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_338_order__less__asym_H,axiom,
% 0.27/0.65 ! [A_70: nat > $o,B_43: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ A_70 @ B_43 )
% 0.27/0.65 => ~ ( ord_less_nat_o @ B_43 @ A_70 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_339_order__less__asym_H,axiom,
% 0.27/0.65 ! [A_70: nat,B_43: nat] :
% 0.27/0.65 ( ( ord_less_nat @ A_70 @ B_43 )
% 0.27/0.65 => ~ ( ord_less_nat @ B_43 @ A_70 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_340_xt1_I9_J,axiom,
% 0.27/0.65 ! [B_42: int,A_69: int] :
% 0.27/0.65 ( ( ord_less_int @ B_42 @ A_69 )
% 0.27/0.65 => ~ ( ord_less_int @ A_69 @ B_42 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_341_xt1_I9_J,axiom,
% 0.27/0.65 ! [B_42: nat > $o,A_69: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ B_42 @ A_69 )
% 0.27/0.65 => ~ ( ord_less_nat_o @ A_69 @ B_42 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_342_xt1_I9_J,axiom,
% 0.27/0.65 ! [B_42: nat,A_69: nat] :
% 0.27/0.65 ( ( ord_less_nat @ B_42 @ A_69 )
% 0.27/0.65 => ~ ( ord_less_nat @ A_69 @ B_42 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_343_ord__eq__less__trans,axiom,
% 0.27/0.65 ! [C_33: int,A_68: int,B_41: int] :
% 0.27/0.65 ( ( A_68 = B_41 )
% 0.27/0.65 => ( ( ord_less_int @ B_41 @ C_33 )
% 0.27/0.65 => ( ord_less_int @ A_68 @ C_33 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_344_ord__eq__less__trans,axiom,
% 0.27/0.65 ! [C_33: nat > $o,A_68: nat > $o,B_41: nat > $o] :
% 0.27/0.65 ( ( A_68 = B_41 )
% 0.27/0.65 => ( ( ord_less_nat_o @ B_41 @ C_33 )
% 0.27/0.65 => ( ord_less_nat_o @ A_68 @ C_33 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_345_ord__eq__less__trans,axiom,
% 0.27/0.65 ! [C_33: nat,A_68: nat,B_41: nat] :
% 0.27/0.65 ( ( A_68 = B_41 )
% 0.27/0.65 => ( ( ord_less_nat @ B_41 @ C_33 )
% 0.27/0.65 => ( ord_less_nat @ A_68 @ C_33 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_346_xt1_I1_J,axiom,
% 0.27/0.65 ! [C_32: int,A_67: int,B_40: int] :
% 0.27/0.65 ( ( A_67 = B_40 )
% 0.27/0.65 => ( ( ord_less_int @ C_32 @ B_40 )
% 0.27/0.65 => ( ord_less_int @ C_32 @ A_67 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_347_xt1_I1_J,axiom,
% 0.27/0.65 ! [C_32: nat > $o,A_67: nat > $o,B_40: nat > $o] :
% 0.27/0.65 ( ( A_67 = B_40 )
% 0.27/0.65 => ( ( ord_less_nat_o @ C_32 @ B_40 )
% 0.27/0.65 => ( ord_less_nat_o @ C_32 @ A_67 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_348_xt1_I1_J,axiom,
% 0.27/0.65 ! [C_32: nat,A_67: nat,B_40: nat] :
% 0.27/0.65 ( ( A_67 = B_40 )
% 0.27/0.65 => ( ( ord_less_nat @ C_32 @ B_40 )
% 0.27/0.65 => ( ord_less_nat @ C_32 @ A_67 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_349_ord__less__eq__trans,axiom,
% 0.27/0.65 ! [C_31: int,A_66: int,B_39: int] :
% 0.27/0.65 ( ( ord_less_int @ A_66 @ B_39 )
% 0.27/0.65 => ( ( B_39 = C_31 )
% 0.27/0.65 => ( ord_less_int @ A_66 @ C_31 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_350_ord__less__eq__trans,axiom,
% 0.27/0.65 ! [C_31: nat > $o,A_66: nat > $o,B_39: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ A_66 @ B_39 )
% 0.27/0.65 => ( ( B_39 = C_31 )
% 0.27/0.65 => ( ord_less_nat_o @ A_66 @ C_31 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_351_ord__less__eq__trans,axiom,
% 0.27/0.65 ! [C_31: nat,A_66: nat,B_39: nat] :
% 0.27/0.65 ( ( ord_less_nat @ A_66 @ B_39 )
% 0.27/0.65 => ( ( B_39 = C_31 )
% 0.27/0.65 => ( ord_less_nat @ A_66 @ C_31 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_352_xt1_I2_J,axiom,
% 0.27/0.65 ! [C_30: int,B_38: int,A_65: int] :
% 0.27/0.65 ( ( ord_less_int @ B_38 @ A_65 )
% 0.27/0.65 => ( ( B_38 = C_30 )
% 0.27/0.65 => ( ord_less_int @ C_30 @ A_65 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_353_xt1_I2_J,axiom,
% 0.27/0.65 ! [C_30: nat > $o,B_38: nat > $o,A_65: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ B_38 @ A_65 )
% 0.27/0.65 => ( ( B_38 = C_30 )
% 0.27/0.65 => ( ord_less_nat_o @ C_30 @ A_65 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_354_xt1_I2_J,axiom,
% 0.27/0.65 ! [C_30: nat,B_38: nat,A_65: nat] :
% 0.27/0.65 ( ( ord_less_nat @ B_38 @ A_65 )
% 0.27/0.65 => ( ( B_38 = C_30 )
% 0.27/0.65 => ( ord_less_nat @ C_30 @ A_65 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_355_order__less__trans,axiom,
% 0.27/0.65 ! [Z_6: int,X_40: int,Y_14: int] :
% 0.27/0.65 ( ( ord_less_int @ X_40 @ Y_14 )
% 0.27/0.65 => ( ( ord_less_int @ Y_14 @ Z_6 )
% 0.27/0.65 => ( ord_less_int @ X_40 @ Z_6 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_356_order__less__trans,axiom,
% 0.27/0.65 ! [Z_6: nat > $o,X_40: nat > $o,Y_14: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ X_40 @ Y_14 )
% 0.27/0.65 => ( ( ord_less_nat_o @ Y_14 @ Z_6 )
% 0.27/0.65 => ( ord_less_nat_o @ X_40 @ Z_6 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_357_order__less__trans,axiom,
% 0.27/0.65 ! [Z_6: nat,X_40: nat,Y_14: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_40 @ Y_14 )
% 0.27/0.65 => ( ( ord_less_nat @ Y_14 @ Z_6 )
% 0.27/0.65 => ( ord_less_nat @ X_40 @ Z_6 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_358_xt1_I10_J,axiom,
% 0.27/0.65 ! [Z_5: int,Y_13: int,X_39: int] :
% 0.27/0.65 ( ( ord_less_int @ Y_13 @ X_39 )
% 0.27/0.65 => ( ( ord_less_int @ Z_5 @ Y_13 )
% 0.27/0.65 => ( ord_less_int @ Z_5 @ X_39 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_359_xt1_I10_J,axiom,
% 0.27/0.65 ! [Z_5: nat > $o,Y_13: nat > $o,X_39: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ Y_13 @ X_39 )
% 0.27/0.65 => ( ( ord_less_nat_o @ Z_5 @ Y_13 )
% 0.27/0.65 => ( ord_less_nat_o @ Z_5 @ X_39 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_360_xt1_I10_J,axiom,
% 0.27/0.65 ! [Z_5: nat,Y_13: nat,X_39: nat] :
% 0.27/0.65 ( ( ord_less_nat @ Y_13 @ X_39 )
% 0.27/0.65 => ( ( ord_less_nat @ Z_5 @ Y_13 )
% 0.27/0.65 => ( ord_less_nat @ Z_5 @ X_39 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_361_order__less__asym,axiom,
% 0.27/0.65 ! [X_38: int,Y_12: int] :
% 0.27/0.65 ( ( ord_less_int @ X_38 @ Y_12 )
% 0.27/0.65 => ~ ( ord_less_int @ Y_12 @ X_38 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_362_order__less__asym,axiom,
% 0.27/0.65 ! [X_38: nat > $o,Y_12: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ X_38 @ Y_12 )
% 0.27/0.65 => ~ ( ord_less_nat_o @ Y_12 @ X_38 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_363_order__less__asym,axiom,
% 0.27/0.65 ! [X_38: nat,Y_12: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_38 @ Y_12 )
% 0.27/0.65 => ~ ( ord_less_nat @ Y_12 @ X_38 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_364_linorder__cases,axiom,
% 0.27/0.65 ! [X_37: int,Y_11: int] :
% 0.27/0.65 ( ~ ( ord_less_int @ X_37 @ Y_11 )
% 0.27/0.65 => ( ( X_37 != Y_11 )
% 0.27/0.65 => ( ord_less_int @ Y_11 @ X_37 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_365_linorder__cases,axiom,
% 0.27/0.65 ! [X_37: nat,Y_11: nat] :
% 0.27/0.65 ( ~ ( ord_less_nat @ X_37 @ Y_11 )
% 0.27/0.65 => ( ( X_37 != Y_11 )
% 0.27/0.65 => ( ord_less_nat @ Y_11 @ X_37 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_366_list__update__append1,axiom,
% 0.27/0.65 ! [Ys_13: list_A2115238852le_alt,X_36: arrow_475358991le_alt,I_23: nat,Xs_78: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ I_23 @ ( size_s1858781230le_alt @ Xs_78 ) )
% 0.27/0.65 => ( ( list_u62477863le_alt @ ( append179082452le_alt @ Xs_78 @ Ys_13 ) @ I_23 @ X_36 )
% 0.27/0.65 = ( append179082452le_alt @ ( list_u62477863le_alt @ Xs_78 @ I_23 @ X_36 ) @ Ys_13 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_367_nth__list__update,axiom,
% 0.27/0.65 ! [X_35: arrow_475358991le_alt,J_6: nat,I_22: nat,Xs_77: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ I_22 @ ( size_s1858781230le_alt @ Xs_77 ) )
% 0.27/0.65 => ( ( ( I_22 = J_6 )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ ( list_u62477863le_alt @ Xs_77 @ I_22 @ X_35 ) @ J_6 )
% 0.27/0.65 = X_35 ) )
% 0.27/0.65 & ( ( I_22 != J_6 )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ ( list_u62477863le_alt @ Xs_77 @ I_22 @ X_35 ) @ J_6 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Xs_77 @ J_6 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_368_nth__list__update,axiom,
% 0.27/0.65 ! [X_35: nat,J_6: nat,I_22: nat,Xs_77: list_nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_22 @ ( size_size_list_nat @ Xs_77 ) )
% 0.27/0.65 => ( ( ( I_22 = J_6 )
% 0.27/0.65 => ( ( nth_nat @ ( list_update_nat @ Xs_77 @ I_22 @ X_35 ) @ J_6 )
% 0.27/0.65 = X_35 ) )
% 0.27/0.65 & ( ( I_22 != J_6 )
% 0.27/0.65 => ( ( nth_nat @ ( list_update_nat @ Xs_77 @ I_22 @ X_35 ) @ J_6 )
% 0.27/0.65 = ( nth_nat @ Xs_77 @ J_6 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_369_list__update__same__conv,axiom,
% 0.27/0.65 ! [X_34: arrow_475358991le_alt,I_21: nat,Xs_76: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ I_21 @ ( size_s1858781230le_alt @ Xs_76 ) )
% 0.27/0.65 => ( ( ( list_u62477863le_alt @ Xs_76 @ I_21 @ X_34 )
% 0.27/0.65 = Xs_76 )
% 0.27/0.65 <=> ( ( nth_Ar125878976le_alt @ Xs_76 @ I_21 )
% 0.27/0.65 = X_34 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_370_list__update__same__conv,axiom,
% 0.27/0.65 ! [X_34: nat,I_21: nat,Xs_76: list_nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_21 @ ( size_size_list_nat @ Xs_76 ) )
% 0.27/0.65 => ( ( ( list_update_nat @ Xs_76 @ I_21 @ X_34 )
% 0.27/0.65 = Xs_76 )
% 0.27/0.65 <=> ( ( nth_nat @ Xs_76 @ I_21 )
% 0.27/0.65 = X_34 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_371_nth__list__update__eq,axiom,
% 0.27/0.65 ! [X_33: arrow_475358991le_alt,I_20: nat,Xs_75: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ I_20 @ ( size_s1858781230le_alt @ Xs_75 ) )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ ( list_u62477863le_alt @ Xs_75 @ I_20 @ X_33 ) @ I_20 )
% 0.27/0.65 = X_33 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_372_nth__list__update__eq,axiom,
% 0.27/0.65 ! [X_33: nat,I_20: nat,Xs_75: list_nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_20 @ ( size_size_list_nat @ Xs_75 ) )
% 0.27/0.65 => ( ( nth_nat @ ( list_update_nat @ Xs_75 @ I_20 @ X_33 ) @ I_20 )
% 0.27/0.65 = X_33 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_373_last__drop,axiom,
% 0.27/0.65 ! [N_43: nat,Xs_74: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ N_43 @ ( size_s1858781230le_alt @ Xs_74 ) )
% 0.27/0.65 => ( ( last_A1217315288le_alt @ ( drop_A1346709759le_alt @ N_43 @ Xs_74 ) )
% 0.27/0.65 = ( last_A1217315288le_alt @ Xs_74 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_374_not__less__bot,axiom,
% 0.27/0.65 ! [A_64: $o] :
% 0.27/0.65 ~ ( ord_less_o @ A_64 @ bot_bot_o ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_375_not__less__bot,axiom,
% 0.27/0.65 ! [A_64: nat] :
% 0.27/0.65 ~ ( ord_less_nat @ A_64 @ bot_bot_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_376_not__less__bot,axiom,
% 0.27/0.65 ! [A_64: nat > $o] :
% 0.27/0.65 ~ ( ord_less_nat_o @ A_64 @ bot_bot_nat_o ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_377_bot__less,axiom,
% 0.27/0.65 ! [A_63: $o] :
% 0.27/0.65 ( ~ ( A_63
% 0.27/0.65 <=> bot_bot_o )
% 0.27/0.65 <=> ( ord_less_o @ bot_bot_o @ A_63 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_378_bot__less,axiom,
% 0.27/0.65 ! [A_63: nat] :
% 0.27/0.65 ( ( A_63 != bot_bot_nat )
% 0.27/0.65 <=> ( ord_less_nat @ bot_bot_nat @ A_63 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_379_bot__less,axiom,
% 0.27/0.65 ! [A_63: nat > $o] :
% 0.27/0.65 ( ( A_63 != bot_bot_nat_o )
% 0.27/0.65 <=> ( ord_less_nat_o @ bot_bot_nat_o @ A_63 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_380_drop__0,axiom,
% 0.27/0.65 ! [Xs_73: list_A2115238852le_alt] :
% 0.27/0.65 ( ( drop_A1346709759le_alt @ zero_zero_nat @ Xs_73 )
% 0.27/0.65 = Xs_73 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_381_drop__Nil,axiom,
% 0.27/0.65 ! [N_42: nat] :
% 0.27/0.65 ( ( drop_nat @ N_42 @ nil_nat )
% 0.27/0.65 = nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_382_drop__Nil,axiom,
% 0.27/0.65 ! [N_42: nat] :
% 0.27/0.65 ( ( drop_A1346709759le_alt @ N_42 @ nil_Ar1286194111le_alt )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_383_less__max__iff__disj,axiom,
% 0.27/0.65 ! [Z_4: int,X_32: int,Y_10: int] :
% 0.27/0.65 ( ( ord_less_int @ Z_4 @ ( ord_max_int @ X_32 @ Y_10 ) )
% 0.27/0.65 <=> ( ( ord_less_int @ Z_4 @ X_32 )
% 0.27/0.65 | ( ord_less_int @ Z_4 @ Y_10 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_384_less__max__iff__disj,axiom,
% 0.27/0.65 ! [Z_4: nat,X_32: nat,Y_10: nat] :
% 0.27/0.65 ( ( ord_less_nat @ Z_4 @ ( ord_max_nat @ X_32 @ Y_10 ) )
% 0.27/0.65 <=> ( ( ord_less_nat @ Z_4 @ X_32 )
% 0.27/0.65 | ( ord_less_nat @ Z_4 @ Y_10 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_385_max__less__iff__conj,axiom,
% 0.27/0.65 ! [X_31: int,Y_9: int,Z_3: int] :
% 0.27/0.65 ( ( ord_less_int @ ( ord_max_int @ X_31 @ Y_9 ) @ Z_3 )
% 0.27/0.65 <=> ( ( ord_less_int @ X_31 @ Z_3 )
% 0.27/0.65 & ( ord_less_int @ Y_9 @ Z_3 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_386_max__less__iff__conj,axiom,
% 0.27/0.65 ! [X_31: nat,Y_9: nat,Z_3: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( ord_max_nat @ X_31 @ Y_9 ) @ Z_3 )
% 0.27/0.65 <=> ( ( ord_less_nat @ X_31 @ Z_3 )
% 0.27/0.65 & ( ord_less_nat @ Y_9 @ Z_3 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_387_min__max_Oless__supI1,axiom,
% 0.27/0.65 ! [B_37: int,X_30: int,A_62: int] :
% 0.27/0.65 ( ( ord_less_int @ X_30 @ A_62 )
% 0.27/0.65 => ( ord_less_int @ X_30 @ ( ord_max_int @ A_62 @ B_37 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_388_min__max_Oless__supI1,axiom,
% 0.27/0.65 ! [B_37: nat,X_30: nat,A_62: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_30 @ A_62 )
% 0.27/0.65 => ( ord_less_nat @ X_30 @ ( ord_max_nat @ A_62 @ B_37 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_389_min__max_Oless__supI2,axiom,
% 0.27/0.65 ! [A_61: int,X_29: int,B_36: int] :
% 0.27/0.65 ( ( ord_less_int @ X_29 @ B_36 )
% 0.27/0.65 => ( ord_less_int @ X_29 @ ( ord_max_int @ A_61 @ B_36 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_390_min__max_Oless__supI2,axiom,
% 0.27/0.65 ! [A_61: nat,X_29: nat,B_36: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X_29 @ B_36 )
% 0.27/0.65 => ( ord_less_nat @ X_29 @ ( ord_max_nat @ A_61 @ B_36 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_391_distinct__drop,axiom,
% 0.27/0.65 ! [I_19: nat,Xs_72: list_A2115238852le_alt] :
% 0.27/0.65 ( ( distin236324274le_alt @ Xs_72 )
% 0.27/0.65 => ( distin236324274le_alt @ ( drop_A1346709759le_alt @ I_19 @ Xs_72 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_392_sorted__drop,axiom,
% 0.27/0.65 ! [N_41: nat,Xs_71: list_nat] :
% 0.27/0.65 ( ( linorder_sorted_nat @ Xs_71 )
% 0.27/0.65 => ( linorder_sorted_nat @ ( drop_nat @ N_41 @ Xs_71 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_393_list__update__nonempty,axiom,
% 0.27/0.65 ! [Xs_70: list_nat,K_7: nat,X_28: nat] :
% 0.27/0.65 ( ( ( list_update_nat @ Xs_70 @ K_7 @ X_28 )
% 0.27/0.65 = nil_nat )
% 0.27/0.65 <=> ( Xs_70 = nil_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_394_list__update__nonempty,axiom,
% 0.27/0.65 ! [Xs_70: list_A2115238852le_alt,K_7: nat,X_28: arrow_475358991le_alt] :
% 0.27/0.65 ( ( ( list_u62477863le_alt @ Xs_70 @ K_7 @ X_28 )
% 0.27/0.65 = nil_Ar1286194111le_alt )
% 0.27/0.65 <=> ( Xs_70 = nil_Ar1286194111le_alt ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_395_list__update_Osimps_I1_J,axiom,
% 0.27/0.65 ! [I_18: nat,V_3: nat] :
% 0.27/0.65 ( ( list_update_nat @ nil_nat @ I_18 @ V_3 )
% 0.27/0.65 = nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_396_list__update_Osimps_I1_J,axiom,
% 0.27/0.65 ! [I_18: nat,V_3: arrow_475358991le_alt] :
% 0.27/0.65 ( ( list_u62477863le_alt @ nil_Ar1286194111le_alt @ I_18 @ V_3 )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_397_list__update__code_I1_J,axiom,
% 0.27/0.65 ! [I_17: nat,Y_8: nat] :
% 0.27/0.65 ( ( list_update_nat @ nil_nat @ I_17 @ Y_8 )
% 0.27/0.65 = nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_398_list__update__code_I1_J,axiom,
% 0.27/0.65 ! [I_17: nat,Y_8: arrow_475358991le_alt] :
% 0.27/0.65 ( ( list_u62477863le_alt @ nil_Ar1286194111le_alt @ I_17 @ Y_8 )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_399_length__list__update,axiom,
% 0.27/0.65 ! [Xs_69: list_A2115238852le_alt,I_16: nat,X_27: arrow_475358991le_alt] :
% 0.27/0.65 ( ( size_s1858781230le_alt @ ( list_u62477863le_alt @ Xs_69 @ I_16 @ X_27 ) )
% 0.27/0.65 = ( size_s1858781230le_alt @ Xs_69 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_400_list__update__id,axiom,
% 0.27/0.65 ! [Xs_68: list_A2115238852le_alt,I_15: nat] :
% 0.27/0.65 ( ( list_u62477863le_alt @ Xs_68 @ I_15 @ ( nth_Ar125878976le_alt @ Xs_68 @ I_15 ) )
% 0.27/0.65 = Xs_68 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_401_list__update__id,axiom,
% 0.27/0.65 ! [Xs_68: list_nat,I_15: nat] :
% 0.27/0.65 ( ( list_update_nat @ Xs_68 @ I_15 @ ( nth_nat @ Xs_68 @ I_15 ) )
% 0.27/0.65 = Xs_68 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_402_nth__list__update__neq,axiom,
% 0.27/0.65 ! [Xs_67: list_A2115238852le_alt,X_26: arrow_475358991le_alt,I_14: nat,J_5: nat] :
% 0.27/0.65 ( ( I_14 != J_5 )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ ( list_u62477863le_alt @ Xs_67 @ I_14 @ X_26 ) @ J_5 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Xs_67 @ J_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_403_nth__list__update__neq,axiom,
% 0.27/0.65 ! [Xs_67: list_nat,X_26: nat,I_14: nat,J_5: nat] :
% 0.27/0.65 ( ( I_14 != J_5 )
% 0.27/0.65 => ( ( nth_nat @ ( list_update_nat @ Xs_67 @ I_14 @ X_26 ) @ J_5 )
% 0.27/0.65 = ( nth_nat @ Xs_67 @ J_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_404_drop__butlast,axiom,
% 0.27/0.65 ! [N_40: nat,Xs_66: list_A2115238852le_alt] :
% 0.27/0.65 ( ( drop_A1346709759le_alt @ N_40 @ ( butlas274947851le_alt @ Xs_66 ) )
% 0.27/0.65 = ( butlas274947851le_alt @ ( drop_A1346709759le_alt @ N_40 @ Xs_66 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_405_butlast__drop,axiom,
% 0.27/0.65 ! [N_39: nat,Xs_65: list_A2115238852le_alt] :
% 0.27/0.65 ( ( butlas274947851le_alt @ ( drop_A1346709759le_alt @ N_39 @ Xs_65 ) )
% 0.27/0.65 = ( drop_A1346709759le_alt @ N_39 @ ( butlas274947851le_alt @ Xs_65 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_406_tl__drop,axiom,
% 0.27/0.65 ! [N_38: nat,Xs_64: list_A2115238852le_alt] :
% 0.27/0.65 ( ( tl_Arr465451158le_alt @ ( drop_A1346709759le_alt @ N_38 @ Xs_64 ) )
% 0.27/0.65 = ( drop_A1346709759le_alt @ N_38 @ ( tl_Arr465451158le_alt @ Xs_64 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_407_drop__tl,axiom,
% 0.27/0.65 ! [N_37: nat,Xs_63: list_A2115238852le_alt] :
% 0.27/0.65 ( ( drop_A1346709759le_alt @ N_37 @ ( tl_Arr465451158le_alt @ Xs_63 ) )
% 0.27/0.65 = ( tl_Arr465451158le_alt @ ( drop_A1346709759le_alt @ N_37 @ Xs_63 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_408_hd__drop__conv__nth,axiom,
% 0.27/0.65 ! [N_36: nat,Xs_62: list_nat] :
% 0.27/0.65 ( ( Xs_62 != nil_nat )
% 0.27/0.65 => ( ( ord_less_nat @ N_36 @ ( size_size_list_nat @ Xs_62 ) )
% 0.27/0.65 => ( ( hd_nat @ ( drop_nat @ N_36 @ Xs_62 ) )
% 0.27/0.65 = ( nth_nat @ Xs_62 @ N_36 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_409_hd__drop__conv__nth,axiom,
% 0.27/0.65 ! [N_36: nat,Xs_62: list_A2115238852le_alt] :
% 0.27/0.65 ( ( Xs_62 != nil_Ar1286194111le_alt )
% 0.27/0.65 => ( ( ord_less_nat @ N_36 @ ( size_s1858781230le_alt @ Xs_62 ) )
% 0.27/0.65 => ( ( hd_Arr1965683346le_alt @ ( drop_A1346709759le_alt @ N_36 @ Xs_62 ) )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Xs_62 @ N_36 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_410_nth__via__drop,axiom,
% 0.27/0.65 ! [N_35: nat,Xs_61: list_nat,Y_7: nat,Ys_12: list_nat] :
% 0.27/0.65 ( ( ( drop_nat @ N_35 @ Xs_61 )
% 0.27/0.65 = ( cons_nat @ Y_7 @ Ys_12 ) )
% 0.27/0.65 => ( ( nth_nat @ Xs_61 @ N_35 )
% 0.27/0.65 = Y_7 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_411_nth__via__drop,axiom,
% 0.27/0.65 ! [N_35: nat,Xs_61: list_A2115238852le_alt,Y_7: arrow_475358991le_alt,Ys_12: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( drop_A1346709759le_alt @ N_35 @ Xs_61 )
% 0.27/0.65 = ( cons_A228743023le_alt @ Y_7 @ Ys_12 ) )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ Xs_61 @ N_35 )
% 0.27/0.65 = Y_7 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_412_list__eq__iff__nth__eq,axiom,
% 0.27/0.65 ! [Xs_60: list_A2115238852le_alt,Ys_11: list_A2115238852le_alt] :
% 0.27/0.65 ( ( Xs_60 = Ys_11 )
% 0.27/0.65 <=> ( ( ( size_s1858781230le_alt @ Xs_60 )
% 0.27/0.65 = ( size_s1858781230le_alt @ Ys_11 ) )
% 0.27/0.65 & ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ ( size_s1858781230le_alt @ Xs_60 ) )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ Xs_60 @ I_4 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Ys_11 @ I_4 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_413_list__eq__iff__nth__eq,axiom,
% 0.27/0.65 ! [Xs_60: list_nat,Ys_11: list_nat] :
% 0.27/0.65 ( ( Xs_60 = Ys_11 )
% 0.27/0.65 <=> ( ( ( size_size_list_nat @ Xs_60 )
% 0.27/0.65 = ( size_size_list_nat @ Ys_11 ) )
% 0.27/0.65 & ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ ( size_size_list_nat @ Xs_60 ) )
% 0.27/0.65 => ( ( nth_nat @ Xs_60 @ I_4 )
% 0.27/0.65 = ( nth_nat @ Ys_11 @ I_4 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_414_list__update__code_I2_J,axiom,
% 0.27/0.65 ! [X_25: arrow_475358991le_alt,Xs_59: list_A2115238852le_alt,Y_6: arrow_475358991le_alt] :
% 0.27/0.65 ( ( list_u62477863le_alt @ ( cons_A228743023le_alt @ X_25 @ Xs_59 ) @ zero_zero_nat @ Y_6 )
% 0.27/0.65 = ( cons_A228743023le_alt @ Y_6 @ Xs_59 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_415_nth__replicate,axiom,
% 0.27/0.65 ! [X_24: nat,I_13: nat,N_34: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_13 @ N_34 )
% 0.27/0.65 => ( ( nth_nat @ ( replicate_nat @ N_34 @ X_24 ) @ I_13 )
% 0.27/0.65 = X_24 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_416_nth__replicate,axiom,
% 0.27/0.65 ! [X_24: arrow_475358991le_alt,I_13: nat,N_34: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_13 @ N_34 )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ ( replic1511538809le_alt @ N_34 @ X_24 ) @ I_13 )
% 0.27/0.65 = X_24 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_417_length__greater__0__conv,axiom,
% 0.27/0.65 ! [Xs_58: list_nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs_58 ) )
% 0.27/0.65 <=> ( Xs_58 != nil_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_418_length__greater__0__conv,axiom,
% 0.27/0.65 ! [Xs_58: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1858781230le_alt @ Xs_58 ) )
% 0.27/0.65 <=> ( Xs_58 != nil_Ar1286194111le_alt ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_419_distinct__conv__nth,axiom,
% 0.27/0.65 ! [Xs_57: list_nat] :
% 0.27/0.65 ( ( distinct_nat @ Xs_57 )
% 0.27/0.65 <=> ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ ( size_size_list_nat @ Xs_57 ) )
% 0.27/0.65 => ! [J_2: nat] :
% 0.27/0.65 ( ( ord_less_nat @ J_2 @ ( size_size_list_nat @ Xs_57 ) )
% 0.27/0.65 => ( ( I_4 != J_2 )
% 0.27/0.65 => ( ( nth_nat @ Xs_57 @ I_4 )
% 0.27/0.65 != ( nth_nat @ Xs_57 @ J_2 ) ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_420_distinct__conv__nth,axiom,
% 0.27/0.65 ! [Xs_57: list_A2115238852le_alt] :
% 0.27/0.65 ( ( distin236324274le_alt @ Xs_57 )
% 0.27/0.65 <=> ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ ( size_s1858781230le_alt @ Xs_57 ) )
% 0.27/0.65 => ! [J_2: nat] :
% 0.27/0.65 ( ( ord_less_nat @ J_2 @ ( size_s1858781230le_alt @ Xs_57 ) )
% 0.27/0.65 => ( ( I_4 != J_2 )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ Xs_57 @ I_4 )
% 0.27/0.65 != ( nth_Ar125878976le_alt @ Xs_57 @ J_2 ) ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_421_nth__eq__iff__index__eq,axiom,
% 0.27/0.65 ! [J_4: nat,I_12: nat,Xs_56: list_nat] :
% 0.27/0.65 ( ( distinct_nat @ Xs_56 )
% 0.27/0.65 => ( ( ord_less_nat @ I_12 @ ( size_size_list_nat @ Xs_56 ) )
% 0.27/0.65 => ( ( ord_less_nat @ J_4 @ ( size_size_list_nat @ Xs_56 ) )
% 0.27/0.65 => ( ( ( nth_nat @ Xs_56 @ I_12 )
% 0.27/0.65 = ( nth_nat @ Xs_56 @ J_4 ) )
% 0.27/0.65 <=> ( I_12 = J_4 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_422_nth__eq__iff__index__eq,axiom,
% 0.27/0.65 ! [J_4: nat,I_12: nat,Xs_56: list_A2115238852le_alt] :
% 0.27/0.65 ( ( distin236324274le_alt @ Xs_56 )
% 0.27/0.65 => ( ( ord_less_nat @ I_12 @ ( size_s1858781230le_alt @ Xs_56 ) )
% 0.27/0.65 => ( ( ord_less_nat @ J_4 @ ( size_s1858781230le_alt @ Xs_56 ) )
% 0.27/0.65 => ( ( ( nth_Ar125878976le_alt @ Xs_56 @ I_12 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Xs_56 @ J_4 ) )
% 0.27/0.65 <=> ( I_12 = J_4 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_423_bot__nat__def,axiom,
% 0.27/0.65 bot_bot_nat = zero_zero_nat ).
% 0.27/0.65
% 0.27/0.65 thf(fact_424_max__0R,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( ord_max_nat @ N_5 @ zero_zero_nat )
% 0.27/0.65 = N_5 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_425_nth__equalityI,axiom,
% 0.27/0.65 ! [Xs_55: list_A2115238852le_alt,Ys_10: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( size_s1858781230le_alt @ Xs_55 )
% 0.27/0.65 = ( size_s1858781230le_alt @ Ys_10 ) )
% 0.27/0.65 => ( ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ ( size_s1858781230le_alt @ Xs_55 ) )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ Xs_55 @ I_4 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Ys_10 @ I_4 ) ) )
% 0.27/0.65 => ( Xs_55 = Ys_10 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_426_nth__equalityI,axiom,
% 0.27/0.65 ! [Xs_55: list_nat,Ys_10: list_nat] :
% 0.27/0.65 ( ( ( size_size_list_nat @ Xs_55 )
% 0.27/0.65 = ( size_size_list_nat @ Ys_10 ) )
% 0.27/0.65 => ( ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ ( size_size_list_nat @ Xs_55 ) )
% 0.27/0.65 => ( ( nth_nat @ Xs_55 @ I_4 )
% 0.27/0.65 = ( nth_nat @ Ys_10 @ I_4 ) ) )
% 0.27/0.65 => ( Xs_55 = Ys_10 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_427_Skolem__list__nth,axiom,
% 0.27/0.65 ! [P_9: nat > arrow_475358991le_alt > $o,K_6: nat] :
% 0.27/0.65 ( ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ K_6 )
% 0.27/0.65 => ( ex2 @ ( P_9 @ I_4 ) ) )
% 0.27/0.65 <=> ? [Xs_54: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( size_s1858781230le_alt @ Xs_54 )
% 0.27/0.65 = K_6 )
% 0.27/0.65 & ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ K_6 )
% 0.27/0.65 => ( P_9 @ I_4 @ ( nth_Ar125878976le_alt @ Xs_54 @ I_4 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_428_Skolem__list__nth,axiom,
% 0.27/0.65 ! [P_9: nat > nat > $o,K_6: nat] :
% 0.27/0.65 ( ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ K_6 )
% 0.27/0.65 => ( ex1 @ ( P_9 @ I_4 ) ) )
% 0.27/0.65 <=> ? [Xs_54: list_nat] :
% 0.27/0.65 ( ( ( size_size_list_nat @ Xs_54 )
% 0.27/0.65 = K_6 )
% 0.27/0.65 & ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ K_6 )
% 0.27/0.65 => ( P_9 @ I_4 @ ( nth_nat @ Xs_54 @ I_4 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_429_dropWhile__nth,axiom,
% 0.27/0.65 ! [J_3: nat,P_8: nat > $o,Xs_53: list_nat] :
% 0.27/0.65 ( ( ord_less_nat @ J_3 @ ( size_size_list_nat @ ( dropWhile_nat @ P_8 @ Xs_53 ) ) )
% 0.27/0.65 => ( ( nth_nat @ ( dropWhile_nat @ P_8 @ Xs_53 ) @ J_3 )
% 0.27/0.65 = ( nth_nat @ Xs_53 @ ( plus_plus_nat @ J_3 @ ( size_size_list_nat @ ( takeWhile_nat @ P_8 @ Xs_53 ) ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_430_dropWhile__nth,axiom,
% 0.27/0.65 ! [J_3: nat,P_8: arrow_475358991le_alt > $o,Xs_53: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ J_3 @ ( size_s1858781230le_alt @ ( dropWh1316781920le_alt @ P_8 @ Xs_53 ) ) )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ ( dropWh1316781920le_alt @ P_8 @ Xs_53 ) @ J_3 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Xs_53 @ ( plus_plus_nat @ J_3 @ ( size_s1858781230le_alt @ ( takeWh1696291512le_alt @ P_8 @ Xs_53 ) ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_431_nth__drop_H,axiom,
% 0.27/0.65 ! [I_11: nat,Xs_52: list_nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_11 @ ( size_size_list_nat @ Xs_52 ) )
% 0.27/0.65 => ( ( cons_nat @ ( nth_nat @ Xs_52 @ I_11 ) @ ( drop_nat @ ( suc @ I_11 ) @ Xs_52 ) )
% 0.27/0.65 = ( drop_nat @ I_11 @ Xs_52 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_432_nth__drop_H,axiom,
% 0.27/0.65 ! [I_11: nat,Xs_52: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ I_11 @ ( size_s1858781230le_alt @ Xs_52 ) )
% 0.27/0.65 => ( ( cons_A228743023le_alt @ ( nth_Ar125878976le_alt @ Xs_52 @ I_11 ) @ ( drop_A1346709759le_alt @ ( suc @ I_11 ) @ Xs_52 ) )
% 0.27/0.65 = ( drop_A1346709759le_alt @ I_11 @ Xs_52 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_433_list__ex__length,axiom,
% 0.27/0.65 ! [P_7: arrow_475358991le_alt > $o,Xs_51: list_A2115238852le_alt] :
% 0.27/0.65 ( ( list_e1252802557le_alt @ P_7 @ Xs_51 )
% 0.27/0.65 <=> ? [N_7: nat] :
% 0.27/0.65 ( ( ord_less_nat @ N_7 @ ( size_s1858781230le_alt @ Xs_51 ) )
% 0.27/0.65 & ( P_7 @ ( nth_Ar125878976le_alt @ Xs_51 @ N_7 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_434_list__ex__length,axiom,
% 0.27/0.65 ! [P_7: nat > $o,Xs_51: list_nat] :
% 0.27/0.65 ( ( list_ex_nat @ P_7 @ Xs_51 )
% 0.27/0.65 <=> ? [N_7: nat] :
% 0.27/0.65 ( ( ord_less_nat @ N_7 @ ( size_size_list_nat @ Xs_51 ) )
% 0.27/0.65 & ( P_7 @ ( nth_nat @ Xs_51 @ N_7 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_435_lessI,axiom,
% 0.27/0.65 ! [N_5: nat] : ( ord_less_nat @ N_5 @ ( suc @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_436_Suc__mono,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_437_zero__less__Suc,axiom,
% 0.27/0.65 ! [N_5: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_438_Suc__inject,axiom,
% 0.27/0.65 ! [X: nat,Y: nat] :
% 0.27/0.65 ( ( ( suc @ X )
% 0.27/0.65 = ( suc @ Y ) )
% 0.27/0.65 => ( X = Y ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_439_nat__add__right__cancel,axiom,
% 0.27/0.65 ! [M: nat,K_3: nat,N_5: nat] :
% 0.27/0.65 ( ( ( plus_plus_nat @ M @ K_3 )
% 0.27/0.65 = ( plus_plus_nat @ N_5 @ K_3 ) )
% 0.27/0.65 <=> ( M = N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_440_nat__add__left__cancel,axiom,
% 0.27/0.65 ! [K_3: nat,M: nat,N_5: nat] :
% 0.27/0.65 ( ( ( plus_plus_nat @ K_3 @ M )
% 0.27/0.65 = ( plus_plus_nat @ K_3 @ N_5 ) )
% 0.27/0.65 <=> ( M = N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_441_nat__add__assoc,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat,K_3: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ ( plus_plus_nat @ M @ N_5 ) @ K_3 )
% 0.27/0.65 = ( plus_plus_nat @ M @ ( plus_plus_nat @ N_5 @ K_3 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_442_nat_Oinject,axiom,
% 0.27/0.65 ! [Nat_3: nat,Nat_2: nat] :
% 0.27/0.65 ( ( ( suc @ Nat_3 )
% 0.27/0.65 = ( suc @ Nat_2 ) )
% 0.27/0.65 <=> ( Nat_3 = Nat_2 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_443_add__Suc__shift,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ ( suc @ M ) @ N_5 )
% 0.27/0.65 = ( plus_plus_nat @ M @ ( suc @ N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_444_add__Suc,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ ( suc @ M ) @ N_5 )
% 0.27/0.65 = ( suc @ ( plus_plus_nat @ M @ N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_445_nat__add__left__commute,axiom,
% 0.27/0.65 ! [X: nat,Y: nat,Z_1: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ X @ ( plus_plus_nat @ Y @ Z_1 ) )
% 0.27/0.65 = ( plus_plus_nat @ Y @ ( plus_plus_nat @ X @ Z_1 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_446_add__Suc__right,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ M @ ( suc @ N_5 ) )
% 0.27/0.65 = ( suc @ ( plus_plus_nat @ M @ N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_447_nat__add__commute,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ M @ N_5 )
% 0.27/0.65 = ( plus_plus_nat @ N_5 @ M ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_448_less__iff__Suc__add,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 <=> ? [K_5: nat] :
% 0.27/0.65 ( N_5
% 0.27/0.65 = ( suc @ ( plus_plus_nat @ M @ K_5 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_449_less__add__Suc2,axiom,
% 0.27/0.65 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_450_less__add__Suc1,axiom,
% 0.27/0.65 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_451_Suc__n__not__n,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( suc @ N_5 )
% 0.27/0.65 != N_5 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_452_n__not__Suc__n,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( N_5
% 0.27/0.65 != ( suc @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_453_add__is__1,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ( plus_plus_nat @ M @ N_5 )
% 0.27/0.65 = ( suc @ zero_zero_nat ) )
% 0.27/0.65 <=> ( ( ( M
% 0.27/0.65 = ( suc @ zero_zero_nat ) )
% 0.27/0.65 & ( N_5 = zero_zero_nat ) )
% 0.27/0.65 | ( ( M = zero_zero_nat )
% 0.27/0.65 & ( N_5
% 0.27/0.65 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_454_one__is__add,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ( suc @ zero_zero_nat )
% 0.27/0.65 = ( plus_plus_nat @ M @ N_5 ) )
% 0.27/0.65 <=> ( ( ( M
% 0.27/0.65 = ( suc @ zero_zero_nat ) )
% 0.27/0.65 & ( N_5 = zero_zero_nat ) )
% 0.27/0.65 | ( ( M = zero_zero_nat )
% 0.27/0.65 & ( N_5
% 0.27/0.65 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_455_add__right__imp__eq,axiom,
% 0.27/0.65 ! [B_35: nat,A_60: nat,C_29: nat] :
% 0.27/0.65 ( ( ( plus_plus_nat @ B_35 @ A_60 )
% 0.27/0.65 = ( plus_plus_nat @ C_29 @ A_60 ) )
% 0.27/0.65 => ( B_35 = C_29 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_456_add__right__imp__eq,axiom,
% 0.27/0.65 ! [B_35: int,A_60: int,C_29: int] :
% 0.27/0.65 ( ( ( plus_plus_int @ B_35 @ A_60 )
% 0.27/0.65 = ( plus_plus_int @ C_29 @ A_60 ) )
% 0.27/0.65 => ( B_35 = C_29 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_457_add__imp__eq,axiom,
% 0.27/0.65 ! [A_59: nat,B_34: nat,C_28: nat] :
% 0.27/0.65 ( ( ( plus_plus_nat @ A_59 @ B_34 )
% 0.27/0.65 = ( plus_plus_nat @ A_59 @ C_28 ) )
% 0.27/0.65 => ( B_34 = C_28 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_458_add__imp__eq,axiom,
% 0.27/0.65 ! [A_59: int,B_34: int,C_28: int] :
% 0.27/0.65 ( ( ( plus_plus_int @ A_59 @ B_34 )
% 0.27/0.65 = ( plus_plus_int @ A_59 @ C_28 ) )
% 0.27/0.65 => ( B_34 = C_28 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_459_add__left__imp__eq,axiom,
% 0.27/0.65 ! [A_58: nat,B_33: nat,C_27: nat] :
% 0.27/0.65 ( ( ( plus_plus_nat @ A_58 @ B_33 )
% 0.27/0.65 = ( plus_plus_nat @ A_58 @ C_27 ) )
% 0.27/0.65 => ( B_33 = C_27 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_460_add__left__imp__eq,axiom,
% 0.27/0.65 ! [A_58: int,B_33: int,C_27: int] :
% 0.27/0.65 ( ( ( plus_plus_int @ A_58 @ B_33 )
% 0.27/0.65 = ( plus_plus_int @ A_58 @ C_27 ) )
% 0.27/0.65 => ( B_33 = C_27 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_461_add__right__cancel,axiom,
% 0.27/0.65 ! [B_32: nat,A_57: nat,C_26: nat] :
% 0.27/0.65 ( ( ( plus_plus_nat @ B_32 @ A_57 )
% 0.27/0.65 = ( plus_plus_nat @ C_26 @ A_57 ) )
% 0.27/0.65 <=> ( B_32 = C_26 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_462_add__right__cancel,axiom,
% 0.27/0.65 ! [B_32: int,A_57: int,C_26: int] :
% 0.27/0.65 ( ( ( plus_plus_int @ B_32 @ A_57 )
% 0.27/0.65 = ( plus_plus_int @ C_26 @ A_57 ) )
% 0.27/0.65 <=> ( B_32 = C_26 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_463_add__left__cancel,axiom,
% 0.27/0.65 ! [A_56: nat,B_31: nat,C_25: nat] :
% 0.27/0.65 ( ( ( plus_plus_nat @ A_56 @ B_31 )
% 0.27/0.65 = ( plus_plus_nat @ A_56 @ C_25 ) )
% 0.27/0.65 <=> ( B_31 = C_25 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_464_add__left__cancel,axiom,
% 0.27/0.65 ! [A_56: int,B_31: int,C_25: int] :
% 0.27/0.65 ( ( ( plus_plus_int @ A_56 @ B_31 )
% 0.27/0.65 = ( plus_plus_int @ A_56 @ C_25 ) )
% 0.27/0.65 <=> ( B_31 = C_25 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_465_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.27/0.65 ! [A_55: nat,B_30: nat,C_24: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ ( plus_plus_nat @ A_55 @ B_30 ) @ C_24 )
% 0.27/0.65 = ( plus_plus_nat @ A_55 @ ( plus_plus_nat @ B_30 @ C_24 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_466_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.27/0.65 ! [A_55: int,B_30: int,C_24: int] :
% 0.27/0.65 ( ( plus_plus_int @ ( plus_plus_int @ A_55 @ B_30 ) @ C_24 )
% 0.27/0.65 = ( plus_plus_int @ A_55 @ ( plus_plus_int @ B_30 @ C_24 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_467_add_Ocomm__neutral,axiom,
% 0.27/0.65 ! [A_54: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ A_54 @ zero_zero_nat )
% 0.27/0.65 = A_54 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_468_add_Ocomm__neutral,axiom,
% 0.27/0.65 ! [A_54: int] :
% 0.27/0.65 ( ( plus_plus_int @ A_54 @ zero_zero_int )
% 0.27/0.65 = A_54 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_469_add__0__right,axiom,
% 0.27/0.65 ! [A_53: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ A_53 @ zero_zero_nat )
% 0.27/0.65 = A_53 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_470_add__0__right,axiom,
% 0.27/0.65 ! [A_53: int] :
% 0.27/0.65 ( ( plus_plus_int @ A_53 @ zero_zero_int )
% 0.27/0.65 = A_53 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_471_double__zero__sym,axiom,
% 0.27/0.65 ! [A_52: int] :
% 0.27/0.65 ( ( zero_zero_int
% 0.27/0.65 = ( plus_plus_int @ A_52 @ A_52 ) )
% 0.27/0.65 <=> ( A_52 = zero_zero_int ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_472_add__0,axiom,
% 0.27/0.65 ! [A_51: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ zero_zero_nat @ A_51 )
% 0.27/0.65 = A_51 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_473_add__0,axiom,
% 0.27/0.65 ! [A_51: int] :
% 0.27/0.65 ( ( plus_plus_int @ zero_zero_int @ A_51 )
% 0.27/0.65 = A_51 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_474_add__0__left,axiom,
% 0.27/0.65 ! [A_50: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ zero_zero_nat @ A_50 )
% 0.27/0.65 = A_50 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_475_add__0__left,axiom,
% 0.27/0.65 ! [A_50: int] :
% 0.27/0.65 ( ( plus_plus_int @ zero_zero_int @ A_50 )
% 0.27/0.65 = A_50 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_476_add__less__imp__less__left,axiom,
% 0.27/0.65 ! [C_23: nat,A_49: nat,B_29: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( plus_plus_nat @ C_23 @ A_49 ) @ ( plus_plus_nat @ C_23 @ B_29 ) )
% 0.27/0.65 => ( ord_less_nat @ A_49 @ B_29 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_477_add__less__imp__less__left,axiom,
% 0.27/0.65 ! [C_23: int,A_49: int,B_29: int] :
% 0.27/0.65 ( ( ord_less_int @ ( plus_plus_int @ C_23 @ A_49 ) @ ( plus_plus_int @ C_23 @ B_29 ) )
% 0.27/0.65 => ( ord_less_int @ A_49 @ B_29 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_478_add__less__imp__less__right,axiom,
% 0.27/0.65 ! [A_48: nat,C_22: nat,B_28: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( plus_plus_nat @ A_48 @ C_22 ) @ ( plus_plus_nat @ B_28 @ C_22 ) )
% 0.27/0.65 => ( ord_less_nat @ A_48 @ B_28 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_479_add__less__imp__less__right,axiom,
% 0.27/0.65 ! [A_48: int,C_22: int,B_28: int] :
% 0.27/0.65 ( ( ord_less_int @ ( plus_plus_int @ A_48 @ C_22 ) @ ( plus_plus_int @ B_28 @ C_22 ) )
% 0.27/0.65 => ( ord_less_int @ A_48 @ B_28 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_480_add__strict__mono,axiom,
% 0.27/0.65 ! [C_21: nat,D_6: nat,A_47: nat,B_27: nat] :
% 0.27/0.65 ( ( ord_less_nat @ A_47 @ B_27 )
% 0.27/0.65 => ( ( ord_less_nat @ C_21 @ D_6 )
% 0.27/0.65 => ( ord_less_nat @ ( plus_plus_nat @ A_47 @ C_21 ) @ ( plus_plus_nat @ B_27 @ D_6 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_481_add__strict__mono,axiom,
% 0.27/0.65 ! [C_21: int,D_6: int,A_47: int,B_27: int] :
% 0.27/0.65 ( ( ord_less_int @ A_47 @ B_27 )
% 0.27/0.65 => ( ( ord_less_int @ C_21 @ D_6 )
% 0.27/0.65 => ( ord_less_int @ ( plus_plus_int @ A_47 @ C_21 ) @ ( plus_plus_int @ B_27 @ D_6 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_482_add__strict__left__mono,axiom,
% 0.27/0.65 ! [C_20: nat,A_46: nat,B_26: nat] :
% 0.27/0.65 ( ( ord_less_nat @ A_46 @ B_26 )
% 0.27/0.65 => ( ord_less_nat @ ( plus_plus_nat @ C_20 @ A_46 ) @ ( plus_plus_nat @ C_20 @ B_26 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_483_add__strict__left__mono,axiom,
% 0.27/0.65 ! [C_20: int,A_46: int,B_26: int] :
% 0.27/0.65 ( ( ord_less_int @ A_46 @ B_26 )
% 0.27/0.65 => ( ord_less_int @ ( plus_plus_int @ C_20 @ A_46 ) @ ( plus_plus_int @ C_20 @ B_26 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_484_add__strict__right__mono,axiom,
% 0.27/0.65 ! [C_19: nat,A_45: nat,B_25: nat] :
% 0.27/0.65 ( ( ord_less_nat @ A_45 @ B_25 )
% 0.27/0.65 => ( ord_less_nat @ ( plus_plus_nat @ A_45 @ C_19 ) @ ( plus_plus_nat @ B_25 @ C_19 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_485_add__strict__right__mono,axiom,
% 0.27/0.65 ! [C_19: int,A_45: int,B_25: int] :
% 0.27/0.65 ( ( ord_less_int @ A_45 @ B_25 )
% 0.27/0.65 => ( ord_less_int @ ( plus_plus_int @ A_45 @ C_19 ) @ ( plus_plus_int @ B_25 @ C_19 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_486_add__less__cancel__left,axiom,
% 0.27/0.65 ! [C_18: nat,A_44: nat,B_24: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( plus_plus_nat @ C_18 @ A_44 ) @ ( plus_plus_nat @ C_18 @ B_24 ) )
% 0.27/0.65 <=> ( ord_less_nat @ A_44 @ B_24 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_487_add__less__cancel__left,axiom,
% 0.27/0.65 ! [C_18: int,A_44: int,B_24: int] :
% 0.27/0.65 ( ( ord_less_int @ ( plus_plus_int @ C_18 @ A_44 ) @ ( plus_plus_int @ C_18 @ B_24 ) )
% 0.27/0.65 <=> ( ord_less_int @ A_44 @ B_24 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_488_add__less__cancel__right,axiom,
% 0.27/0.65 ! [A_43: nat,C_17: nat,B_23: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( plus_plus_nat @ A_43 @ C_17 ) @ ( plus_plus_nat @ B_23 @ C_17 ) )
% 0.27/0.65 <=> ( ord_less_nat @ A_43 @ B_23 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_489_add__less__cancel__right,axiom,
% 0.27/0.65 ! [A_43: int,C_17: int,B_23: int] :
% 0.27/0.65 ( ( ord_less_int @ ( plus_plus_int @ A_43 @ C_17 ) @ ( plus_plus_int @ B_23 @ C_17 ) )
% 0.27/0.65 <=> ( ord_less_int @ A_43 @ B_23 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_490_Zero__not__Suc,axiom,
% 0.27/0.65 ! [M: nat] :
% 0.27/0.65 ( zero_zero_nat
% 0.27/0.65 != ( suc @ M ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_491_nat_Osimps_I2_J,axiom,
% 0.27/0.65 ! [Nat_2: nat] :
% 0.27/0.65 ( zero_zero_nat
% 0.27/0.65 != ( suc @ Nat_2 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_492_Suc__not__Zero,axiom,
% 0.27/0.65 ! [M: nat] :
% 0.27/0.65 ( ( suc @ M )
% 0.27/0.65 != zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_493_nat_Osimps_I3_J,axiom,
% 0.27/0.65 ! [Nat_1: nat] :
% 0.27/0.65 ( ( suc @ Nat_1 )
% 0.27/0.65 != zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_494_Zero__neq__Suc,axiom,
% 0.27/0.65 ! [M: nat] :
% 0.27/0.65 ( zero_zero_nat
% 0.27/0.65 != ( suc @ M ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_495_Suc__neq__Zero,axiom,
% 0.27/0.65 ! [M: nat] :
% 0.27/0.65 ( ( suc @ M )
% 0.27/0.65 != zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_496_not__less__eq,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ~ ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 <=> ( ord_less_nat @ N_5 @ ( suc @ M ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_497_less__Suc__eq,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ M @ ( suc @ N_5 ) )
% 0.27/0.65 <=> ( ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 | ( M = N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_498_Suc__less__eq,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N_5 ) )
% 0.27/0.65 <=> ( ord_less_nat @ M @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_499_not__less__less__Suc__eq,axiom,
% 0.27/0.65 ! [N_5: nat,M: nat] :
% 0.27/0.65 ( ~ ( ord_less_nat @ N_5 @ M )
% 0.27/0.65 => ( ( ord_less_nat @ N_5 @ ( suc @ M ) )
% 0.27/0.65 <=> ( N_5 = M ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_500_less__antisym,axiom,
% 0.27/0.65 ! [N_5: nat,M: nat] :
% 0.27/0.65 ( ~ ( ord_less_nat @ N_5 @ M )
% 0.27/0.65 => ( ( ord_less_nat @ N_5 @ ( suc @ M ) )
% 0.27/0.65 => ( M = N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_501_less__SucI,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 => ( ord_less_nat @ M @ ( suc @ N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_502_Suc__lessI,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 => ( ( ( suc @ M )
% 0.27/0.65 != N_5 )
% 0.27/0.65 => ( ord_less_nat @ ( suc @ M ) @ N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_503_less__trans__Suc,axiom,
% 0.27/0.65 ! [K_3: nat,I: nat,J: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I @ J )
% 0.27/0.65 => ( ( ord_less_nat @ J @ K_3 )
% 0.27/0.65 => ( ord_less_nat @ ( suc @ I ) @ K_3 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_504_less__SucE,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ M @ ( suc @ N_5 ) )
% 0.27/0.65 => ( ~ ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 => ( M = N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_505_Suc__lessD,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( suc @ M ) @ N_5 )
% 0.27/0.65 => ( ord_less_nat @ M @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_506_Suc__less__SucD,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N_5 ) )
% 0.27/0.65 => ( ord_less_nat @ M @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_507_not__psubset__empty,axiom,
% 0.27/0.65 ! [A_42: nat > $o] :
% 0.27/0.65 ~ ( ord_less_nat_o @ A_42 @ bot_bot_nat_o ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_508_plus__nat_Oadd__0,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ zero_zero_nat @ N_5 )
% 0.27/0.65 = N_5 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_509_Nat_Oadd__0__right,axiom,
% 0.27/0.65 ! [M: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.27/0.65 = M ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_510_add__is__0,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ( plus_plus_nat @ M @ N_5 )
% 0.27/0.65 = zero_zero_nat )
% 0.27/0.65 <=> ( ( M = zero_zero_nat )
% 0.27/0.65 & ( N_5 = zero_zero_nat ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_511_add__eq__self__zero,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ( plus_plus_nat @ M @ N_5 )
% 0.27/0.65 = M )
% 0.27/0.65 => ( N_5 = zero_zero_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_512_not__add__less1,axiom,
% 0.27/0.65 ! [I: nat,J: nat] :
% 0.27/0.65 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_513_not__add__less2,axiom,
% 0.27/0.65 ! [J: nat,I: nat] :
% 0.27/0.65 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_514_nat__add__left__cancel__less,axiom,
% 0.27/0.65 ! [K_3: nat,M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( plus_plus_nat @ K_3 @ M ) @ ( plus_plus_nat @ K_3 @ N_5 ) )
% 0.27/0.65 <=> ( ord_less_nat @ M @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_515_trans__less__add1,axiom,
% 0.27/0.65 ! [M: nat,I: nat,J: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I @ J )
% 0.27/0.65 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_516_trans__less__add2,axiom,
% 0.27/0.65 ! [M: nat,I: nat,J: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I @ J )
% 0.27/0.65 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_517_add__less__mono1,axiom,
% 0.27/0.65 ! [K_3: nat,I: nat,J: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I @ J )
% 0.27/0.65 => ( ord_less_nat @ ( plus_plus_nat @ I @ K_3 ) @ ( plus_plus_nat @ J @ K_3 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_518_add__less__mono,axiom,
% 0.27/0.65 ! [K_3: nat,L: nat,I: nat,J: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I @ J )
% 0.27/0.65 => ( ( ord_less_nat @ K_3 @ L )
% 0.27/0.65 => ( ord_less_nat @ ( plus_plus_nat @ I @ K_3 ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_519_less__add__eq__less,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat,K_3: nat,L: nat] :
% 0.27/0.65 ( ( ord_less_nat @ K_3 @ L )
% 0.27/0.65 => ( ( ( plus_plus_nat @ M @ L )
% 0.27/0.65 = ( plus_plus_nat @ K_3 @ N_5 ) )
% 0.27/0.65 => ( ord_less_nat @ M @ N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_520_add__lessD1,axiom,
% 0.27/0.65 ! [I: nat,J: nat,K_3: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K_3 )
% 0.27/0.65 => ( ord_less_nat @ I @ K_3 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_521_max__add__distrib__left,axiom,
% 0.27/0.65 ! [X_23: nat,Y_5: nat,Z_2: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ ( ord_max_nat @ X_23 @ Y_5 ) @ Z_2 )
% 0.27/0.65 = ( ord_max_nat @ ( plus_plus_nat @ X_23 @ Z_2 ) @ ( plus_plus_nat @ Y_5 @ Z_2 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_522_max__add__distrib__left,axiom,
% 0.27/0.65 ! [X_23: int,Y_5: int,Z_2: int] :
% 0.27/0.65 ( ( plus_plus_int @ ( ord_max_int @ X_23 @ Y_5 ) @ Z_2 )
% 0.27/0.65 = ( ord_max_int @ ( plus_plus_int @ X_23 @ Z_2 ) @ ( plus_plus_int @ Y_5 @ Z_2 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_523_drop__drop,axiom,
% 0.27/0.65 ! [N_33: nat,M_4: nat,Xs_50: list_A2115238852le_alt] :
% 0.27/0.65 ( ( drop_A1346709759le_alt @ N_33 @ ( drop_A1346709759le_alt @ M_4 @ Xs_50 ) )
% 0.27/0.65 = ( drop_A1346709759le_alt @ ( plus_plus_nat @ N_33 @ M_4 ) @ Xs_50 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_524_max__Suc__Suc,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N_5 ) )
% 0.27/0.65 = ( suc @ ( ord_max_nat @ M @ N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_525_list_Osize_I4_J,axiom,
% 0.27/0.65 ! [A_41: arrow_475358991le_alt,List_1: list_A2115238852le_alt] :
% 0.27/0.65 ( ( size_s1858781230le_alt @ ( cons_A228743023le_alt @ A_41 @ List_1 ) )
% 0.27/0.65 = ( plus_plus_nat @ ( size_s1858781230le_alt @ List_1 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_526_list_Osize_I2_J,axiom,
% 0.27/0.65 ! [Fa: arrow_475358991le_alt > nat,A_40: arrow_475358991le_alt,List: list_A2115238852le_alt] :
% 0.27/0.65 ( ( list_s250295873le_alt @ Fa @ ( cons_A228743023le_alt @ A_40 @ List ) )
% 0.27/0.65 = ( plus_plus_nat @ ( plus_plus_nat @ ( Fa @ A_40 ) @ ( list_s250295873le_alt @ Fa @ List ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_527_list__ex__simps_I1_J,axiom,
% 0.27/0.65 ! [P_6: arrow_475358991le_alt > $o,X_22: arrow_475358991le_alt,Xs_49: list_A2115238852le_alt] :
% 0.27/0.65 ( ( list_e1252802557le_alt @ P_6 @ ( cons_A228743023le_alt @ X_22 @ Xs_49 ) )
% 0.27/0.65 <=> ( ( P_6 @ X_22 )
% 0.27/0.65 | ( list_e1252802557le_alt @ P_6 @ Xs_49 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_528_list__ex__simps_I2_J,axiom,
% 0.27/0.65 ! [P_5: nat > $o] :
% 0.27/0.65 ~ ( list_ex_nat @ P_5 @ nil_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_529_list__ex__simps_I2_J,axiom,
% 0.27/0.65 ! [P_5: arrow_475358991le_alt > $o] :
% 0.27/0.65 ~ ( list_e1252802557le_alt @ P_5 @ nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_530_list__ex__append,axiom,
% 0.27/0.65 ! [P_4: arrow_475358991le_alt > $o,Xs_48: list_A2115238852le_alt,Ys_9: list_A2115238852le_alt] :
% 0.27/0.65 ( ( list_e1252802557le_alt @ P_4 @ ( append179082452le_alt @ Xs_48 @ Ys_9 ) )
% 0.27/0.65 <=> ( ( list_e1252802557le_alt @ P_4 @ Xs_48 )
% 0.27/0.65 | ( list_e1252802557le_alt @ P_4 @ Ys_9 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_531_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.27/0.65 ! [A_39: int] :
% 0.27/0.65 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A_39 @ A_39 ) )
% 0.27/0.65 <=> ( ord_less_int @ zero_zero_int @ A_39 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_532_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.27/0.65 ! [A_38: int] :
% 0.27/0.65 ( ( ord_less_int @ ( plus_plus_int @ A_38 @ A_38 ) @ zero_zero_int )
% 0.27/0.65 <=> ( ord_less_int @ A_38 @ zero_zero_int ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_533_add__pos__pos,axiom,
% 0.27/0.65 ! [B_22: nat,A_37: nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ A_37 )
% 0.27/0.65 => ( ( ord_less_nat @ zero_zero_nat @ B_22 )
% 0.27/0.65 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A_37 @ B_22 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_534_add__pos__pos,axiom,
% 0.27/0.65 ! [B_22: int,A_37: int] :
% 0.27/0.65 ( ( ord_less_int @ zero_zero_int @ A_37 )
% 0.27/0.65 => ( ( ord_less_int @ zero_zero_int @ B_22 )
% 0.27/0.65 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A_37 @ B_22 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_535_add__neg__neg,axiom,
% 0.27/0.65 ! [B_21: nat,A_36: nat] :
% 0.27/0.65 ( ( ord_less_nat @ A_36 @ zero_zero_nat )
% 0.27/0.65 => ( ( ord_less_nat @ B_21 @ zero_zero_nat )
% 0.27/0.65 => ( ord_less_nat @ ( plus_plus_nat @ A_36 @ B_21 ) @ zero_zero_nat ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_536_add__neg__neg,axiom,
% 0.27/0.65 ! [B_21: int,A_36: int] :
% 0.27/0.65 ( ( ord_less_int @ A_36 @ zero_zero_int )
% 0.27/0.65 => ( ( ord_less_int @ B_21 @ zero_zero_int )
% 0.27/0.65 => ( ord_less_int @ ( plus_plus_int @ A_36 @ B_21 ) @ zero_zero_int ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_537_list__ex__rev,axiom,
% 0.27/0.65 ! [P_3: nat > $o,Xs_47: list_nat] :
% 0.27/0.65 ( ( list_ex_nat @ P_3 @ ( rev_nat @ Xs_47 ) )
% 0.27/0.65 <=> ( list_ex_nat @ P_3 @ Xs_47 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_538_list__ex__rev,axiom,
% 0.27/0.65 ! [P_3: arrow_475358991le_alt > $o,Xs_47: list_A2115238852le_alt] :
% 0.27/0.65 ( ( list_e1252802557le_alt @ P_3 @ ( rev_Ar1106406943le_alt @ Xs_47 ) )
% 0.27/0.65 <=> ( list_e1252802557le_alt @ P_3 @ Xs_47 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_539_gr0__conv__Suc,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ N_5 )
% 0.27/0.65 <=> ? [M_1: nat] :
% 0.27/0.65 ( N_5
% 0.27/0.65 = ( suc @ M_1 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_540_less__Suc0,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ N_5 @ ( suc @ zero_zero_nat ) )
% 0.27/0.65 <=> ( N_5 = zero_zero_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_541_less__Suc__eq__0__disj,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ M @ ( suc @ N_5 ) )
% 0.27/0.65 <=> ( ( M = zero_zero_nat )
% 0.27/0.65 | ? [J_2: nat] :
% 0.27/0.65 ( ( M
% 0.27/0.65 = ( suc @ J_2 ) )
% 0.27/0.65 & ( ord_less_nat @ J_2 @ N_5 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_542_add__gr__0,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N_5 ) )
% 0.27/0.65 <=> ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.27/0.65 | ( ord_less_nat @ zero_zero_nat @ N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_543_nth__Cons__Suc,axiom,
% 0.27/0.65 ! [X_21: nat,Xs_46: list_nat,N_32: nat] :
% 0.27/0.65 ( ( nth_nat @ ( cons_nat @ X_21 @ Xs_46 ) @ ( suc @ N_32 ) )
% 0.27/0.65 = ( nth_nat @ Xs_46 @ N_32 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_544_nth__Cons__Suc,axiom,
% 0.27/0.65 ! [X_21: arrow_475358991le_alt,Xs_46: list_A2115238852le_alt,N_32: nat] :
% 0.27/0.65 ( ( nth_Ar125878976le_alt @ ( cons_A228743023le_alt @ X_21 @ Xs_46 ) @ ( suc @ N_32 ) )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Xs_46 @ N_32 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_545_length__append,axiom,
% 0.27/0.65 ! [Xs_45: list_A2115238852le_alt,Ys_8: list_A2115238852le_alt] :
% 0.27/0.65 ( ( size_s1858781230le_alt @ ( append179082452le_alt @ Xs_45 @ Ys_8 ) )
% 0.27/0.65 = ( plus_plus_nat @ ( size_s1858781230le_alt @ Xs_45 ) @ ( size_s1858781230le_alt @ Ys_8 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_546_drop__Suc__Cons,axiom,
% 0.27/0.65 ! [N_31: nat,X_20: arrow_475358991le_alt,Xs_44: list_A2115238852le_alt] :
% 0.27/0.65 ( ( drop_A1346709759le_alt @ ( suc @ N_31 ) @ ( cons_A228743023le_alt @ X_20 @ Xs_44 ) )
% 0.27/0.65 = ( drop_A1346709759le_alt @ N_31 @ Xs_44 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_547_list__update__code_I3_J,axiom,
% 0.27/0.65 ! [X_19: arrow_475358991le_alt,Xs_43: list_A2115238852le_alt,I_10: nat,Y_4: arrow_475358991le_alt] :
% 0.27/0.65 ( ( list_u62477863le_alt @ ( cons_A228743023le_alt @ X_19 @ Xs_43 ) @ ( suc @ I_10 ) @ Y_4 )
% 0.27/0.65 = ( cons_A228743023le_alt @ X_19 @ ( list_u62477863le_alt @ Xs_43 @ I_10 @ Y_4 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_548_replicate__Suc,axiom,
% 0.27/0.65 ! [N_30: nat,X_18: arrow_475358991le_alt] :
% 0.27/0.65 ( ( replic1511538809le_alt @ ( suc @ N_30 ) @ X_18 )
% 0.27/0.65 = ( cons_A228743023le_alt @ X_18 @ ( replic1511538809le_alt @ N_30 @ X_18 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_549_replicate__add,axiom,
% 0.27/0.65 ! [N_29: nat,M_3: nat,X_17: arrow_475358991le_alt] :
% 0.27/0.65 ( ( replic1511538809le_alt @ ( plus_plus_nat @ N_29 @ M_3 ) @ X_17 )
% 0.27/0.65 = ( append179082452le_alt @ ( replic1511538809le_alt @ N_29 @ X_17 ) @ ( replic1511538809le_alt @ M_3 @ X_17 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_550_drop__Suc,axiom,
% 0.27/0.65 ! [N_28: nat,Xs_42: list_A2115238852le_alt] :
% 0.27/0.65 ( ( drop_A1346709759le_alt @ ( suc @ N_28 ) @ Xs_42 )
% 0.27/0.65 = ( drop_A1346709759le_alt @ N_28 @ ( tl_Arr465451158le_alt @ Xs_42 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_551_length__splice,axiom,
% 0.27/0.65 ! [Xs_41: list_A2115238852le_alt,Ys_7: list_A2115238852le_alt] :
% 0.27/0.65 ( ( size_s1858781230le_alt @ ( splice1520898450le_alt @ Xs_41 @ Ys_7 ) )
% 0.27/0.65 = ( plus_plus_nat @ ( size_s1858781230le_alt @ Xs_41 ) @ ( size_s1858781230le_alt @ Ys_7 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_552_nth__append__length__plus,axiom,
% 0.27/0.65 ! [Xs_40: list_nat,Ys_6: list_nat,N_27: nat] :
% 0.27/0.65 ( ( nth_nat @ ( append_nat @ Xs_40 @ Ys_6 ) @ ( plus_plus_nat @ ( size_size_list_nat @ Xs_40 ) @ N_27 ) )
% 0.27/0.65 = ( nth_nat @ Ys_6 @ N_27 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_553_nth__append__length__plus,axiom,
% 0.27/0.65 ! [Xs_40: list_A2115238852le_alt,Ys_6: list_A2115238852le_alt,N_27: nat] :
% 0.27/0.65 ( ( nth_Ar125878976le_alt @ ( append179082452le_alt @ Xs_40 @ Ys_6 ) @ ( plus_plus_nat @ ( size_s1858781230le_alt @ Xs_40 ) @ N_27 ) )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Ys_6 @ N_27 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_554_less__imp__Suc__add,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 => ? [K_5: nat] :
% 0.27/0.65 ( N_5
% 0.27/0.65 = ( suc @ ( plus_plus_nat @ M @ K_5 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_555_length__Suc__conv,axiom,
% 0.27/0.65 ! [Xs_39: list_A2115238852le_alt,N_26: nat] :
% 0.27/0.65 ( ( ( size_s1858781230le_alt @ Xs_39 )
% 0.27/0.65 = ( suc @ N_26 ) )
% 0.27/0.65 <=> ? [Y_3: arrow_475358991le_alt,Ys_5: list_A2115238852le_alt] :
% 0.27/0.65 ( ( Xs_39
% 0.27/0.65 = ( cons_A228743023le_alt @ Y_3 @ Ys_5 ) )
% 0.27/0.65 & ( ( size_s1858781230le_alt @ Ys_5 )
% 0.27/0.65 = N_26 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_556_Suc__length__conv,axiom,
% 0.27/0.65 ! [N_25: nat,Xs_38: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( suc @ N_25 )
% 0.27/0.65 = ( size_s1858781230le_alt @ Xs_38 ) )
% 0.27/0.65 <=> ? [Y_3: arrow_475358991le_alt,Ys_5: list_A2115238852le_alt] :
% 0.27/0.65 ( ( Xs_38
% 0.27/0.65 = ( cons_A228743023le_alt @ Y_3 @ Ys_5 ) )
% 0.27/0.65 & ( ( size_s1858781230le_alt @ Ys_5 )
% 0.27/0.65 = N_25 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_557_less__imp__add__positive,axiom,
% 0.27/0.65 ! [I: nat,J: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I @ J )
% 0.27/0.65 => ? [K_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ K_5 )
% 0.27/0.65 & ( ( plus_plus_nat @ I @ K_5 )
% 0.27/0.65 = J ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_558_psubsetD,axiom,
% 0.27/0.65 ! [C_16: int,A_35: int > $o,B_20: int > $o] :
% 0.27/0.65 ( ( ord_less_int_o @ A_35 @ B_20 )
% 0.27/0.65 => ( ( member_int @ C_16 @ A_35 )
% 0.27/0.65 => ( member_int @ C_16 @ B_20 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_559_psubsetD,axiom,
% 0.27/0.65 ! [C_16: nat,A_35: nat > $o,B_20: nat > $o] :
% 0.27/0.65 ( ( ord_less_nat_o @ A_35 @ B_20 )
% 0.27/0.65 => ( ( member_nat @ C_16 @ A_35 )
% 0.27/0.65 => ( member_nat @ C_16 @ B_20 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_560_gr0__implies__Suc,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ N_5 )
% 0.27/0.65 => ? [M_1: nat] :
% 0.27/0.65 ( N_5
% 0.27/0.65 = ( suc @ M_1 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_561_lift__Suc__mono__less,axiom,
% 0.27/0.65 ! [N_24: nat,N_23: nat,F_1: nat > nat] :
% 0.27/0.65 ( ! [N_7: nat] : ( ord_less_nat @ ( F_1 @ N_7 ) @ ( F_1 @ ( suc @ N_7 ) ) )
% 0.27/0.65 => ( ( ord_less_nat @ N_24 @ N_23 )
% 0.27/0.65 => ( ord_less_nat @ ( F_1 @ N_24 ) @ ( F_1 @ N_23 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_562_lift__Suc__mono__less__iff,axiom,
% 0.27/0.65 ! [N_22: nat,M_2: nat,F: nat > nat] :
% 0.27/0.65 ( ! [N_7: nat] : ( ord_less_nat @ ( F @ N_7 ) @ ( F @ ( suc @ N_7 ) ) )
% 0.27/0.65 => ( ( ord_less_nat @ ( F @ N_22 ) @ ( F @ M_2 ) )
% 0.27/0.65 <=> ( ord_less_nat @ N_22 @ M_2 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_563_even__less__0__iff,axiom,
% 0.27/0.65 ! [A_34: int] :
% 0.27/0.65 ( ( ord_less_int @ ( plus_plus_int @ A_34 @ A_34 ) @ zero_zero_int )
% 0.27/0.65 <=> ( ord_less_int @ A_34 @ zero_zero_int ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_564_pos__add__strict,axiom,
% 0.27/0.65 ! [B_19: int,C_15: int,A_33: int] :
% 0.27/0.65 ( ( ord_less_int @ zero_zero_int @ A_33 )
% 0.27/0.65 => ( ( ord_less_int @ B_19 @ C_15 )
% 0.27/0.65 => ( ord_less_int @ B_19 @ ( plus_plus_int @ A_33 @ C_15 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_565_pos__add__strict,axiom,
% 0.27/0.65 ! [B_19: nat,C_15: nat,A_33: nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ A_33 )
% 0.27/0.65 => ( ( ord_less_nat @ B_19 @ C_15 )
% 0.27/0.65 => ( ord_less_nat @ B_19 @ ( plus_plus_nat @ A_33 @ C_15 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_566_double__eq__0__iff,axiom,
% 0.27/0.65 ! [A_32: int] :
% 0.27/0.65 ( ( ( plus_plus_int @ A_32 @ A_32 )
% 0.27/0.65 = zero_zero_int )
% 0.27/0.65 <=> ( A_32 = zero_zero_int ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_567_lessE,axiom,
% 0.27/0.65 ! [I: nat,K_3: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I @ K_3 )
% 0.27/0.65 => ( ( K_3
% 0.27/0.65 != ( suc @ I ) )
% 0.27/0.65 => ~ ! [J_2: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I @ J_2 )
% 0.27/0.65 => ( K_3
% 0.27/0.65 != ( suc @ J_2 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_568_Suc__lessE,axiom,
% 0.27/0.65 ! [I: nat,K_3: nat] :
% 0.27/0.65 ( ( ord_less_nat @ ( suc @ I ) @ K_3 )
% 0.27/0.65 => ~ ! [J_2: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I @ J_2 )
% 0.27/0.65 => ( K_3
% 0.27/0.65 != ( suc @ J_2 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_569_nat_Oexhaust,axiom,
% 0.27/0.65 ! [Y: nat] :
% 0.27/0.65 ( ( Y != zero_zero_nat )
% 0.27/0.65 => ~ ! [Nat: nat] :
% 0.27/0.65 ( Y
% 0.27/0.65 != ( suc @ Nat ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_570_not0__implies__Suc,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( N_5 != zero_zero_nat )
% 0.27/0.65 => ? [M_1: nat] :
% 0.27/0.65 ( N_5
% 0.27/0.65 = ( suc @ M_1 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_571_nat__induct,axiom,
% 0.27/0.65 ! [N_5: nat,P: nat > $o] :
% 0.27/0.65 ( ( P @ zero_zero_nat )
% 0.27/0.65 => ( ! [N_7: nat] :
% 0.27/0.65 ( ( P @ N_7 )
% 0.27/0.65 => ( P @ ( suc @ N_7 ) ) )
% 0.27/0.65 => ( P @ N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_572_zero__induct,axiom,
% 0.27/0.65 ! [P: nat > $o,K_3: nat] :
% 0.27/0.65 ( ( P @ K_3 )
% 0.27/0.65 => ( ! [N_7: nat] :
% 0.27/0.65 ( ( P @ ( suc @ N_7 ) )
% 0.27/0.65 => ( P @ N_7 ) )
% 0.27/0.65 => ( P @ zero_zero_nat ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_573_take__hd__drop,axiom,
% 0.27/0.65 ! [N_21: nat,Xs_37: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ N_21 @ ( size_s1858781230le_alt @ Xs_37 ) )
% 0.27/0.65 => ( ( append179082452le_alt @ ( take_A614047655le_alt @ N_21 @ Xs_37 ) @ ( cons_A228743023le_alt @ ( hd_Arr1965683346le_alt @ ( drop_A1346709759le_alt @ N_21 @ Xs_37 ) ) @ nil_Ar1286194111le_alt ) )
% 0.27/0.65 = ( take_A614047655le_alt @ ( suc @ N_21 ) @ Xs_37 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_574_take__tl,axiom,
% 0.27/0.65 ! [N_20: nat,Xs_36: list_A2115238852le_alt] :
% 0.27/0.65 ( ( take_A614047655le_alt @ N_20 @ ( tl_Arr465451158le_alt @ Xs_36 ) )
% 0.27/0.65 = ( tl_Arr465451158le_alt @ ( take_A614047655le_alt @ ( suc @ N_20 ) @ Xs_36 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_575_take__Nil,axiom,
% 0.27/0.65 ! [N_19: nat] :
% 0.27/0.65 ( ( take_A614047655le_alt @ N_19 @ nil_Ar1286194111le_alt )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_576_distinct__take,axiom,
% 0.27/0.65 ! [I_9: nat,Xs_35: list_A2115238852le_alt] :
% 0.27/0.65 ( ( distin236324274le_alt @ Xs_35 )
% 0.27/0.65 => ( distin236324274le_alt @ ( take_A614047655le_alt @ I_9 @ Xs_35 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_577_takeWhile__eq__take,axiom,
% 0.27/0.65 ! [P_2: arrow_475358991le_alt > $o,Xs_34: list_A2115238852le_alt] :
% 0.27/0.65 ( ( takeWh1696291512le_alt @ P_2 @ Xs_34 )
% 0.27/0.65 = ( take_A614047655le_alt @ ( size_s1858781230le_alt @ ( takeWh1696291512le_alt @ P_2 @ Xs_34 ) ) @ Xs_34 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_578_append__take__drop__id,axiom,
% 0.27/0.65 ! [N_18: nat,Xs_33: list_A2115238852le_alt] :
% 0.27/0.65 ( ( append179082452le_alt @ ( take_A614047655le_alt @ N_18 @ Xs_33 ) @ ( drop_A1346709759le_alt @ N_18 @ Xs_33 ) )
% 0.27/0.65 = Xs_33 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_579_take__Suc__Cons,axiom,
% 0.27/0.65 ! [N_17: nat,X_16: arrow_475358991le_alt,Xs_32: list_A2115238852le_alt] :
% 0.27/0.65 ( ( take_A614047655le_alt @ ( suc @ N_17 ) @ ( cons_A228743023le_alt @ X_16 @ Xs_32 ) )
% 0.27/0.65 = ( cons_A228743023le_alt @ X_16 @ ( take_A614047655le_alt @ N_17 @ Xs_32 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_580_take__eq__Nil,axiom,
% 0.27/0.65 ! [N_16: nat,Xs_31: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( take_A614047655le_alt @ N_16 @ Xs_31 )
% 0.27/0.65 = nil_Ar1286194111le_alt )
% 0.27/0.65 <=> ( ( N_16 = zero_zero_nat )
% 0.27/0.65 | ( Xs_31 = nil_Ar1286194111le_alt ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_581_take__0,axiom,
% 0.27/0.65 ! [Xs_30: list_A2115238852le_alt] :
% 0.27/0.65 ( ( take_A614047655le_alt @ zero_zero_nat @ Xs_30 )
% 0.27/0.65 = nil_Ar1286194111le_alt ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_582_append__eq__conv__conj,axiom,
% 0.27/0.65 ! [Xs_29: list_A2115238852le_alt,Ys_4: list_A2115238852le_alt,Zs: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( append179082452le_alt @ Xs_29 @ Ys_4 )
% 0.27/0.65 = Zs )
% 0.27/0.65 <=> ( ( Xs_29
% 0.27/0.65 = ( take_A614047655le_alt @ ( size_s1858781230le_alt @ Xs_29 ) @ Zs ) )
% 0.27/0.65 & ( Ys_4
% 0.27/0.65 = ( drop_A1346709759le_alt @ ( size_s1858781230le_alt @ Xs_29 ) @ Zs ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_583_take__add,axiom,
% 0.27/0.65 ! [I_8: nat,J_1: nat,Xs_28: list_A2115238852le_alt] :
% 0.27/0.65 ( ( take_A614047655le_alt @ ( plus_plus_nat @ I_8 @ J_1 ) @ Xs_28 )
% 0.27/0.65 = ( append179082452le_alt @ ( take_A614047655le_alt @ I_8 @ Xs_28 ) @ ( take_A614047655le_alt @ J_1 @ ( drop_A1346709759le_alt @ I_8 @ Xs_28 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_584_take__butlast,axiom,
% 0.27/0.65 ! [N_15: nat,Xs_27: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ N_15 @ ( size_s1858781230le_alt @ Xs_27 ) )
% 0.27/0.65 => ( ( take_A614047655le_alt @ N_15 @ ( butlas274947851le_alt @ Xs_27 ) )
% 0.27/0.65 = ( take_A614047655le_alt @ N_15 @ Xs_27 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_585_take__Suc,axiom,
% 0.27/0.65 ! [N_14: nat,Xs_26: list_A2115238852le_alt] :
% 0.27/0.65 ( ( Xs_26 != nil_Ar1286194111le_alt )
% 0.27/0.65 => ( ( take_A614047655le_alt @ ( suc @ N_14 ) @ Xs_26 )
% 0.27/0.65 = ( cons_A228743023le_alt @ ( hd_Arr1965683346le_alt @ Xs_26 ) @ ( take_A614047655le_alt @ N_14 @ ( tl_Arr465451158le_alt @ Xs_26 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_586_take__Suc__conv__app__nth,axiom,
% 0.27/0.65 ! [I_7: nat,Xs_25: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ I_7 @ ( size_s1858781230le_alt @ Xs_25 ) )
% 0.27/0.65 => ( ( take_A614047655le_alt @ ( suc @ I_7 ) @ Xs_25 )
% 0.27/0.65 = ( append179082452le_alt @ ( take_A614047655le_alt @ I_7 @ Xs_25 ) @ ( cons_A228743023le_alt @ ( nth_Ar125878976le_alt @ Xs_25 @ I_7 ) @ nil_Ar1286194111le_alt ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_587_id__take__nth__drop,axiom,
% 0.27/0.65 ! [I_6: nat,Xs_24: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ I_6 @ ( size_s1858781230le_alt @ Xs_24 ) )
% 0.27/0.65 => ( Xs_24
% 0.27/0.65 = ( append179082452le_alt @ ( take_A614047655le_alt @ I_6 @ Xs_24 ) @ ( cons_A228743023le_alt @ ( nth_Ar125878976le_alt @ Xs_24 @ I_6 ) @ ( drop_A1346709759le_alt @ ( suc @ I_6 ) @ Xs_24 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_588_upd__conv__take__nth__drop,axiom,
% 0.27/0.65 ! [A_31: arrow_475358991le_alt,I_5: nat,Xs_23: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ I_5 @ ( size_s1858781230le_alt @ Xs_23 ) )
% 0.27/0.65 => ( ( list_u62477863le_alt @ Xs_23 @ I_5 @ A_31 )
% 0.27/0.65 = ( append179082452le_alt @ ( take_A614047655le_alt @ I_5 @ Xs_23 ) @ ( cons_A228743023le_alt @ A_31 @ ( drop_A1346709759le_alt @ ( suc @ I_5 ) @ Xs_23 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_589_takeWhile__eq__take__P__nth,axiom,
% 0.27/0.65 ! [P_1: arrow_475358991le_alt > $o,Xs_22: list_A2115238852le_alt,N_13: nat] :
% 0.27/0.65 ( ! [I_4: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I_4 @ N_13 )
% 0.27/0.65 => ( ( ord_less_nat @ I_4 @ ( size_s1858781230le_alt @ Xs_22 ) )
% 0.27/0.65 => ( P_1 @ ( nth_Ar125878976le_alt @ Xs_22 @ I_4 ) ) ) )
% 0.27/0.65 => ( ( ( ord_less_nat @ N_13 @ ( size_s1858781230le_alt @ Xs_22 ) )
% 0.27/0.65 => ~ ( P_1 @ ( nth_Ar125878976le_alt @ Xs_22 @ N_13 ) ) )
% 0.27/0.65 => ( ( takeWh1696291512le_alt @ P_1 @ Xs_22 )
% 0.27/0.65 = ( take_A614047655le_alt @ N_13 @ Xs_22 ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_590_termination__basic__simps_I1_J,axiom,
% 0.27/0.65 ! [Z_1: nat,X: nat,Y: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X @ Y )
% 0.27/0.65 => ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z_1 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_591_termination__basic__simps_I2_J,axiom,
% 0.27/0.65 ! [Y: nat,X: nat,Z_1: nat] :
% 0.27/0.65 ( ( ord_less_nat @ X @ Z_1 )
% 0.27/0.65 => ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z_1 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 0.27/0.65 ! [A_30: int] :
% 0.27/0.65 ( ( plus_plus_int @ zero_zero_int @ A_30 )
% 0.27/0.65 = A_30 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 0.27/0.65 ! [A_30: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ zero_zero_nat @ A_30 )
% 0.27/0.65 = A_30 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_594_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 0.27/0.65 ! [A_29: int] :
% 0.27/0.65 ( ( plus_plus_int @ A_29 @ zero_zero_int )
% 0.27/0.65 = A_29 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_595_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 0.27/0.65 ! [A_29: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ A_29 @ zero_zero_nat )
% 0.27/0.65 = A_29 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_596_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.27/0.65 ! [A_28: int,B_18: int,C_14: int,D_5: int] :
% 0.27/0.65 ( ( plus_plus_int @ ( plus_plus_int @ A_28 @ B_18 ) @ ( plus_plus_int @ C_14 @ D_5 ) )
% 0.27/0.65 = ( plus_plus_int @ ( plus_plus_int @ A_28 @ C_14 ) @ ( plus_plus_int @ B_18 @ D_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_597_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.27/0.65 ! [A_28: nat,B_18: nat,C_14: nat,D_5: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ ( plus_plus_nat @ A_28 @ B_18 ) @ ( plus_plus_nat @ C_14 @ D_5 ) )
% 0.27/0.65 = ( plus_plus_nat @ ( plus_plus_nat @ A_28 @ C_14 ) @ ( plus_plus_nat @ B_18 @ D_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_598_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.27/0.65 ! [A_27: int,B_17: int,C_13: int] :
% 0.27/0.65 ( ( plus_plus_int @ ( plus_plus_int @ A_27 @ B_17 ) @ C_13 )
% 0.27/0.65 = ( plus_plus_int @ ( plus_plus_int @ A_27 @ C_13 ) @ B_17 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_599_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.27/0.65 ! [A_27: nat,B_17: nat,C_13: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ ( plus_plus_nat @ A_27 @ B_17 ) @ C_13 )
% 0.27/0.65 = ( plus_plus_nat @ ( plus_plus_nat @ A_27 @ C_13 ) @ B_17 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_600_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.27/0.65 ! [A_26: int,B_16: int,C_12: int] :
% 0.27/0.65 ( ( plus_plus_int @ ( plus_plus_int @ A_26 @ B_16 ) @ C_12 )
% 0.27/0.65 = ( plus_plus_int @ A_26 @ ( plus_plus_int @ B_16 @ C_12 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_601_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.27/0.65 ! [A_26: nat,B_16: nat,C_12: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ ( plus_plus_nat @ A_26 @ B_16 ) @ C_12 )
% 0.27/0.65 = ( plus_plus_nat @ A_26 @ ( plus_plus_nat @ B_16 @ C_12 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_602_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.27/0.65 ! [A_25: int,C_11: int,D_4: int] :
% 0.27/0.65 ( ( plus_plus_int @ A_25 @ ( plus_plus_int @ C_11 @ D_4 ) )
% 0.27/0.65 = ( plus_plus_int @ ( plus_plus_int @ A_25 @ C_11 ) @ D_4 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_603_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.27/0.65 ! [A_25: nat,C_11: nat,D_4: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ A_25 @ ( plus_plus_nat @ C_11 @ D_4 ) )
% 0.27/0.65 = ( plus_plus_nat @ ( plus_plus_nat @ A_25 @ C_11 ) @ D_4 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_604_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.27/0.65 ! [A_24: int,C_10: int,D_3: int] :
% 0.27/0.65 ( ( plus_plus_int @ A_24 @ ( plus_plus_int @ C_10 @ D_3 ) )
% 0.27/0.65 = ( plus_plus_int @ C_10 @ ( plus_plus_int @ A_24 @ D_3 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_605_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.27/0.65 ! [A_24: nat,C_10: nat,D_3: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ A_24 @ ( plus_plus_nat @ C_10 @ D_3 ) )
% 0.27/0.65 = ( plus_plus_nat @ C_10 @ ( plus_plus_nat @ A_24 @ D_3 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_606_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.27/0.65 ! [A_23: int,C_9: int] :
% 0.27/0.65 ( ( plus_plus_int @ A_23 @ C_9 )
% 0.27/0.65 = ( plus_plus_int @ C_9 @ A_23 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_607_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.27/0.65 ! [A_23: nat,C_9: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ A_23 @ C_9 )
% 0.27/0.65 = ( plus_plus_nat @ C_9 @ A_23 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_608_add__0__iff,axiom,
% 0.27/0.65 ! [B_15: int,A_22: int] :
% 0.27/0.65 ( ( B_15
% 0.27/0.65 = ( plus_plus_int @ B_15 @ A_22 ) )
% 0.27/0.65 <=> ( A_22 = zero_zero_int ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_609_add__0__iff,axiom,
% 0.27/0.65 ! [B_15: nat,A_22: nat] :
% 0.27/0.65 ( ( B_15
% 0.27/0.65 = ( plus_plus_nat @ B_15 @ A_22 ) )
% 0.27/0.65 <=> ( A_22 = zero_zero_nat ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_610_rev__nth,axiom,
% 0.27/0.65 ! [N_12: nat,Xs_21: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ord_less_nat @ N_12 @ ( size_s1858781230le_alt @ Xs_21 ) )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ ( rev_Ar1106406943le_alt @ Xs_21 ) @ N_12 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Xs_21 @ ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_21 ) @ ( suc @ N_12 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_611_drop__replicate,axiom,
% 0.27/0.65 ! [I_3: nat,K_4: nat,X_15: arrow_475358991le_alt] :
% 0.27/0.65 ( ( drop_A1346709759le_alt @ I_3 @ ( replic1511538809le_alt @ K_4 @ X_15 ) )
% 0.27/0.65 = ( replic1511538809le_alt @ ( minus_minus_nat @ K_4 @ I_3 ) @ X_15 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_612_diff__cancel2,axiom,
% 0.27/0.65 ! [M: nat,K_3: nat,N_5: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K_3 ) @ ( plus_plus_nat @ N_5 @ K_3 ) )
% 0.27/0.65 = ( minus_minus_nat @ M @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_613_diff__cancel,axiom,
% 0.27/0.65 ! [K_3: nat,M: nat,N_5: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ ( plus_plus_nat @ K_3 @ M ) @ ( plus_plus_nat @ K_3 @ N_5 ) )
% 0.27/0.65 = ( minus_minus_nat @ M @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_614_diff__diff__left,axiom,
% 0.27/0.65 ! [I: nat,J: nat,K_3: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K_3 )
% 0.27/0.65 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K_3 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_615_diff__add__inverse,axiom,
% 0.27/0.65 ! [N_5: nat,M: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ ( plus_plus_nat @ N_5 @ M ) @ N_5 )
% 0.27/0.65 = M ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_616_diff__add__inverse2,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N_5 ) @ N_5 )
% 0.27/0.65 = M ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_617_diff__eq__diff__less,axiom,
% 0.27/0.65 ! [A_21: int,B_14: int,C_8: int,D_2: int] :
% 0.27/0.65 ( ( ( minus_minus_int @ A_21 @ B_14 )
% 0.27/0.65 = ( minus_minus_int @ C_8 @ D_2 ) )
% 0.27/0.65 => ( ( ord_less_int @ A_21 @ B_14 )
% 0.27/0.65 <=> ( ord_less_int @ C_8 @ D_2 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_618_add__diff__cancel,axiom,
% 0.27/0.65 ! [A_20: int,B_13: int] :
% 0.27/0.65 ( ( minus_minus_int @ ( plus_plus_int @ A_20 @ B_13 ) @ B_13 )
% 0.27/0.65 = A_20 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_619_diff__add__cancel,axiom,
% 0.27/0.65 ! [A_19: int,B_12: int] :
% 0.27/0.65 ( ( plus_plus_int @ ( minus_minus_int @ A_19 @ B_12 ) @ B_12 )
% 0.27/0.65 = A_19 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_620_less__imp__diff__less,axiom,
% 0.27/0.65 ! [N_5: nat,J: nat,K_3: nat] :
% 0.27/0.65 ( ( ord_less_nat @ J @ K_3 )
% 0.27/0.65 => ( ord_less_nat @ ( minus_minus_nat @ J @ N_5 ) @ K_3 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_621_diff__less__mono2,axiom,
% 0.27/0.65 ! [L: nat,M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 => ( ( ord_less_nat @ M @ L )
% 0.27/0.65 => ( ord_less_nat @ ( minus_minus_nat @ L @ N_5 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_622_less__iff__diff__less__0,axiom,
% 0.27/0.65 ! [A_18: int,B_11: int] :
% 0.27/0.65 ( ( ord_less_int @ A_18 @ B_11 )
% 0.27/0.65 <=> ( ord_less_int @ ( minus_minus_int @ A_18 @ B_11 ) @ zero_zero_int ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_623_diff__less,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ N_5 )
% 0.27/0.65 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.27/0.65 => ( ord_less_nat @ ( minus_minus_nat @ M @ N_5 ) @ M ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_624_zero__less__diff,axiom,
% 0.27/0.65 ! [N_5: nat,M: nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N_5 @ M ) )
% 0.27/0.65 <=> ( ord_less_nat @ M @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_625_diff__less__Suc,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N_5 ) @ ( suc @ M ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_626_diff__add__0,axiom,
% 0.27/0.65 ! [N_5: nat,M: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ N_5 @ ( plus_plus_nat @ N_5 @ M ) )
% 0.27/0.65 = zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_627_less__diff__conv,axiom,
% 0.27/0.65 ! [I: nat,J: nat,K_3: nat] :
% 0.27/0.65 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K_3 ) )
% 0.27/0.65 <=> ( ord_less_nat @ ( plus_plus_nat @ I @ K_3 ) @ J ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_628_add__diff__inverse,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ~ ( ord_less_nat @ M @ N_5 )
% 0.27/0.65 => ( ( plus_plus_nat @ N_5 @ ( minus_minus_nat @ M @ N_5 ) )
% 0.27/0.65 = M ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_629_diff__commute,axiom,
% 0.27/0.65 ! [I: nat,J: nat,K_3: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K_3 )
% 0.27/0.65 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K_3 ) @ J ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_630_max__diff__distrib__left,axiom,
% 0.27/0.65 ! [X_14: int,Y_2: int,Z: int] :
% 0.27/0.65 ( ( minus_minus_int @ ( ord_max_int @ X_14 @ Y_2 ) @ Z )
% 0.27/0.65 = ( ord_max_int @ ( minus_minus_int @ X_14 @ Z ) @ ( minus_minus_int @ Y_2 @ Z ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_631_diff__eq__diff__eq,axiom,
% 0.27/0.65 ! [A_17: int,B_10: int,C_7: int,D_1: int] :
% 0.27/0.65 ( ( ( minus_minus_int @ A_17 @ B_10 )
% 0.27/0.65 = ( minus_minus_int @ C_7 @ D_1 ) )
% 0.27/0.65 => ( ( A_17 = B_10 )
% 0.27/0.65 <=> ( C_7 = D_1 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_632_diff__0__right,axiom,
% 0.27/0.65 ! [A_16: int] :
% 0.27/0.65 ( ( minus_minus_int @ A_16 @ zero_zero_int )
% 0.27/0.65 = A_16 ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_633_diff__self,axiom,
% 0.27/0.65 ! [A_15: int] :
% 0.27/0.65 ( ( minus_minus_int @ A_15 @ A_15 )
% 0.27/0.65 = zero_zero_int ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_634_eq__iff__diff__eq__0,axiom,
% 0.27/0.65 ! [A_14: int,B_9: int] :
% 0.27/0.65 ( ( A_14 = B_9 )
% 0.27/0.65 <=> ( ( minus_minus_int @ A_14 @ B_9 )
% 0.27/0.65 = zero_zero_int ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_635_right__minus__eq,axiom,
% 0.27/0.65 ! [A_13: int,B_8: int] :
% 0.27/0.65 ( ( ( minus_minus_int @ A_13 @ B_8 )
% 0.27/0.65 = zero_zero_int )
% 0.27/0.65 <=> ( A_13 = B_8 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_636_diffs0__imp__equal,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( ( minus_minus_nat @ M @ N_5 )
% 0.27/0.65 = zero_zero_nat )
% 0.27/0.65 => ( ( ( minus_minus_nat @ N_5 @ M )
% 0.27/0.65 = zero_zero_nat )
% 0.27/0.65 => ( M = N_5 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_637_diff__self__eq__0,axiom,
% 0.27/0.65 ! [M: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ M @ M )
% 0.27/0.65 = zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_638_minus__nat_Odiff__0,axiom,
% 0.27/0.65 ! [M: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.27/0.65 = M ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_639_diff__0__eq__0,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ zero_zero_nat @ N_5 )
% 0.27/0.65 = zero_zero_nat ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_640_diff__Suc__Suc,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N_5 ) )
% 0.27/0.65 = ( minus_minus_nat @ M @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_641_Suc__diff__diff,axiom,
% 0.27/0.65 ! [M: nat,N_5: nat,K_3: nat] :
% 0.27/0.65 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N_5 ) @ ( suc @ K_3 ) )
% 0.27/0.65 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N_5 ) @ K_3 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_642_nat__minus__add__max,axiom,
% 0.27/0.65 ! [N_5: nat,M: nat] :
% 0.27/0.65 ( ( plus_plus_nat @ ( minus_minus_nat @ N_5 @ M ) @ M )
% 0.27/0.65 = ( ord_max_nat @ N_5 @ M ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_643_diff__Suc__less,axiom,
% 0.27/0.65 ! [I: nat,N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ N_5 )
% 0.27/0.65 => ( ord_less_nat @ ( minus_minus_nat @ N_5 @ ( suc @ I ) ) @ N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_644_Suc__pred,axiom,
% 0.27/0.65 ! [N_5: nat] :
% 0.27/0.65 ( ( ord_less_nat @ zero_zero_nat @ N_5 )
% 0.27/0.65 => ( ( suc @ ( minus_minus_nat @ N_5 @ ( suc @ zero_zero_nat ) ) )
% 0.27/0.65 = N_5 ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_645_nat__diff__split,axiom,
% 0.27/0.65 ! [P: nat > $o,A_12: nat,B_7: nat] :
% 0.27/0.65 ( ( P @ ( minus_minus_nat @ A_12 @ B_7 ) )
% 0.27/0.65 <=> ( ( ( ord_less_nat @ A_12 @ B_7 )
% 0.27/0.65 => ( P @ zero_zero_nat ) )
% 0.27/0.65 & ! [D: nat] :
% 0.27/0.65 ( ( A_12
% 0.27/0.65 = ( plus_plus_nat @ B_7 @ D ) )
% 0.27/0.65 => ( P @ D ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_646_nat__diff__split__asm,axiom,
% 0.27/0.65 ! [P: nat > $o,A_12: nat,B_7: nat] :
% 0.27/0.65 ( ( P @ ( minus_minus_nat @ A_12 @ B_7 ) )
% 0.27/0.65 <=> ~ ( ( ( ord_less_nat @ A_12 @ B_7 )
% 0.27/0.65 & ~ ( P @ zero_zero_nat ) )
% 0.27/0.65 | ? [D: nat] :
% 0.27/0.65 ( ( A_12
% 0.27/0.65 = ( plus_plus_nat @ B_7 @ D ) )
% 0.27/0.65 & ~ ( P @ D ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_647_take__append,axiom,
% 0.27/0.65 ! [N_11: nat,Xs_20: list_A2115238852le_alt,Ys_3: list_A2115238852le_alt] :
% 0.27/0.65 ( ( take_A614047655le_alt @ N_11 @ ( append179082452le_alt @ Xs_20 @ Ys_3 ) )
% 0.27/0.65 = ( append179082452le_alt @ ( take_A614047655le_alt @ N_11 @ Xs_20 ) @ ( take_A614047655le_alt @ ( minus_minus_nat @ N_11 @ ( size_s1858781230le_alt @ Xs_20 ) ) @ Ys_3 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_648_drop__append,axiom,
% 0.27/0.65 ! [N_10: nat,Xs_19: list_A2115238852le_alt,Ys_2: list_A2115238852le_alt] :
% 0.27/0.65 ( ( drop_A1346709759le_alt @ N_10 @ ( append179082452le_alt @ Xs_19 @ Ys_2 ) )
% 0.27/0.65 = ( append179082452le_alt @ ( drop_A1346709759le_alt @ N_10 @ Xs_19 ) @ ( drop_A1346709759le_alt @ ( minus_minus_nat @ N_10 @ ( size_s1858781230le_alt @ Xs_19 ) ) @ Ys_2 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_649_nth__append,axiom,
% 0.27/0.65 ! [Ys_1: list_A2115238852le_alt,N_9: nat,Xs_18: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( ord_less_nat @ N_9 @ ( size_s1858781230le_alt @ Xs_18 ) )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ ( append179082452le_alt @ Xs_18 @ Ys_1 ) @ N_9 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Xs_18 @ N_9 ) ) )
% 0.27/0.65 & ( ~ ( ord_less_nat @ N_9 @ ( size_s1858781230le_alt @ Xs_18 ) )
% 0.27/0.65 => ( ( nth_Ar125878976le_alt @ ( append179082452le_alt @ Xs_18 @ Ys_1 ) @ N_9 )
% 0.27/0.65 = ( nth_Ar125878976le_alt @ Ys_1 @ ( minus_minus_nat @ N_9 @ ( size_s1858781230le_alt @ Xs_18 ) ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_650_list__update__append,axiom,
% 0.27/0.65 ! [Ys: list_A2115238852le_alt,X_13: arrow_475358991le_alt,N_8: nat,Xs_17: list_A2115238852le_alt] :
% 0.27/0.65 ( ( ( ord_less_nat @ N_8 @ ( size_s1858781230le_alt @ Xs_17 ) )
% 0.27/0.65 => ( ( list_u62477863le_alt @ ( append179082452le_alt @ Xs_17 @ Ys ) @ N_8 @ X_13 )
% 0.27/0.65 = ( append179082452le_alt @ ( list_u62477863le_alt @ Xs_17 @ N_8 @ X_13 ) @ Ys ) ) )
% 0.27/0.65 & ( ~ ( ord_less_nat @ N_8 @ ( size_s1858781230le_alt @ Xs_17 ) )
% 0.27/0.65 => ( ( list_u62477863le_alt @ ( append179082452le_alt @ Xs_17 @ Ys ) @ N_8 @ X_13 )
% 0.27/0.65 = ( append179082452le_alt @ Xs_17 @ ( list_u62477863le_alt @ Ys @ ( minus_minus_nat @ N_8 @ ( size_s1858781230le_alt @ Xs_17 ) ) @ X_13 ) ) ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_651_rev__drop,axiom,
% 0.27/0.65 ! [I_2: nat,Xs_16: list_A2115238852le_alt] :
% 0.27/0.65 ( ( rev_Ar1106406943le_alt @ ( drop_A1346709759le_alt @ I_2 @ Xs_16 ) )
% 0.27/0.65 = ( take_A614047655le_alt @ ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_16 ) @ I_2 ) @ ( rev_Ar1106406943le_alt @ Xs_16 ) ) ) ).
% 0.27/0.65
% 0.27/0.65 thf(fact_652_rev__take,axiom,
% 0.27/0.65 ! [I_1: nat,Xs_15: list_A2115238852le_alt] :
% 0.27/0.65 ( ( rev_Ar1106406943le_alt @ ( take_A614047655le_alt @ I_1 @ Xs_15 ) )
% 0.27/0.65 = ( drop_A1346709759le_alt @ ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_15 ) @ I_1 ) @ ( rev_Ar1106406943le_alt @ Xs_15 ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_653_zero__induct__lemma,axiom,
% 0.27/0.66 ! [I: nat,P: nat > $o,K_3: nat] :
% 0.27/0.66 ( ( P @ K_3 )
% 0.27/0.66 => ( ! [N_7: nat] :
% 0.27/0.66 ( ( P @ ( suc @ N_7 ) )
% 0.27/0.66 => ( P @ N_7 ) )
% 0.27/0.66 => ( P @ ( minus_minus_nat @ K_3 @ I ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_654_last__list__update,axiom,
% 0.27/0.66 ! [X_12: arrow_475358991le_alt,K_2: nat,Xs_14: list_A2115238852le_alt] :
% 0.27/0.66 ( ( Xs_14 != nil_Ar1286194111le_alt )
% 0.27/0.66 => ( ( ( K_2
% 0.27/0.66 = ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_14 ) @ one_one_nat ) )
% 0.27/0.66 => ( ( last_A1217315288le_alt @ ( list_u62477863le_alt @ Xs_14 @ K_2 @ X_12 ) )
% 0.27/0.66 = X_12 ) )
% 0.27/0.66 & ( ( K_2
% 0.27/0.66 != ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_14 ) @ one_one_nat ) )
% 0.27/0.66 => ( ( last_A1217315288le_alt @ ( list_u62477863le_alt @ Xs_14 @ K_2 @ X_12 ) )
% 0.27/0.66 = ( last_A1217315288le_alt @ Xs_14 ) ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_655_empty__Diff,axiom,
% 0.27/0.66 ! [A_11: nat > $o] :
% 0.27/0.66 ( ( minus_minus_nat_o @ bot_bot_nat_o @ A_11 )
% 0.27/0.66 = bot_bot_nat_o ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_656_Diff__empty,axiom,
% 0.27/0.66 ! [A_10: nat > $o] :
% 0.27/0.66 ( ( minus_minus_nat_o @ A_10 @ bot_bot_nat_o )
% 0.27/0.66 = A_10 ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_657_Diff__cancel,axiom,
% 0.27/0.66 ! [A_9: nat > $o] :
% 0.27/0.66 ( ( minus_minus_nat_o @ A_9 @ A_9 )
% 0.27/0.66 = bot_bot_nat_o ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_658_diff__Suc__1,axiom,
% 0.27/0.66 ! [N_5: nat] :
% 0.27/0.66 ( ( minus_minus_nat @ ( suc @ N_5 ) @ one_one_nat )
% 0.27/0.66 = N_5 ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_659_diff__Suc__eq__diff__pred,axiom,
% 0.27/0.66 ! [M: nat,N_5: nat] :
% 0.27/0.66 ( ( minus_minus_nat @ M @ ( suc @ N_5 ) )
% 0.27/0.66 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N_5 ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_660_Suc__eq__plus1__left,axiom,
% 0.27/0.66 ! [N_5: nat] :
% 0.27/0.66 ( ( suc @ N_5 )
% 0.27/0.66 = ( plus_plus_nat @ one_one_nat @ N_5 ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_661_Suc__eq__plus1,axiom,
% 0.27/0.66 ! [N_5: nat] :
% 0.27/0.66 ( ( suc @ N_5 )
% 0.27/0.66 = ( plus_plus_nat @ N_5 @ one_one_nat ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_662_drop__1__Cons,axiom,
% 0.27/0.66 ! [X_11: arrow_475358991le_alt,Xs_13: list_A2115238852le_alt] :
% 0.27/0.66 ( ( drop_A1346709759le_alt @ one_one_nat @ ( cons_A228743023le_alt @ X_11 @ Xs_13 ) )
% 0.27/0.66 = Xs_13 ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_663_one__reorient,axiom,
% 0.27/0.66 ! [X_10: nat] :
% 0.27/0.66 ( ( one_one_nat = X_10 )
% 0.27/0.66 <=> ( X_10 = one_one_nat ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_664_One__nat__def,axiom,
% 0.27/0.66 ( one_one_nat
% 0.27/0.66 = ( suc @ zero_zero_nat ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_665_less__add__one,axiom,
% 0.27/0.66 ! [A_8: nat] : ( ord_less_nat @ A_8 @ ( plus_plus_nat @ A_8 @ one_one_nat ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_666_less__add__one,axiom,
% 0.27/0.66 ! [A_8: int] : ( ord_less_int @ A_8 @ ( plus_plus_int @ A_8 @ one_one_int ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_667_not__one__less__zero,axiom,
% 0.27/0.66 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_668_zero__less__one,axiom,
% 0.27/0.66 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.27/0.66
% 0.27/0.66 thf(fact_669_one__neq__zero,axiom,
% 0.27/0.66 one_one_nat != zero_zero_nat ).
% 0.27/0.66
% 0.27/0.66 thf(fact_670_zero__neq__one,axiom,
% 0.27/0.66 zero_zero_nat != one_one_nat ).
% 0.27/0.66
% 0.27/0.66 thf(fact_671_zero__less__two,axiom,
% 0.27/0.66 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_672_zero__less__two,axiom,
% 0.27/0.66 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_673_take__1__Cons,axiom,
% 0.27/0.66 ! [X_9: arrow_475358991le_alt,Xs_12: list_A2115238852le_alt] :
% 0.27/0.66 ( ( take_A614047655le_alt @ one_one_nat @ ( cons_A228743023le_alt @ X_9 @ Xs_12 ) )
% 0.27/0.66 = ( cons_A228743023le_alt @ X_9 @ nil_Ar1286194111le_alt ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_674_length__butlast,axiom,
% 0.27/0.66 ! [Xs_11: list_A2115238852le_alt] :
% 0.27/0.66 ( ( size_s1858781230le_alt @ ( butlas274947851le_alt @ Xs_11 ) )
% 0.27/0.66 = ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_11 ) @ one_one_nat ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_675_length__tl,axiom,
% 0.27/0.66 ! [Xs_10: list_A2115238852le_alt] :
% 0.27/0.66 ( ( size_s1858781230le_alt @ ( tl_Arr465451158le_alt @ Xs_10 ) )
% 0.27/0.66 = ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_10 ) @ one_one_nat ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_676_tl__take,axiom,
% 0.27/0.66 ! [N_6: nat,Xs_9: list_A2115238852le_alt] :
% 0.27/0.66 ( ( tl_Arr465451158le_alt @ ( take_A614047655le_alt @ N_6 @ Xs_9 ) )
% 0.27/0.66 = ( take_A614047655le_alt @ ( minus_minus_nat @ N_6 @ one_one_nat ) @ ( tl_Arr465451158le_alt @ Xs_9 ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_677_Suc__pred_H,axiom,
% 0.27/0.66 ! [N_5: nat] :
% 0.27/0.66 ( ( ord_less_nat @ zero_zero_nat @ N_5 )
% 0.27/0.66 => ( N_5
% 0.27/0.66 = ( suc @ ( minus_minus_nat @ N_5 @ one_one_nat ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_678_Suc__diff__1,axiom,
% 0.27/0.66 ! [N_5: nat] :
% 0.27/0.66 ( ( ord_less_nat @ zero_zero_nat @ N_5 )
% 0.27/0.66 => ( ( suc @ ( minus_minus_nat @ N_5 @ one_one_nat ) )
% 0.27/0.66 = N_5 ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_679_add__eq__if,axiom,
% 0.27/0.66 ! [N_5: nat,M: nat] :
% 0.27/0.66 ( ( ( M = zero_zero_nat )
% 0.27/0.66 => ( ( plus_plus_nat @ M @ N_5 )
% 0.27/0.66 = N_5 ) )
% 0.27/0.66 & ( ( M != zero_zero_nat )
% 0.27/0.66 => ( ( plus_plus_nat @ M @ N_5 )
% 0.27/0.66 = ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N_5 ) ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_680_nth__Cons_H,axiom,
% 0.27/0.66 ! [X_8: arrow_475358991le_alt,Xs_8: list_A2115238852le_alt,N_4: nat] :
% 0.27/0.66 ( ( ( N_4 = zero_zero_nat )
% 0.27/0.66 => ( ( nth_Ar125878976le_alt @ ( cons_A228743023le_alt @ X_8 @ Xs_8 ) @ N_4 )
% 0.27/0.66 = X_8 ) )
% 0.27/0.66 & ( ( N_4 != zero_zero_nat )
% 0.27/0.66 => ( ( nth_Ar125878976le_alt @ ( cons_A228743023le_alt @ X_8 @ Xs_8 ) @ N_4 )
% 0.27/0.66 = ( nth_Ar125878976le_alt @ Xs_8 @ ( minus_minus_nat @ N_4 @ one_one_nat ) ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_681_drop__Cons_H,axiom,
% 0.27/0.66 ! [X_7: arrow_475358991le_alt,Xs_7: list_A2115238852le_alt,N_3: nat] :
% 0.27/0.66 ( ( ( N_3 = zero_zero_nat )
% 0.27/0.66 => ( ( drop_A1346709759le_alt @ N_3 @ ( cons_A228743023le_alt @ X_7 @ Xs_7 ) )
% 0.27/0.66 = ( cons_A228743023le_alt @ X_7 @ Xs_7 ) ) )
% 0.27/0.66 & ( ( N_3 != zero_zero_nat )
% 0.27/0.66 => ( ( drop_A1346709759le_alt @ N_3 @ ( cons_A228743023le_alt @ X_7 @ Xs_7 ) )
% 0.27/0.66 = ( drop_A1346709759le_alt @ ( minus_minus_nat @ N_3 @ one_one_nat ) @ Xs_7 ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_682_butlast__conv__take,axiom,
% 0.27/0.66 ! [Xs_6: list_A2115238852le_alt] :
% 0.27/0.66 ( ( butlas274947851le_alt @ Xs_6 )
% 0.27/0.66 = ( take_A614047655le_alt @ ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_6 ) @ one_one_nat ) @ Xs_6 ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_683_butlast__list__update,axiom,
% 0.27/0.66 ! [X_6: arrow_475358991le_alt,K_1: nat,Xs_5: list_A2115238852le_alt] :
% 0.27/0.66 ( ( ( K_1
% 0.27/0.66 = ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_5 ) @ one_one_nat ) )
% 0.27/0.66 => ( ( butlas274947851le_alt @ ( list_u62477863le_alt @ Xs_5 @ K_1 @ X_6 ) )
% 0.27/0.66 = ( butlas274947851le_alt @ Xs_5 ) ) )
% 0.27/0.66 & ( ( K_1
% 0.27/0.66 != ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_5 ) @ one_one_nat ) )
% 0.27/0.66 => ( ( butlas274947851le_alt @ ( list_u62477863le_alt @ Xs_5 @ K_1 @ X_6 ) )
% 0.27/0.66 = ( list_u62477863le_alt @ ( butlas274947851le_alt @ Xs_5 ) @ K_1 @ X_6 ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_684_tl__replicate,axiom,
% 0.27/0.66 ! [X_5: arrow_475358991le_alt,N_2: nat] :
% 0.27/0.66 ( ( N_2 != zero_zero_nat )
% 0.27/0.66 => ( ( tl_Arr465451158le_alt @ ( replic1511538809le_alt @ N_2 @ X_5 ) )
% 0.27/0.66 = ( replic1511538809le_alt @ ( minus_minus_nat @ N_2 @ one_one_nat ) @ X_5 ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_685_nth__Cons__pos,axiom,
% 0.27/0.66 ! [X_4: arrow_475358991le_alt,Xs_4: list_A2115238852le_alt,N_1: nat] :
% 0.27/0.66 ( ( ord_less_nat @ zero_zero_nat @ N_1 )
% 0.27/0.66 => ( ( nth_Ar125878976le_alt @ ( cons_A228743023le_alt @ X_4 @ Xs_4 ) @ N_1 )
% 0.27/0.66 = ( nth_Ar125878976le_alt @ Xs_4 @ ( minus_minus_nat @ N_1 @ one_one_nat ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_686_take__Cons_H,axiom,
% 0.27/0.66 ! [X_3: arrow_475358991le_alt,Xs_3: list_A2115238852le_alt,N: nat] :
% 0.27/0.66 ( ( ( N = zero_zero_nat )
% 0.27/0.66 => ( ( take_A614047655le_alt @ N @ ( cons_A228743023le_alt @ X_3 @ Xs_3 ) )
% 0.27/0.66 = nil_Ar1286194111le_alt ) )
% 0.27/0.66 & ( ( N != zero_zero_nat )
% 0.27/0.66 => ( ( take_A614047655le_alt @ N @ ( cons_A228743023le_alt @ X_3 @ Xs_3 ) )
% 0.27/0.66 = ( cons_A228743023le_alt @ X_3 @ ( take_A614047655le_alt @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs_3 ) ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_687_rev__update,axiom,
% 0.27/0.66 ! [Y_1: arrow_475358991le_alt,K: nat,Xs_2: list_A2115238852le_alt] :
% 0.27/0.66 ( ( ord_less_nat @ K @ ( size_s1858781230le_alt @ Xs_2 ) )
% 0.27/0.66 => ( ( rev_Ar1106406943le_alt @ ( list_u62477863le_alt @ Xs_2 @ K @ Y_1 ) )
% 0.27/0.66 = ( list_u62477863le_alt @ ( rev_Ar1106406943le_alt @ Xs_2 ) @ ( minus_minus_nat @ ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_2 ) @ K ) @ one_one_nat ) @ Y_1 ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_688_last__conv__nth,axiom,
% 0.27/0.66 ! [Xs_1: list_A2115238852le_alt] :
% 0.27/0.66 ( ( Xs_1 != nil_Ar1286194111le_alt )
% 0.27/0.66 => ( ( last_A1217315288le_alt @ Xs_1 )
% 0.27/0.66 = ( nth_Ar125878976le_alt @ Xs_1 @ ( minus_minus_nat @ ( size_s1858781230le_alt @ Xs_1 ) @ one_one_nat ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_689_take__Cons__number__of,axiom,
% 0.27/0.66 ! [X_2: arrow_475358991le_alt,Xs: list_A2115238852le_alt,V_2: int] :
% 0.27/0.66 ( ( ( ( number_number_of_nat @ V_2 )
% 0.27/0.66 = zero_zero_nat )
% 0.27/0.66 => ( ( take_A614047655le_alt @ ( number_number_of_nat @ V_2 ) @ ( cons_A228743023le_alt @ X_2 @ Xs ) )
% 0.27/0.66 = nil_Ar1286194111le_alt ) )
% 0.27/0.66 & ( ( ( number_number_of_nat @ V_2 )
% 0.27/0.66 != zero_zero_nat )
% 0.27/0.66 => ( ( take_A614047655le_alt @ ( number_number_of_nat @ V_2 ) @ ( cons_A228743023le_alt @ X_2 @ Xs ) )
% 0.27/0.66 = ( cons_A228743023le_alt @ X_2 @ ( take_A614047655le_alt @ ( minus_minus_nat @ ( number_number_of_nat @ V_2 ) @ one_one_nat ) @ Xs ) ) ) ) ) ).
% 0.27/0.66
% 0.27/0.66 thf(fact_690_Ints__odd__less__0,axiom,
% 0.27/0.66 ! [A_7: int] :
% 0.51/0.76 ( ( member_int @ A_7 @ ring_1_Ints_int )
% 0.51/0.76 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A_7 ) @ A_7 ) @ zero_zero_int )
% 0.51/0.76 <=> ( ord_less_int @ A_7 @ zero_zero_int ) ) ) ).
% 0.51/0.76
% 0.51/0.76 thf(fact_691_DiffE,axiom,
% 0.51/0.76 ! [C_6: nat,A_6: nat > $o,B_6: nat > $o] :
% 0.51/0.76 ( ( member_nat @ C_6 @ ( minus_minus_nat_o @ A_6 @ B_6 ) )
% 0.51/0.76 => ~ ( ( member_nat @ C_6 @ A_6 )
% 0.51/0.76 => ( member_nat @ C_6 @ B_6 ) ) ) ).
% 0.51/0.76
% 0.51/0.76 thf(fact_692_DiffI,axiom,
% 0.51/0.76 ! [B_5: nat > $o,C_5: nat,A_5: nat > $o] :
% 0.51/0.76 ( ( member_nat @ C_5 @ A_5 )
% 0.51/0.76 => ( ~ ( member_nat @ C_5 @ B_5 )
% 0.51/0.76 => ( member_nat @ C_5 @ ( minus_minus_nat_o @ A_5 @ B_5 ) ) ) ) ).
% 0.51/0.76
% 0.51/0.76 thf(fact_693_Ints__diff,axiom,
% 0.51/0.76 ! [B_4: int,A_4: int] :
% 0.51/0.76 ( ( member_int @ A_4 @ ring_1_Ints_int )
% 0.51/0.76 => ( ( member_int @ B_4 @ ring_1_Ints_int )
% 0.51/0.76 => ( member_int @ ( minus_minus_int @ A_4 @ B_4 ) @ ring_1_Ints_int ) ) ) ).
% 0.51/0.76
% 0.51/0.76 thf(fact_694_number__of__diff,axiom,
% 0.51/0.76 ! [V_1: int,W_1: int] :
% 0.51/0.76 ( ( number_number_of_int @ ( minus_minus_int @ V_1 @ W_1 ) )
% 0.51/0.76 = ( minus_minus_int @ ( number_number_of_int @ V_1 ) @ ( number_number_of_int @ W_1 ) ) ) ).
% 0.51/0.76
% 0.51/0.76 thf(fact_695_add__number__of__diff1,axiom,
% 0.51/0.76 ! [V: int,W: int,C_4: int] :
% 0.51/0.76 ( ( plus_plus_int @ ( number_number_of_int @ V ) @ ( minus_minus_int @ ( number_number_of_int @ W ) @ C_4 ) )
% 0.51/0.76 = ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ V @ W ) ) @ C_4 ) ) ).
% 0.51/0.76
% 0.51/0.76 thf(fact_696_DiffD2,axiom,
% 0.51/0.76 ! [C_3: nat,A_3: nat > $o,B_3: nat > $o] :
% 0.51/0.76 ( ( member_nat @ C_3 @ ( minus_minus_nat_o @ A_3 @ B_3 ) )
% 0.51/0.76 => ~ ( member_nat @ C_3 @ B_3 ) ) ).
% 0.51/0.76
% 0.51/0.76 thf(fact_697_DiffD1,axiom,
% 0.51/0.76 ! [C_2: nat,A_2: nat > $o,B_2: nat > $o] :
% 0.51/0.76 ( ( member_nat @ C_2 @ ( minus_minus_nat_o @ A_2 @ B_2 ) )
% 0.51/0.76 => ( member_nat @ C_2 @ A_2 ) ) ).
% 0.51/0.76
% 0.51/0.76 thf(fact_698_Diff__iff,axiom,
% 0.51/0.76 ! [C_1: nat,A_1: nat > $o,B_1: nat > $o] :
% 0.51/0.76 ( ( member_nat @ C_1 @ ( minus_minus_nat_o @ A_1 @ B_1 ) )
% 0.51/0.76 <=> ( ( member_nat @ C_1 @ A_1 )
% 0.51/0.76 & ~ ( member_nat @ C_1 @ B_1 ) ) ) ).
% 0.51/0.76
% 0.51/0.76 thf(fact_699_set__diff__eq,axiom,
% 0.51/0.76 ! [A: nat > $o,B: nat > $o] :
% 0.51/0.76 ( ( minus_minus_nat_o @ A @ B )
% 0.51/0.76 = ( collect_nat
% 0.51/0.76 @ ^ [X_1: nat] : ( (&) @ ( member_nat @ X_1 @ A ) @ ( (~) @ ( member_nat @ X_1 @ B ) ) ) ) ) ).
% 0.51/0.76
% 0.51/0.76 %----Helper facts (2)
% 0.51/0.76 thf(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lc,axiom,
% 0.51/0.76 ! [X: list_A2115238852le_alt,Y: list_A2115238852le_alt] :
% 0.51/0.76 ( ~ ( fequal781288069le_alt @ X @ Y )
% 0.51/0.76 | ( X = Y ) ) ).
% 0.51/0.76
% 0.51/0.76 thf(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____lc,axiom,
% 0.51/0.76 ! [X: list_A2115238852le_alt,Y: list_A2115238852le_alt] :
% 0.51/0.76 ( ( X != Y )
% 0.51/0.76 | ( fequal781288069le_alt @ X @ Y ) ) ).
% 0.51/0.76
% 0.51/0.76 %----Conjectures (2)
% 0.51/0.76 thf(conj_0,hypothesis,
% 0.51/0.76 a != b ).
% 0.51/0.76
% 0.51/0.76 thf(conj_1,conjecture,
% 0.51/0.76 ? [C: arrow_475358991le_alt] : ( distin236324274le_alt @ ( cons_A228743023le_alt @ a @ ( cons_A228743023le_alt @ b @ ( cons_A228743023le_alt @ C @ nil_Ar1286194111le_alt ) ) ) ) ).
% 0.51/0.76
% 0.51/0.76 %------------------------------------------------------------------------------
% 0.51/0.76 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.JjVe2NM7OM/cvc5---1.0.5_19231.p...
% 0.51/0.76 (declare-sort $$unsorted 0)
% 0.51/0.76 (declare-sort tptp.arrow_475358991le_alt 0)
% 0.51/0.76 (declare-sort tptp.int 0)
% 0.51/0.76 (declare-sort tptp.list_A2115238852le_alt 0)
% 0.51/0.76 (declare-sort tptp.list_int 0)
% 0.51/0.76 (declare-sort tptp.list_nat 0)
% 0.51/0.76 (declare-sort tptp.nat 0)
% 0.51/0.76 (declare-sort tptp.option514678660le_alt 0)
% 0.51/0.76 (declare-sort tptp.option_nat 0)
% 0.51/0.76 (declare-fun tptp.ex1 ((-> tptp.nat Bool)) Bool)
% 0.51/0.76 (declare-fun tptp.ex2 ((-> tptp.arrow_475358991le_alt Bool)) Bool)
% 0.51/0.76 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 0.51/0.76 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 0.51/0.76 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.51/0.76 (declare-fun tptp.one_one_int () tptp.int)
% 0.51/0.76 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.51/0.76 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 0.51/0.76 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.51/0.76 (declare-fun tptp.zero_zero_int () tptp.int)
% 0.51/0.76 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.51/0.76 (declare-fun tptp.equal_484611810le_alt (tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt) Bool)
% 0.51/0.76 (declare-fun tptp.equal_equal_list_nat (tptp.list_nat tptp.list_nat) Bool)
% 0.51/0.76 (declare-fun tptp.number_number_of_int (tptp.int) tptp.int)
% 0.51/0.76 (declare-fun tptp.number_number_of_nat (tptp.int) tptp.nat)
% 0.51/0.76 (declare-fun tptp.ring_1_Ints_int (tptp.int) Bool)
% 0.51/0.76 (declare-fun tptp.listMe78047147le_alt (tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt) Bool)
% 0.51/0.76 (declare-fun tptp.append179082452le_alt (tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.butlas274947851le_alt (tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.butlast_nat (tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.distin236324274le_alt (tptp.list_A2115238852le_alt) Bool)
% 0.51/0.76 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 0.51/0.76 (declare-fun tptp.dropWh1316781920le_alt ((-> tptp.arrow_475358991le_alt Bool) tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.dropWhile_nat ((-> tptp.nat Bool) tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.drop_A1346709759le_alt (tptp.nat tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.foldr_int_int ((-> tptp.int tptp.int tptp.int) tptp.list_int tptp.int) tptp.int)
% 0.51/0.76 (declare-fun tptp.foldr_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 0.51/0.76 (declare-fun tptp.hd_Arr1965683346le_alt (tptp.list_A2115238852le_alt) tptp.arrow_475358991le_alt)
% 0.51/0.76 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 0.51/0.76 (declare-fun tptp.insert2120566741le_alt (tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.insert_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.last_A1217315288le_alt (tptp.list_A2115238852le_alt) tptp.arrow_475358991le_alt)
% 0.51/0.76 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 0.51/0.76 (declare-fun tptp.linorder_sorted_int (tptp.list_int) Bool)
% 0.51/0.76 (declare-fun tptp.linorder_sorted_nat (tptp.list_nat) Bool)
% 0.51/0.76 (declare-fun tptp.linord810813188et_nat ((-> tptp.nat Bool)) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.cons_A228743023le_alt (tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.nil_Ar1286194111le_alt () tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.nil_int () tptp.list_int)
% 0.51/0.76 (declare-fun tptp.nil_nat () tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.list_s250295873le_alt ((-> tptp.arrow_475358991le_alt tptp.nat) tptp.list_A2115238852le_alt) tptp.nat)
% 0.51/0.76 (declare-fun tptp.list_size_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.nat)
% 0.51/0.76 (declare-fun tptp.list_e239244930le_alt ((-> tptp.arrow_475358991le_alt Bool) tptp.list_A2115238852le_alt) Bool)
% 0.51/0.76 (declare-fun tptp.list_ex1_nat ((-> tptp.nat Bool) tptp.list_nat) Bool)
% 0.51/0.76 (declare-fun tptp.list_e1252802557le_alt ((-> tptp.arrow_475358991le_alt Bool) tptp.list_A2115238852le_alt) Bool)
% 0.51/0.76 (declare-fun tptp.list_ex_nat ((-> tptp.nat Bool) tptp.list_nat) Bool)
% 0.51/0.76 (declare-fun tptp.list_u62477863le_alt (tptp.list_A2115238852le_alt tptp.nat tptp.arrow_475358991le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.listre1213162009le_alt ((-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool) tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt) Bool)
% 0.51/0.76 (declare-fun tptp.listrelp_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat tptp.list_nat) Bool)
% 0.51/0.76 (declare-fun tptp.map_fi312151301lt_nat ((-> tptp.arrow_475358991le_alt tptp.option_nat) tptp.list_A2115238852le_alt) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.map_fi1462697295le_alt ((-> tptp.nat tptp.option514678660le_alt) tptp.list_nat) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.maps_A409156225le_alt ((-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.maps_A2124894076lt_nat ((-> tptp.arrow_475358991le_alt tptp.list_nat) tptp.list_A2115238852le_alt) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.maps_n1127956422le_alt ((-> tptp.nat tptp.list_A2115238852le_alt) tptp.list_nat) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.member1504968148le_alt (tptp.list_A2115238852le_alt tptp.arrow_475358991le_alt) Bool)
% 0.51/0.76 (declare-fun tptp.member_nat_1 (tptp.list_nat tptp.nat) Bool)
% 0.51/0.76 (declare-fun tptp.nth_Ar125878976le_alt (tptp.list_A2115238852le_alt tptp.nat) tptp.arrow_475358991le_alt)
% 0.51/0.76 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 0.51/0.76 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 0.51/0.76 (declare-fun tptp.null_A1520965063le_alt (tptp.list_A2115238852le_alt) Bool)
% 0.51/0.76 (declare-fun tptp.null_nat (tptp.list_nat) Bool)
% 0.51/0.76 (declare-fun tptp.replic1511538809le_alt (tptp.nat tptp.arrow_475358991le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.rev_Ar1106406943le_alt (tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.rev_int (tptp.list_int) tptp.list_int)
% 0.51/0.76 (declare-fun tptp.rev_nat (tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.rotate335349260le_alt (tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.rotate1_nat (tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.splice1520898450le_alt (tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.splice_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.sublis2047953604le_alt (tptp.list_A2115238852le_alt (-> tptp.nat Bool)) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.sublist_nat (tptp.list_nat (-> tptp.nat Bool)) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.takeWh1696291512le_alt ((-> tptp.arrow_475358991le_alt Bool) tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.takeWhile_nat ((-> tptp.nat Bool) tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.take_A614047655le_alt (tptp.nat tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.tl_Arr465451158le_alt (tptp.list_A2115238852le_alt) tptp.list_A2115238852le_alt)
% 0.51/0.76 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 0.51/0.76 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.51/0.76 (declare-fun tptp.size_s1858781230le_alt (tptp.list_A2115238852le_alt) tptp.nat)
% 0.51/0.76 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 0.51/0.76 (declare-fun tptp.bot_bot_int_o (tptp.int) Bool)
% 0.51/0.76 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 0.51/0.76 (declare-fun tptp.bot_bot_o () Bool)
% 0.51/0.76 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 0.51/0.76 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 0.51/0.76 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 0.51/0.76 (declare-fun tptp.ord_less_o (Bool Bool) Bool)
% 0.51/0.76 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 0.51/0.76 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.51/0.76 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 0.51/0.76 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 0.51/0.76 (declare-fun tptp.collect_nat ((-> tptp.nat Bool) tptp.nat) Bool)
% 0.51/0.76 (declare-fun tptp.fequal781288069le_alt (tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt) Bool)
% 0.51/0.76 (declare-fun tptp.member_int (tptp.int (-> tptp.int Bool)) Bool)
% 0.51/0.76 (declare-fun tptp.member_nat (tptp.nat (-> tptp.nat Bool)) Bool)
% 0.51/0.76 (declare-fun tptp.a () tptp.arrow_475358991le_alt)
% 0.51/0.76 (declare-fun tptp.b () tptp.arrow_475358991le_alt)
% 0.51/0.76 (assert (exists ((A_90 tptp.arrow_475358991le_alt) (B_48 tptp.arrow_475358991le_alt) (C tptp.arrow_475358991le_alt)) (@ tptp.distin236324274le_alt (@ (@ tptp.cons_A228743023le_alt A_90) (@ (@ tptp.cons_A228743023le_alt B_48) (@ (@ tptp.cons_A228743023le_alt C) tptp.nil_Ar1286194111le_alt))))))
% 0.51/0.76 (assert (@ tptp.distin236324274le_alt tptp.nil_Ar1286194111le_alt))
% 0.51/0.76 (assert (@ tptp.distinct_nat tptp.nil_nat))
% 0.51/0.76 (assert (forall ((A_92 tptp.arrow_475358991le_alt) (List_6 tptp.list_A2115238852le_alt)) (not (= tptp.nil_Ar1286194111le_alt (@ (@ tptp.cons_A228743023le_alt A_92) List_6)))))
% 0.51/0.76 (assert (forall ((A_92 tptp.nat) (List_6 tptp.list_nat)) (not (= tptp.nil_nat (@ (@ tptp.cons_nat A_92) List_6)))))
% 0.51/0.76 (assert (forall ((A_91 tptp.arrow_475358991le_alt) (List_5 tptp.list_A2115238852le_alt)) (not (= (@ (@ tptp.cons_A228743023le_alt A_91) List_5) tptp.nil_Ar1286194111le_alt))))
% 0.51/0.76 (assert (forall ((A_91 tptp.nat) (List_5 tptp.list_nat)) (not (= (@ (@ tptp.cons_nat A_91) List_5) tptp.nil_nat))))
% 0.51/0.76 (assert (forall ((Xs_183 tptp.list_A2115238852le_alt)) (= (not (= Xs_183 tptp.nil_Ar1286194111le_alt)) (exists ((Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (= Xs_183 (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5))))))
% 0.51/0.76 (assert (forall ((Xs_183 tptp.list_nat)) (= (not (= Xs_183 tptp.nil_nat)) (exists ((Y_3 tptp.nat) (Ys_5 tptp.list_nat)) (= Xs_183 (@ (@ tptp.cons_nat Y_3) Ys_5))))))
% 0.51/0.76 (assert (forall ((Y_44 tptp.list_A2115238852le_alt)) (=> (not (= Y_44 tptp.nil_Ar1286194111le_alt)) (not (forall ((A_90 tptp.arrow_475358991le_alt) (List_4 tptp.list_A2115238852le_alt)) (not (= Y_44 (@ (@ tptp.cons_A228743023le_alt A_90) List_4))))))))
% 0.51/0.76 (assert (forall ((Y_44 tptp.list_nat)) (=> (not (= Y_44 tptp.nil_nat)) (not (forall ((A_90 tptp.nat) (List_4 tptp.list_nat)) (not (= Y_44 (@ (@ tptp.cons_nat A_90) List_4))))))))
% 0.51/0.76 (assert (forall ((Xs_182 tptp.list_A2115238852le_alt) (X_115 tptp.arrow_475358991le_alt)) (not (= Xs_182 (@ (@ tptp.cons_A228743023le_alt X_115) Xs_182)))))
% 0.51/0.76 (assert (forall ((X_114 tptp.arrow_475358991le_alt) (Xs_181 tptp.list_A2115238852le_alt)) (not (= (@ (@ tptp.cons_A228743023le_alt X_114) Xs_181) Xs_181))))
% 0.51/0.76 (assert (forall ((A_89 tptp.arrow_475358991le_alt) (List_3 tptp.list_A2115238852le_alt) (A_88 tptp.arrow_475358991le_alt) (List_2 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.cons_A228743023le_alt A_89) List_3) (@ (@ tptp.cons_A228743023le_alt A_88) List_2)) (and (= A_89 A_88) (= List_3 List_2)))))
% 0.51/0.76 (assert (forall ((V_4 tptp.arrow_475358991le_alt) (Va tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt V_4) Va))) (= (@ (@ tptp.splice1520898450le_alt _let_1) tptp.nil_Ar1286194111le_alt) _let_1))))
% 0.51/0.76 (assert (forall ((V_4 tptp.nat) (Va tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat V_4) Va))) (= (@ (@ tptp.splice_nat _let_1) tptp.nil_nat) _let_1))))
% 0.51/0.76 (assert (forall ((X_113 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.insert2120566741le_alt X_113) tptp.nil_Ar1286194111le_alt) (@ (@ tptp.cons_A228743023le_alt X_113) tptp.nil_Ar1286194111le_alt))))
% 0.51/0.76 (assert (forall ((X_113 tptp.nat)) (= (@ (@ tptp.insert_nat X_113) tptp.nil_nat) (@ (@ tptp.cons_nat X_113) tptp.nil_nat))))
% 0.51/0.76 (assert (forall ((P_33 (-> tptp.list_A2115238852le_alt Bool)) (Xs_180 tptp.list_A2115238852le_alt)) (=> (not (= Xs_180 tptp.nil_Ar1286194111le_alt)) (=> (forall ((X_1 tptp.arrow_475358991le_alt)) (@ P_33 (@ (@ tptp.cons_A228743023le_alt X_1) tptp.nil_Ar1286194111le_alt))) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt)) (=> (not (= Xs_54 tptp.nil_Ar1286194111le_alt)) (=> (@ P_33 Xs_54) (@ P_33 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54))))) (@ P_33 Xs_180))))))
% 0.51/0.76 (assert (forall ((P_33 (-> tptp.list_nat Bool)) (Xs_180 tptp.list_nat)) (=> (not (= Xs_180 tptp.nil_nat)) (=> (forall ((X_1 tptp.nat)) (@ P_33 (@ (@ tptp.cons_nat X_1) tptp.nil_nat))) (=> (forall ((X_1 tptp.nat) (Xs_54 tptp.list_nat)) (=> (not (= Xs_54 tptp.nil_nat)) (=> (@ P_33 Xs_54) (@ P_33 (@ (@ tptp.cons_nat X_1) Xs_54))))) (@ P_33 Xs_180))))))
% 0.51/0.76 (assert (forall ((Xs_179 tptp.list_A2115238852le_alt)) (=> (not (= Xs_179 tptp.nil_Ar1286194111le_alt)) (=> (@ tptp.distin236324274le_alt Xs_179) (@ tptp.distin236324274le_alt (@ tptp.butlas274947851le_alt Xs_179))))))
% 0.51/0.76 (assert (forall ((Xs_179 tptp.list_nat)) (=> (not (= Xs_179 tptp.nil_nat)) (=> (@ tptp.distinct_nat Xs_179) (@ tptp.distinct_nat (@ tptp.butlast_nat Xs_179))))))
% 0.51/0.76 (assert (= (@ tptp.butlas274947851le_alt tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt))
% 0.51/0.76 (assert (= (@ tptp.butlast_nat tptp.nil_nat) tptp.nil_nat))
% 0.51/0.76 (assert (forall ((X_112 tptp.arrow_475358991le_alt) (Xs_178 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_178) (@ tptp.distin236324274le_alt (@ (@ tptp.insert2120566741le_alt X_112) Xs_178)))))
% 0.51/0.76 (assert (forall ((X_111 tptp.arrow_475358991le_alt) (Xs_177 tptp.list_A2115238852le_alt) (Y_43 tptp.arrow_475358991le_alt) (Ys_54 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt Y_43))) (let ((_let_2 (@ tptp.cons_A228743023le_alt X_111))) (= (@ (@ tptp.splice1520898450le_alt (@ _let_2 Xs_177)) (@ _let_1 Ys_54)) (@ _let_2 (@ _let_1 (@ (@ tptp.splice1520898450le_alt Xs_177) Ys_54))))))))
% 0.51/0.76 (assert (forall ((Xs_176 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.splice1520898450le_alt Xs_176) tptp.nil_Ar1286194111le_alt) Xs_176)))
% 0.51/0.76 (assert (forall ((Xs_176 tptp.list_nat)) (= (@ (@ tptp.splice_nat Xs_176) tptp.nil_nat) Xs_176)))
% 0.51/0.76 (assert (forall ((Ys_53 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.splice1520898450le_alt tptp.nil_Ar1286194111le_alt) Ys_53) Ys_53)))
% 0.51/0.76 (assert (forall ((Ys_53 tptp.list_nat)) (= (@ (@ tptp.splice_nat tptp.nil_nat) Ys_53) Ys_53)))
% 0.51/0.76 (assert (forall ((X_110 tptp.arrow_475358991le_alt) (Xs_175 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_110))) (let ((_let_2 (@ tptp.butlas274947851le_alt (@ _let_1 Xs_175)))) (let ((_let_3 (= Xs_175 tptp.nil_Ar1286194111le_alt))) (and (=> _let_3 (= _let_2 tptp.nil_Ar1286194111le_alt)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlas274947851le_alt Xs_175))))))))))
% 0.51/0.76 (assert (forall ((X_110 tptp.nat) (Xs_175 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X_110))) (let ((_let_2 (@ tptp.butlast_nat (@ _let_1 Xs_175)))) (let ((_let_3 (= Xs_175 tptp.nil_nat))) (and (=> _let_3 (= _let_2 tptp.nil_nat)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_nat Xs_175))))))))))
% 0.51/0.76 (assert (forall ((Xs_174 tptp.list_A2115238852le_alt)) (= (= Xs_174 tptp.nil_Ar1286194111le_alt) (@ tptp.null_A1520965063le_alt Xs_174))))
% 0.51/0.76 (assert (forall ((Xs_174 tptp.list_nat)) (= (= Xs_174 tptp.nil_nat) (@ tptp.null_nat Xs_174))))
% 0.51/0.76 (assert (forall ((Xs_173 tptp.list_A2115238852le_alt)) (= (@ tptp.null_A1520965063le_alt Xs_173) (= Xs_173 tptp.nil_Ar1286194111le_alt))))
% 0.51/0.76 (assert (forall ((Xs_173 tptp.list_nat)) (= (@ tptp.null_nat Xs_173) (= Xs_173 tptp.nil_nat))))
% 0.51/0.76 (assert (@ tptp.null_A1520965063le_alt tptp.nil_Ar1286194111le_alt))
% 0.51/0.76 (assert (@ tptp.null_nat tptp.nil_nat))
% 0.51/0.76 (assert (forall ((X_109 tptp.arrow_475358991le_alt) (Xs_172 tptp.list_A2115238852le_alt)) (not (@ tptp.null_A1520965063le_alt (@ (@ tptp.cons_A228743023le_alt X_109) Xs_172)))))
% 0.51/0.76 (assert (forall ((Xs_171 tptp.list_A2115238852le_alt) (X_108 tptp.arrow_475358991le_alt)) (= (@ tptp.butlas274947851le_alt (@ (@ tptp.append179082452le_alt Xs_171) (@ (@ tptp.cons_A228743023le_alt X_108) tptp.nil_Ar1286194111le_alt))) Xs_171)))
% 0.51/0.76 (assert (forall ((Xs_171 tptp.list_nat) (X_108 tptp.nat)) (= (@ tptp.butlast_nat (@ (@ tptp.append_nat Xs_171) (@ (@ tptp.cons_nat X_108) tptp.nil_nat))) Xs_171)))
% 0.51/0.76 (assert (forall ((F_7 (-> tptp.nat tptp.list_A2115238852le_alt))) (= (@ (@ tptp.maps_n1127956422le_alt F_7) tptp.nil_nat) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.76 (assert (forall ((F_7 (-> tptp.arrow_475358991le_alt tptp.list_nat))) (= (@ (@ tptp.maps_A2124894076lt_nat F_7) tptp.nil_Ar1286194111le_alt) tptp.nil_nat)))
% 0.51/0.76 (assert (forall ((F_7 (-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt))) (= (@ (@ tptp.maps_A409156225le_alt F_7) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.76 (assert (forall ((X_107 tptp.nat)) (@ tptp.linorder_sorted_nat (@ (@ tptp.cons_nat X_107) tptp.nil_nat))))
% 0.51/0.76 (assert (@ tptp.linorder_sorted_nat tptp.nil_nat))
% 0.51/0.76 (assert (forall ((Xs_170 tptp.list_A2115238852le_alt) (Ys_52 tptp.list_A2115238852le_alt) (Zs_9 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Xs_170))) (= (@ (@ tptp.append179082452le_alt (@ _let_1 Ys_52)) Zs_9) (@ _let_1 (@ (@ tptp.append179082452le_alt Ys_52) Zs_9))))))
% 0.51/0.76 (assert (forall ((Xs_169 tptp.list_A2115238852le_alt) (Ys_51 tptp.list_A2115238852le_alt) (Zs_8 tptp.list_A2115238852le_alt) (Ts tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Xs_169) Ys_51) (@ (@ tptp.append179082452le_alt Zs_8) Ts)) (exists ((Us_1 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Us_1))) (or (and (= Xs_169 (@ (@ tptp.append179082452le_alt Zs_8) Us_1)) (= (@ _let_1 Ys_51) Ts)) (and (= (@ (@ tptp.append179082452le_alt Xs_169) Us_1) Zs_8) (= Ys_51 (@ _let_1 Ts)))))))))
% 0.51/0.76 (assert (forall ((Xs_168 tptp.list_A2115238852le_alt) (Ys_50 tptp.list_A2115238852le_alt) (Zs_7 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Xs_168))) (= (= (@ _let_1 Ys_50) (@ _let_1 Zs_7)) (= Ys_50 Zs_7)))))
% 0.51/0.76 (assert (forall ((Ys_49 tptp.list_A2115238852le_alt) (Xs_167 tptp.list_A2115238852le_alt) (Zs_6 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Ys_49) Xs_167) (@ (@ tptp.append179082452le_alt Zs_6) Xs_167)) (= Ys_49 Zs_6))))
% 0.51/0.76 (assert (forall ((Ys_48 tptp.list_A2115238852le_alt) (Us tptp.list_A2115238852le_alt) (Xs_166 tptp.list_A2115238852le_alt) (Xs1_1 tptp.list_A2115238852le_alt) (Zs_5 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Xs_166))) (=> (= (@ _let_1 Xs1_1) Zs_5) (=> (= Ys_48 (@ (@ tptp.append179082452le_alt Xs1_1) Us)) (= (@ _let_1 Ys_48) (@ (@ tptp.append179082452le_alt Zs_5) Us)))))))
% 0.51/0.76 (assert (forall ((F_6 (-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)) (X_106 tptp.arrow_475358991le_alt) (Xs_165 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.maps_A409156225le_alt F_6))) (= (@ _let_1 (@ (@ tptp.cons_A228743023le_alt X_106) Xs_165)) (@ (@ tptp.append179082452le_alt (@ F_6 X_106)) (@ _let_1 Xs_165))))))
% 0.51/0.76 (assert (forall ((X_105 tptp.arrow_475358991le_alt) (Xs_164 tptp.list_A2115238852le_alt) (Ys_47 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_105))) (= (@ (@ tptp.append179082452le_alt (@ _let_1 Xs_164)) Ys_47) (@ _let_1 (@ (@ tptp.append179082452le_alt Xs_164) Ys_47))))))
% 0.51/0.76 (assert (forall ((Xs_163 tptp.list_A2115238852le_alt) (Zs_4 tptp.list_A2115238852le_alt) (X_104 tptp.arrow_475358991le_alt) (Xs1 tptp.list_A2115238852le_alt) (Ys_46 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_104))) (=> (= (@ _let_1 Xs1) Ys_46) (=> (= Xs_163 (@ (@ tptp.append179082452le_alt Xs1) Zs_4)) (= (@ _let_1 Xs_163) (@ (@ tptp.append179082452le_alt Ys_46) Zs_4)))))))
% 0.51/0.76 (assert (forall ((Ys_45 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.append179082452le_alt tptp.nil_Ar1286194111le_alt) Ys_45) Ys_45)))
% 0.51/0.76 (assert (forall ((Ys_45 tptp.list_nat)) (= (@ (@ tptp.append_nat tptp.nil_nat) Ys_45) Ys_45)))
% 0.51/0.76 (assert (forall ((Xs_162 tptp.list_A2115238852le_alt) (Ys_44 tptp.list_A2115238852le_alt)) (= (= tptp.nil_Ar1286194111le_alt (@ (@ tptp.append179082452le_alt Xs_162) Ys_44)) (and (= Xs_162 tptp.nil_Ar1286194111le_alt) (= Ys_44 tptp.nil_Ar1286194111le_alt)))))
% 0.51/0.76 (assert (forall ((Xs_162 tptp.list_nat) (Ys_44 tptp.list_nat)) (= (= tptp.nil_nat (@ (@ tptp.append_nat Xs_162) Ys_44)) (and (= Xs_162 tptp.nil_nat) (= Ys_44 tptp.nil_nat)))))
% 0.51/0.76 (assert (forall ((Xs_161 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.append179082452le_alt Xs_161) tptp.nil_Ar1286194111le_alt) Xs_161)))
% 0.51/0.76 (assert (forall ((Xs_161 tptp.list_nat)) (= (@ (@ tptp.append_nat Xs_161) tptp.nil_nat) Xs_161)))
% 0.51/0.76 (assert (forall ((Xs_160 tptp.list_A2115238852le_alt) (Ys_43 tptp.list_A2115238852le_alt)) (= (= Xs_160 (@ (@ tptp.append179082452le_alt Xs_160) Ys_43)) (= Ys_43 tptp.nil_Ar1286194111le_alt))))
% 0.51/0.76 (assert (forall ((Xs_160 tptp.list_nat) (Ys_43 tptp.list_nat)) (= (= Xs_160 (@ (@ tptp.append_nat Xs_160) Ys_43)) (= Ys_43 tptp.nil_nat))))
% 0.51/0.76 (assert (forall ((Ys_42 tptp.list_A2115238852le_alt) (Xs_159 tptp.list_A2115238852le_alt)) (= (= Ys_42 (@ (@ tptp.append179082452le_alt Xs_159) Ys_42)) (= Xs_159 tptp.nil_Ar1286194111le_alt))))
% 0.51/0.76 (assert (forall ((Ys_42 tptp.list_nat) (Xs_159 tptp.list_nat)) (= (= Ys_42 (@ (@ tptp.append_nat Xs_159) Ys_42)) (= Xs_159 tptp.nil_nat))))
% 0.51/0.76 (assert (forall ((Xs_158 tptp.list_A2115238852le_alt) (Ys_41 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Xs_158) Ys_41) tptp.nil_Ar1286194111le_alt) (and (= Xs_158 tptp.nil_Ar1286194111le_alt) (= Ys_41 tptp.nil_Ar1286194111le_alt)))))
% 0.51/0.76 (assert (forall ((Xs_158 tptp.list_nat) (Ys_41 tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs_158) Ys_41) tptp.nil_nat) (and (= Xs_158 tptp.nil_nat) (= Ys_41 tptp.nil_nat)))))
% 0.51/0.76 (assert (forall ((Xs_157 tptp.list_A2115238852le_alt) (Ys_40 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Xs_157) Ys_40) Xs_157) (= Ys_40 tptp.nil_Ar1286194111le_alt))))
% 0.51/0.76 (assert (forall ((Xs_157 tptp.list_nat) (Ys_40 tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs_157) Ys_40) Xs_157) (= Ys_40 tptp.nil_nat))))
% 0.51/0.76 (assert (forall ((Xs_156 tptp.list_A2115238852le_alt) (Ys_39 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Xs_156) Ys_39) Ys_39) (= Xs_156 tptp.nil_Ar1286194111le_alt))))
% 0.51/0.76 (assert (forall ((Xs_156 tptp.list_nat) (Ys_39 tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs_156) Ys_39) Ys_39) (= Xs_156 tptp.nil_nat))))
% 0.51/0.76 (assert (forall ((Xs_155 tptp.list_A2115238852le_alt) (Ys_38 tptp.list_A2115238852le_alt)) (=> (= Xs_155 Ys_38) (= Xs_155 (@ (@ tptp.append179082452le_alt tptp.nil_Ar1286194111le_alt) Ys_38)))))
% 0.51/0.76 (assert (forall ((Xs_155 tptp.list_nat) (Ys_38 tptp.list_nat)) (=> (= Xs_155 Ys_38) (= Xs_155 (@ (@ tptp.append_nat tptp.nil_nat) Ys_38)))))
% 0.51/0.76 (assert (forall ((Ys_37 tptp.list_A2115238852le_alt) (Zs_3 tptp.list_A2115238852le_alt) (X_103 tptp.arrow_475358991le_alt) (Xs_154 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_103) Xs_154))) (= (= (@ (@ tptp.append179082452le_alt Ys_37) Zs_3) _let_1) (or (and (= Ys_37 tptp.nil_Ar1286194111le_alt) (= Zs_3 _let_1)) (exists ((Ys_36 tptp.list_A2115238852le_alt)) (and (= Ys_37 (@ (@ tptp.cons_A228743023le_alt X_103) Ys_36)) (= (@ (@ tptp.append179082452le_alt Ys_36) Zs_3) Xs_154))))))))
% 0.51/0.76 (assert (forall ((Ys_37 tptp.list_nat) (Zs_3 tptp.list_nat) (X_103 tptp.nat) (Xs_154 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X_103) Xs_154))) (= (= (@ (@ tptp.append_nat Ys_37) Zs_3) _let_1) (or (and (= Ys_37 tptp.nil_nat) (= Zs_3 _let_1)) (exists ((Ys_36 tptp.list_nat)) (and (= Ys_37 (@ (@ tptp.cons_nat X_103) Ys_36)) (= (@ (@ tptp.append_nat Ys_36) Zs_3) Xs_154))))))))
% 0.51/0.76 (assert (forall ((X_102 tptp.arrow_475358991le_alt) (Xs_153 tptp.list_A2115238852le_alt) (Ys_35 tptp.list_A2115238852le_alt) (Zs_2 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_102) Xs_153))) (= (= _let_1 (@ (@ tptp.append179082452le_alt Ys_35) Zs_2)) (or (and (= Ys_35 tptp.nil_Ar1286194111le_alt) (= _let_1 Zs_2)) (exists ((Ys_36 tptp.list_A2115238852le_alt)) (and (= (@ (@ tptp.cons_A228743023le_alt X_102) Ys_36) Ys_35) (= Xs_153 (@ (@ tptp.append179082452le_alt Ys_36) Zs_2)))))))))
% 0.51/0.76 (assert (forall ((X_102 tptp.nat) (Xs_153 tptp.list_nat) (Ys_35 tptp.list_nat) (Zs_2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X_102) Xs_153))) (= (= _let_1 (@ (@ tptp.append_nat Ys_35) Zs_2)) (or (and (= Ys_35 tptp.nil_nat) (= _let_1 Zs_2)) (exists ((Ys_36 tptp.list_nat)) (and (= (@ (@ tptp.cons_nat X_102) Ys_36) Ys_35) (= Xs_153 (@ (@ tptp.append_nat Ys_36) Zs_2)))))))))
% 0.51/0.76 (assert (forall ((Xs_152 tptp.list_A2115238852le_alt) (X_101 tptp.arrow_475358991le_alt) (Ys_34 tptp.list_A2115238852le_alt) (Y_42 tptp.arrow_475358991le_alt)) (= (= (@ (@ tptp.append179082452le_alt Xs_152) (@ (@ tptp.cons_A228743023le_alt X_101) tptp.nil_Ar1286194111le_alt)) (@ (@ tptp.append179082452le_alt Ys_34) (@ (@ tptp.cons_A228743023le_alt Y_42) tptp.nil_Ar1286194111le_alt))) (and (= Xs_152 Ys_34) (= X_101 Y_42)))))
% 0.51/0.76 (assert (forall ((Xs_152 tptp.list_nat) (X_101 tptp.nat) (Ys_34 tptp.list_nat) (Y_42 tptp.nat)) (= (= (@ (@ tptp.append_nat Xs_152) (@ (@ tptp.cons_nat X_101) tptp.nil_nat)) (@ (@ tptp.append_nat Ys_34) (@ (@ tptp.cons_nat Y_42) tptp.nil_nat))) (and (= Xs_152 Ys_34) (= X_101 Y_42)))))
% 0.51/0.76 (assert (forall ((Xs_151 tptp.list_A2115238852le_alt) (Ys_33 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Xs_151))) (let ((_let_2 (@ tptp.butlas274947851le_alt (@ _let_1 Ys_33)))) (let ((_let_3 (= Ys_33 tptp.nil_Ar1286194111le_alt))) (and (=> _let_3 (= _let_2 (@ tptp.butlas274947851le_alt Xs_151))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlas274947851le_alt Ys_33))))))))))
% 0.51/0.76 (assert (forall ((Xs_151 tptp.list_nat) (Ys_33 tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Xs_151))) (let ((_let_2 (@ tptp.butlast_nat (@ _let_1 Ys_33)))) (let ((_let_3 (= Ys_33 tptp.nil_nat))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_nat Xs_151))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_nat Ys_33))))))))))
% 0.51/0.76 (assert (forall ((Xs_150 tptp.list_nat)) (=> (not (= Xs_150 tptp.nil_nat)) (=> (@ tptp.linorder_sorted_nat Xs_150) (@ tptp.linorder_sorted_nat (@ tptp.butlast_nat Xs_150))))))
% 0.51/0.76 (assert (forall ((Xs_149 tptp.list_A2115238852le_alt) (P_32 (-> tptp.list_A2115238852le_alt Bool))) (=> (@ P_32 tptp.nil_Ar1286194111le_alt) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt)) (=> (@ P_32 Xs_54) (@ P_32 (@ (@ tptp.append179082452le_alt Xs_54) (@ (@ tptp.cons_A228743023le_alt X_1) tptp.nil_Ar1286194111le_alt))))) (@ P_32 Xs_149)))))
% 0.51/0.76 (assert (forall ((Xs_149 tptp.list_nat) (P_32 (-> tptp.list_nat Bool))) (=> (@ P_32 tptp.nil_nat) (=> (forall ((X_1 tptp.nat) (Xs_54 tptp.list_nat)) (=> (@ P_32 Xs_54) (@ P_32 (@ (@ tptp.append_nat Xs_54) (@ (@ tptp.cons_nat X_1) tptp.nil_nat))))) (@ P_32 Xs_149)))))
% 0.51/0.76 (assert (forall ((Xs_148 tptp.list_A2115238852le_alt)) (=> (not (= Xs_148 tptp.nil_Ar1286194111le_alt)) (not (forall ((Ys_5 tptp.list_A2115238852le_alt) (Y_3 tptp.arrow_475358991le_alt)) (not (= Xs_148 (@ (@ tptp.append179082452le_alt Ys_5) (@ (@ tptp.cons_A228743023le_alt Y_3) tptp.nil_Ar1286194111le_alt)))))))))
% 0.51/0.76 (assert (forall ((Xs_148 tptp.list_nat)) (=> (not (= Xs_148 tptp.nil_nat)) (not (forall ((Ys_5 tptp.list_nat) (Y_3 tptp.nat)) (not (= Xs_148 (@ (@ tptp.append_nat Ys_5) (@ (@ tptp.cons_nat Y_3) tptp.nil_nat)))))))))
% 0.51/0.76 (assert (forall ((Xs_147 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.equal_484611810le_alt Xs_147) tptp.nil_Ar1286194111le_alt) (@ tptp.null_A1520965063le_alt Xs_147))))
% 0.51/0.76 (assert (forall ((Xs_147 tptp.list_nat)) (= (@ (@ tptp.equal_equal_list_nat Xs_147) tptp.nil_nat) (@ tptp.null_nat Xs_147))))
% 0.51/0.76 (assert (forall ((Xs_146 tptp.list_A2115238852le_alt) (X_100 tptp.arrow_475358991le_alt) (Ys_32 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Xs_146) (@ (@ tptp.cons_A228743023le_alt X_100) tptp.nil_Ar1286194111le_alt)) Ys_32) (and (not (= Ys_32 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.butlas274947851le_alt Ys_32) Xs_146) (= (@ tptp.last_A1217315288le_alt Ys_32) X_100)))))
% 0.51/0.76 (assert (forall ((Xs_146 tptp.list_nat) (X_100 tptp.nat) (Ys_32 tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs_146) (@ (@ tptp.cons_nat X_100) tptp.nil_nat)) Ys_32) (and (not (= Ys_32 tptp.nil_nat)) (= (@ tptp.butlast_nat Ys_32) Xs_146) (= (@ tptp.last_nat Ys_32) X_100)))))
% 0.51/0.76 (assert (forall ((Xs_145 tptp.list_A2115238852le_alt)) (=> (not (= Xs_145 tptp.nil_Ar1286194111le_alt)) (= (@ (@ tptp.append179082452le_alt (@ tptp.butlas274947851le_alt Xs_145)) (@ (@ tptp.cons_A228743023le_alt (@ tptp.last_A1217315288le_alt Xs_145)) tptp.nil_Ar1286194111le_alt)) Xs_145))))
% 0.51/0.76 (assert (forall ((Xs_145 tptp.list_nat)) (=> (not (= Xs_145 tptp.nil_nat)) (= (@ (@ tptp.append_nat (@ tptp.butlast_nat Xs_145)) (@ (@ tptp.cons_nat (@ tptp.last_nat Xs_145)) tptp.nil_nat)) Xs_145))))
% 0.51/0.76 (assert (forall ((X_99 tptp.arrow_475358991le_alt) (Xs_144 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_99))) (and (= (@ tptp.rotate1_nat tptp.nil_nat) tptp.nil_nat) (= (@ tptp.rotate335349260le_alt (@ _let_1 Xs_144)) (@ (@ tptp.append179082452le_alt Xs_144) (@ _let_1 tptp.nil_Ar1286194111le_alt)))))))
% 0.51/0.76 (assert (forall ((X_99 tptp.arrow_475358991le_alt) (Xs_144 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_99))) (and (= (@ tptp.rotate335349260le_alt tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt) (= (@ tptp.rotate335349260le_alt (@ _let_1 Xs_144)) (@ (@ tptp.append179082452le_alt Xs_144) (@ _let_1 tptp.nil_Ar1286194111le_alt)))))))
% 0.51/0.76 (assert (forall ((X_99 tptp.nat) (Xs_144 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X_99))) (and (= (@ tptp.rotate335349260le_alt tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt) (= (@ tptp.rotate1_nat (@ _let_1 Xs_144)) (@ (@ tptp.append_nat Xs_144) (@ _let_1 tptp.nil_nat)))))))
% 0.51/0.76 (assert (forall ((Xs_143 tptp.list_A2115238852le_alt) (X_98 tptp.arrow_475358991le_alt)) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.append179082452le_alt Xs_143) (@ (@ tptp.cons_A228743023le_alt X_98) tptp.nil_Ar1286194111le_alt))) X_98)))
% 0.51/0.76 (assert (forall ((Xs_143 tptp.list_nat) (X_98 tptp.nat)) (= (@ tptp.last_nat (@ (@ tptp.append_nat Xs_143) (@ (@ tptp.cons_nat X_98) tptp.nil_nat))) X_98)))
% 0.51/0.76 (assert (forall ((Ws tptp.list_A2115238852le_alt)) (=> (not (@ tptp.distin236324274le_alt Ws)) (exists ((Xs_54 tptp.list_A2115238852le_alt) (Ys_5 tptp.list_A2115238852le_alt) (Zs_1 tptp.list_A2115238852le_alt) (Y_3 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt (@ (@ tptp.cons_A228743023le_alt Y_3) tptp.nil_Ar1286194111le_alt)))) (= Ws (@ (@ tptp.append179082452le_alt Xs_54) (@ _let_1 (@ (@ tptp.append179082452le_alt Ys_5) (@ _let_1 Zs_1))))))))))
% 0.51/0.76 (assert (forall ((Ws tptp.list_nat)) (=> (not (@ tptp.distinct_nat Ws)) (exists ((Xs_54 tptp.list_nat) (Ys_5 tptp.list_nat) (Zs_1 tptp.list_nat) (Y_3 tptp.nat)) (let ((_let_1 (@ tptp.append_nat (@ (@ tptp.cons_nat Y_3) tptp.nil_nat)))) (= Ws (@ (@ tptp.append_nat Xs_54) (@ _let_1 (@ (@ tptp.append_nat Ys_5) (@ _let_1 Zs_1))))))))))
% 0.51/0.76 (assert (forall ((I_28 tptp.nat) (X_97 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ (@ tptp.replic1511538809le_alt I_28) X_97))) (let ((_let_2 (@ tptp.cons_A228743023le_alt X_97))) (= (@ (@ tptp.append179082452le_alt _let_1) (@ _let_2 tptp.nil_Ar1286194111le_alt)) (@ _let_2 _let_1))))))
% 0.51/0.76 (assert (forall ((I_28 tptp.nat) (X_97 tptp.nat)) (let ((_let_1 (@ (@ tptp.replicate_nat I_28) X_97))) (let ((_let_2 (@ tptp.cons_nat X_97))) (= (@ (@ tptp.append_nat _let_1) (@ _let_2 tptp.nil_nat)) (@ _let_2 _let_1))))))
% 0.51/0.76 (assert (forall ((X_96 tptp.arrow_475358991le_alt) (Xs_142 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_96))) (= (@ tptp.rev_Ar1106406943le_alt (@ _let_1 Xs_142)) (@ (@ tptp.append179082452le_alt (@ tptp.rev_Ar1106406943le_alt Xs_142)) (@ _let_1 tptp.nil_Ar1286194111le_alt))))))
% 0.51/0.76 (assert (forall ((X_96 tptp.nat) (Xs_142 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X_96))) (= (@ tptp.rev_nat (@ _let_1 Xs_142)) (@ (@ tptp.append_nat (@ tptp.rev_nat Xs_142)) (@ _let_1 tptp.nil_nat))))))
% 0.51/0.76 (assert (forall ((Xs_141 tptp.list_nat) (Ys_31 tptp.list_nat)) (= (= (@ tptp.rev_nat Xs_141) (@ tptp.rev_nat Ys_31)) (= Xs_141 Ys_31))))
% 0.51/0.76 (assert (forall ((Xs_141 tptp.list_A2115238852le_alt) (Ys_31 tptp.list_A2115238852le_alt)) (= (= (@ tptp.rev_Ar1106406943le_alt Xs_141) (@ tptp.rev_Ar1106406943le_alt Ys_31)) (= Xs_141 Ys_31))))
% 0.51/0.76 (assert (forall ((Xs_140 tptp.list_nat) (Ys_30 tptp.list_nat)) (= (= (@ tptp.rev_nat Xs_140) Ys_30) (= Xs_140 (@ tptp.rev_nat Ys_30)))))
% 0.51/0.76 (assert (forall ((Xs_140 tptp.list_A2115238852le_alt) (Ys_30 tptp.list_A2115238852le_alt)) (= (= (@ tptp.rev_Ar1106406943le_alt Xs_140) Ys_30) (= Xs_140 (@ tptp.rev_Ar1106406943le_alt Ys_30)))))
% 0.51/0.76 (assert (forall ((N_53 tptp.nat) (X_95 tptp.nat)) (let ((_let_1 (@ (@ tptp.replicate_nat N_53) X_95))) (= (@ tptp.rev_nat _let_1) _let_1))))
% 0.51/0.76 (assert (forall ((N_53 tptp.nat) (X_95 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ (@ tptp.replic1511538809le_alt N_53) X_95))) (= (@ tptp.rev_Ar1106406943le_alt _let_1) _let_1))))
% 0.51/0.76 (assert (forall ((Xs_139 tptp.list_nat)) (= (@ tptp.rev_nat (@ tptp.rev_nat Xs_139)) Xs_139)))
% 0.51/0.76 (assert (forall ((Xs_139 tptp.list_A2115238852le_alt)) (= (@ tptp.rev_Ar1106406943le_alt (@ tptp.rev_Ar1106406943le_alt Xs_139)) Xs_139)))
% 0.51/0.76 (assert (forall ((X_94 tptp.list_A2115238852le_alt) (Y_41 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.equal_484611810le_alt X_94) Y_41) (= X_94 Y_41))))
% 0.51/0.76 (assert (forall ((Xs_138 tptp.list_A2115238852le_alt)) (= (= (@ tptp.rev_Ar1106406943le_alt Xs_138) tptp.nil_Ar1286194111le_alt) (= Xs_138 tptp.nil_Ar1286194111le_alt))))
% 0.51/0.76 (assert (forall ((Xs_138 tptp.list_nat)) (= (= (@ tptp.rev_nat Xs_138) tptp.nil_nat) (= Xs_138 tptp.nil_nat))))
% 0.51/0.76 (assert (forall ((Xs_137 tptp.list_A2115238852le_alt)) (= (= tptp.nil_Ar1286194111le_alt (@ tptp.rev_Ar1106406943le_alt Xs_137)) (= Xs_137 tptp.nil_Ar1286194111le_alt))))
% 0.51/0.76 (assert (forall ((Xs_137 tptp.list_nat)) (= (= tptp.nil_nat (@ tptp.rev_nat Xs_137)) (= Xs_137 tptp.nil_nat))))
% 0.51/0.76 (assert (= (@ tptp.rev_Ar1106406943le_alt tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt))
% 0.51/0.76 (assert (= (@ tptp.rev_nat tptp.nil_nat) tptp.nil_nat))
% 0.51/0.76 (assert (forall ((Xs_136 tptp.list_nat) (Ys_29 tptp.list_nat)) (= (@ tptp.rev_nat (@ (@ tptp.append_nat Xs_136) Ys_29)) (@ (@ tptp.append_nat (@ tptp.rev_nat Ys_29)) (@ tptp.rev_nat Xs_136)))))
% 0.51/0.76 (assert (forall ((Xs_136 tptp.list_A2115238852le_alt) (Ys_29 tptp.list_A2115238852le_alt)) (= (@ tptp.rev_Ar1106406943le_alt (@ (@ tptp.append179082452le_alt Xs_136) Ys_29)) (@ (@ tptp.append179082452le_alt (@ tptp.rev_Ar1106406943le_alt Ys_29)) (@ tptp.rev_Ar1106406943le_alt Xs_136)))))
% 0.51/0.76 (assert (forall ((Xs_135 tptp.list_A2115238852le_alt)) (= (@ tptp.distin236324274le_alt (@ tptp.rev_Ar1106406943le_alt Xs_135)) (@ tptp.distin236324274le_alt Xs_135))))
% 0.51/0.76 (assert (forall ((Xs_135 tptp.list_nat)) (= (@ tptp.distinct_nat (@ tptp.rev_nat Xs_135)) (@ tptp.distinct_nat Xs_135))))
% 0.51/0.76 (assert (forall ((N_52 tptp.nat) (X_93 tptp.arrow_475358991le_alt) (K_8 tptp.nat)) (let ((_let_1 (@ (@ tptp.replic1511538809le_alt N_52) X_93))) (let ((_let_2 (@ (@ tptp.replic1511538809le_alt K_8) X_93))) (= (@ (@ tptp.append179082452le_alt _let_1) _let_2) (@ (@ tptp.append179082452le_alt _let_2) _let_1))))))
% 0.51/0.76 (assert (forall ((Xs_134 tptp.list_A2115238852le_alt)) (= (= (@ tptp.rotate335349260le_alt Xs_134) tptp.nil_Ar1286194111le_alt) (= Xs_134 tptp.nil_Ar1286194111le_alt))))
% 0.51/0.76 (assert (forall ((Xs_134 tptp.list_nat)) (= (= (@ tptp.rotate1_nat Xs_134) tptp.nil_nat) (= Xs_134 tptp.nil_nat))))
% 0.51/0.76 (assert (forall ((X_92 tptp.nat) (A_87 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat X_92) A_87) (@ A_87 X_92))))
% 0.51/0.76 (assert (forall ((X_92 tptp.int) (A_87 (-> tptp.int Bool))) (= (@ (@ tptp.member_int X_92) A_87) (@ A_87 X_92))))
% 0.51/0.76 (assert (forall ((P_31 (-> tptp.nat Bool))) (= (@ tptp.collect_nat P_31) P_31)))
% 0.51/0.76 (assert (forall ((Xs_133 tptp.list_A2115238852le_alt)) (= (@ tptp.distin236324274le_alt (@ tptp.rotate335349260le_alt Xs_133)) (@ tptp.distin236324274le_alt Xs_133))))
% 0.51/0.76 (assert (forall ((X_91 tptp.arrow_475358991le_alt) (Xs_132 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_91) tptp.nil_Ar1286194111le_alt))) (= (= _let_1 (@ tptp.rev_Ar1106406943le_alt Xs_132)) (= Xs_132 _let_1)))))
% 0.51/0.76 (assert (forall ((X_91 tptp.nat) (Xs_132 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X_91) tptp.nil_nat))) (= (= _let_1 (@ tptp.rev_nat Xs_132)) (= Xs_132 _let_1)))))
% 0.51/0.76 (assert (forall ((Xs_131 tptp.list_A2115238852le_alt) (X_90 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_90) tptp.nil_Ar1286194111le_alt))) (= (= (@ tptp.rev_Ar1106406943le_alt Xs_131) _let_1) (= Xs_131 _let_1)))))
% 0.51/0.76 (assert (forall ((Xs_131 tptp.list_nat) (X_90 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat X_90) tptp.nil_nat))) (= (= (@ tptp.rev_nat Xs_131) _let_1) (= Xs_131 _let_1)))))
% 0.51/0.76 (assert (forall ((N_51 tptp.nat) (X_89 tptp.arrow_475358991le_alt) (Xs_130 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt (@ (@ tptp.replic1511538809le_alt N_51) X_89)))) (let ((_let_2 (@ tptp.cons_A228743023le_alt X_89))) (= (@ _let_1 (@ _let_2 Xs_130)) (@ _let_2 (@ _let_1 Xs_130)))))))
% 0.51/0.76 (assert (forall ((X_88 tptp.arrow_475358991le_alt) (Xs_129 tptp.list_A2115238852le_alt)) (=> (= Xs_129 tptp.nil_Ar1286194111le_alt) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.cons_A228743023le_alt X_88) Xs_129)) X_88))))
% 0.51/0.76 (assert (forall ((X_88 tptp.nat) (Xs_129 tptp.list_nat)) (=> (= Xs_129 tptp.nil_nat) (= (@ tptp.last_nat (@ (@ tptp.cons_nat X_88) Xs_129)) X_88))))
% 0.51/0.76 (assert (forall ((X_87 tptp.arrow_475358991le_alt) (Xs_128 tptp.list_A2115238852le_alt)) (=> (not (= Xs_128 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.cons_A228743023le_alt X_87) Xs_128)) (@ tptp.last_A1217315288le_alt Xs_128)))))
% 0.51/0.76 (assert (forall ((X_87 tptp.nat) (Xs_128 tptp.list_nat)) (=> (not (= Xs_128 tptp.nil_nat)) (= (@ tptp.last_nat (@ (@ tptp.cons_nat X_87) Xs_128)) (@ tptp.last_nat Xs_128)))))
% 0.51/0.76 (assert (forall ((X_86 tptp.arrow_475358991le_alt) (Xs_127 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.last_A1217315288le_alt (@ (@ tptp.cons_A228743023le_alt X_86) Xs_127)))) (let ((_let_2 (= Xs_127 tptp.nil_Ar1286194111le_alt))) (and (=> _let_2 (= _let_1 X_86)) (=> (not _let_2) (= _let_1 (@ tptp.last_A1217315288le_alt Xs_127))))))))
% 0.51/0.76 (assert (forall ((X_86 tptp.nat) (Xs_127 tptp.list_nat)) (let ((_let_1 (@ tptp.last_nat (@ (@ tptp.cons_nat X_86) Xs_127)))) (let ((_let_2 (= Xs_127 tptp.nil_nat))) (and (=> _let_2 (= _let_1 X_86)) (=> (not _let_2) (= _let_1 (@ tptp.last_nat Xs_127))))))))
% 0.51/0.76 (assert (forall ((Xs_126 tptp.list_A2115238852le_alt) (Ys_28 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.last_A1217315288le_alt (@ (@ tptp.append179082452le_alt Xs_126) Ys_28)))) (let ((_let_2 (= Ys_28 tptp.nil_Ar1286194111le_alt))) (and (=> _let_2 (= _let_1 (@ tptp.last_A1217315288le_alt Xs_126))) (=> (not _let_2) (= _let_1 (@ tptp.last_A1217315288le_alt Ys_28))))))))
% 0.51/0.76 (assert (forall ((Xs_126 tptp.list_nat) (Ys_28 tptp.list_nat)) (let ((_let_1 (@ tptp.last_nat (@ (@ tptp.append_nat Xs_126) Ys_28)))) (let ((_let_2 (= Ys_28 tptp.nil_nat))) (and (=> _let_2 (= _let_1 (@ tptp.last_nat Xs_126))) (=> (not _let_2) (= _let_1 (@ tptp.last_nat Ys_28))))))))
% 0.51/0.77 (assert (forall ((Xs_125 tptp.list_A2115238852le_alt) (Ys_27 tptp.list_A2115238852le_alt)) (=> (not (= Ys_27 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.append179082452le_alt Xs_125) Ys_27)) (@ tptp.last_A1217315288le_alt Ys_27)))))
% 0.51/0.77 (assert (forall ((Xs_125 tptp.list_nat) (Ys_27 tptp.list_nat)) (=> (not (= Ys_27 tptp.nil_nat)) (= (@ tptp.last_nat (@ (@ tptp.append_nat Xs_125) Ys_27)) (@ tptp.last_nat Ys_27)))))
% 0.51/0.77 (assert (forall ((Xs_124 tptp.list_A2115238852le_alt) (Ys_26 tptp.list_A2115238852le_alt)) (=> (= Ys_26 tptp.nil_Ar1286194111le_alt) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.append179082452le_alt Xs_124) Ys_26)) (@ tptp.last_A1217315288le_alt Xs_124)))))
% 0.51/0.77 (assert (forall ((Xs_124 tptp.list_nat) (Ys_26 tptp.list_nat)) (=> (= Ys_26 tptp.nil_nat) (= (@ tptp.last_nat (@ (@ tptp.append_nat Xs_124) Ys_26)) (@ tptp.last_nat Xs_124)))))
% 0.51/0.77 (assert (forall ((Xs_123 tptp.list_A2115238852le_alt) (Y_40 tptp.arrow_475358991le_alt) (Ys_25 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt Y_40))) (= (= (@ tptp.rev_Ar1106406943le_alt Xs_123) (@ _let_1 Ys_25)) (= Xs_123 (@ (@ tptp.append179082452le_alt (@ tptp.rev_Ar1106406943le_alt Ys_25)) (@ _let_1 tptp.nil_Ar1286194111le_alt)))))))
% 0.51/0.77 (assert (forall ((Xs_123 tptp.list_nat) (Y_40 tptp.nat) (Ys_25 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat Y_40))) (= (= (@ tptp.rev_nat Xs_123) (@ _let_1 Ys_25)) (= Xs_123 (@ (@ tptp.append_nat (@ tptp.rev_nat Ys_25)) (@ _let_1 tptp.nil_nat)))))))
% 0.51/0.77 (assert (forall ((Xs_122 tptp.list_A2115238852le_alt)) (=> (not (= Xs_122 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.last_A1217315288le_alt (@ tptp.rev_Ar1106406943le_alt Xs_122)) (@ tptp.hd_Arr1965683346le_alt Xs_122)))))
% 0.51/0.77 (assert (forall ((Xs_122 tptp.list_nat)) (=> (not (= Xs_122 tptp.nil_nat)) (= (@ tptp.last_nat (@ tptp.rev_nat Xs_122)) (@ tptp.hd_nat Xs_122)))))
% 0.51/0.77 (assert (forall ((Xs_121 tptp.list_A2115238852le_alt)) (=> (not (= Xs_121 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.hd_Arr1965683346le_alt (@ tptp.rev_Ar1106406943le_alt Xs_121)) (@ tptp.last_A1217315288le_alt Xs_121)))))
% 0.51/0.77 (assert (forall ((Xs_121 tptp.list_nat)) (=> (not (= Xs_121 tptp.nil_nat)) (= (@ tptp.hd_nat (@ tptp.rev_nat Xs_121)) (@ tptp.last_nat Xs_121)))))
% 0.51/0.77 (assert (= tptp.equal_484611810le_alt tptp.fequal781288069le_alt))
% 0.51/0.77 (assert (forall ((X_85 tptp.list_A2115238852le_alt)) (@ (@ tptp.equal_484611810le_alt X_85) X_85)))
% 0.51/0.77 (assert (forall ((X_84 tptp.list_A2115238852le_alt) (Y_39 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.equal_484611810le_alt X_84) Y_39) (= X_84 Y_39))))
% 0.51/0.77 (assert (= tptp.fequal781288069le_alt tptp.equal_484611810le_alt))
% 0.51/0.77 (assert (forall ((Ys_24 tptp.list_A2115238852le_alt) (Xs_120 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.append179082452le_alt Xs_120) Ys_24)))) (let ((_let_2 (= Xs_120 tptp.nil_Ar1286194111le_alt))) (and (=> _let_2 (= _let_1 (@ tptp.hd_Arr1965683346le_alt Ys_24))) (=> (not _let_2) (= _let_1 (@ tptp.hd_Arr1965683346le_alt Xs_120))))))))
% 0.51/0.77 (assert (forall ((Ys_24 tptp.list_nat) (Xs_120 tptp.list_nat)) (let ((_let_1 (@ tptp.hd_nat (@ (@ tptp.append_nat Xs_120) Ys_24)))) (let ((_let_2 (= Xs_120 tptp.nil_nat))) (and (=> _let_2 (= _let_1 (@ tptp.hd_nat Ys_24))) (=> (not _let_2) (= _let_1 (@ tptp.hd_nat Xs_120))))))))
% 0.51/0.77 (assert (forall ((Ys_23 tptp.list_A2115238852le_alt) (Xs_119 tptp.list_A2115238852le_alt)) (=> (not (= Xs_119 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.append179082452le_alt Xs_119) Ys_23)) (@ tptp.hd_Arr1965683346le_alt Xs_119)))))
% 0.51/0.77 (assert (forall ((Ys_23 tptp.list_nat) (Xs_119 tptp.list_nat)) (=> (not (= Xs_119 tptp.nil_nat)) (= (@ tptp.hd_nat (@ (@ tptp.append_nat Xs_119) Ys_23)) (@ tptp.hd_nat Xs_119)))))
% 0.51/0.77 (assert (forall ((Xs_118 tptp.list_A2115238852le_alt)) (=> (not (= Xs_118 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.rotate335349260le_alt Xs_118) (@ (@ tptp.append179082452le_alt (@ tptp.tl_Arr465451158le_alt Xs_118)) (@ (@ tptp.cons_A228743023le_alt (@ tptp.hd_Arr1965683346le_alt Xs_118)) tptp.nil_Ar1286194111le_alt))))))
% 0.51/0.77 (assert (forall ((Xs_118 tptp.list_nat)) (=> (not (= Xs_118 tptp.nil_nat)) (= (@ tptp.rotate1_nat Xs_118) (@ (@ tptp.append_nat (@ tptp.tl_nat Xs_118)) (@ (@ tptp.cons_nat (@ tptp.hd_nat Xs_118)) tptp.nil_nat))))))
% 0.51/0.77 (assert (forall ((X_83 tptp.arrow_475358991le_alt) (Xs_117 tptp.list_A2115238852le_alt)) (= (@ tptp.tl_Arr465451158le_alt (@ (@ tptp.cons_A228743023le_alt X_83) Xs_117)) Xs_117)))
% 0.51/0.77 (assert (= (@ tptp.tl_Arr465451158le_alt tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt))
% 0.51/0.77 (assert (= (@ tptp.tl_nat tptp.nil_nat) tptp.nil_nat))
% 0.51/0.77 (assert (forall ((X_82 tptp.arrow_475358991le_alt) (Xs_116 tptp.list_A2115238852le_alt)) (= (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.cons_A228743023le_alt X_82) Xs_116)) X_82)))
% 0.51/0.77 (assert (forall ((Xs_115 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_115) (@ tptp.distin236324274le_alt (@ tptp.tl_Arr465451158le_alt Xs_115)))))
% 0.51/0.77 (assert (forall ((Xs_114 tptp.list_nat)) (=> (@ tptp.linorder_sorted_nat Xs_114) (@ tptp.linorder_sorted_nat (@ tptp.tl_nat Xs_114)))))
% 0.51/0.77 (assert (forall ((Ys_22 tptp.list_A2115238852le_alt) (Xs_113 tptp.list_A2115238852le_alt)) (=> (not (= Xs_113 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.tl_Arr465451158le_alt (@ (@ tptp.append179082452le_alt Xs_113) Ys_22)) (@ (@ tptp.append179082452le_alt (@ tptp.tl_Arr465451158le_alt Xs_113)) Ys_22)))))
% 0.51/0.77 (assert (forall ((Ys_22 tptp.list_nat) (Xs_113 tptp.list_nat)) (=> (not (= Xs_113 tptp.nil_nat)) (= (@ tptp.tl_nat (@ (@ tptp.append_nat Xs_113) Ys_22)) (@ (@ tptp.append_nat (@ tptp.tl_nat Xs_113)) Ys_22)))))
% 0.51/0.77 (assert (forall ((P_30 (-> tptp.arrow_475358991le_alt Bool)) (Xs_112 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.dropWh1316781920le_alt P_30) Xs_112))) (=> (not (= _let_1 tptp.nil_Ar1286194111le_alt)) (not (@ P_30 (@ tptp.hd_Arr1965683346le_alt _let_1)))))))
% 0.51/0.77 (assert (forall ((P_30 (-> tptp.nat Bool)) (Xs_112 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.dropWhile_nat P_30) Xs_112))) (=> (not (= _let_1 tptp.nil_nat)) (not (@ P_30 (@ tptp.hd_nat _let_1)))))))
% 0.51/0.77 (assert (forall ((Y_38 tptp.arrow_475358991le_alt)) (not (@ (@ tptp.member1504968148le_alt tptp.nil_Ar1286194111le_alt) Y_38))))
% 0.51/0.77 (assert (forall ((Y_38 tptp.nat)) (not (@ (@ tptp.member_nat_1 tptp.nil_nat) Y_38))))
% 0.51/0.77 (assert (forall ((P_29 (-> tptp.arrow_475358991le_alt Bool))) (not (@ (@ tptp.list_e239244930le_alt P_29) tptp.nil_Ar1286194111le_alt))))
% 0.51/0.77 (assert (forall ((P_29 (-> tptp.nat Bool))) (not (@ (@ tptp.list_ex1_nat P_29) tptp.nil_nat))))
% 0.51/0.77 (assert (forall ((X_81 tptp.arrow_475358991le_alt) (Xs_111 tptp.list_A2115238852le_alt)) (@ (@ tptp.listMe78047147le_alt X_81) (@ (@ tptp.cons_A228743023le_alt X_81) Xs_111))))
% 0.51/0.77 (assert (forall ((X_80 tptp.arrow_475358991le_alt) (Xs_110 tptp.list_A2115238852le_alt) (Y_37 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.member1504968148le_alt (@ (@ tptp.cons_A228743023le_alt X_80) Xs_110)) Y_37) (or (= X_80 Y_37) (@ (@ tptp.member1504968148le_alt Xs_110) Y_37)))))
% 0.51/0.77 (assert (forall ((Y_36 tptp.arrow_475358991le_alt) (X_79 tptp.arrow_475358991le_alt) (Xs_109 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.listMe78047147le_alt X_79))) (=> (@ _let_1 Xs_109) (@ _let_1 (@ (@ tptp.cons_A228743023le_alt Y_36) Xs_109))))))
% 0.51/0.77 (assert (forall ((X_78 tptp.arrow_475358991le_alt) (N_50 tptp.nat)) (=> (not (= N_50 tptp.zero_zero_nat)) (= (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.replic1511538809le_alt N_50) X_78)) X_78))))
% 0.51/0.77 (assert (forall ((X_77 tptp.arrow_475358991le_alt) (N_49 tptp.nat)) (=> (not (= N_49 tptp.zero_zero_nat)) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.replic1511538809le_alt N_49) X_77)) X_77))))
% 0.51/0.77 (assert (forall ((M_5 tptp.nat) (X_76 tptp.arrow_475358991le_alt) (N_48 tptp.nat) (Y_35 tptp.arrow_475358991le_alt)) (= (= (@ (@ tptp.replic1511538809le_alt M_5) X_76) (@ (@ tptp.replic1511538809le_alt N_48) Y_35)) (and (= M_5 N_48) (=> (not (= M_5 tptp.zero_zero_nat)) (= X_76 Y_35))))))
% 0.51/0.77 (assert (forall ((Xs_108 tptp.list_A2115238852le_alt) (P_28 (-> tptp.arrow_475358991le_alt Bool)) (X_75 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_75) Xs_108))) (let ((_let_2 (@ tptp.dropWh1316781920le_alt P_28))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ P_28 X_75))) (and (=> _let_4 (= _let_3 (@ _let_2 Xs_108))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 0.51/0.77 (assert (forall ((P_27 (-> tptp.arrow_475358991le_alt Bool))) (= (@ (@ tptp.dropWh1316781920le_alt P_27) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((P_27 (-> tptp.nat Bool))) (= (@ (@ tptp.dropWhile_nat P_27) tptp.nil_nat) tptp.nil_nat)))
% 0.51/0.77 (assert (forall ((P_26 (-> tptp.arrow_475358991le_alt Bool)) (Xs_107 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_107) (@ tptp.distin236324274le_alt (@ (@ tptp.dropWh1316781920le_alt P_26) Xs_107)))))
% 0.51/0.77 (assert (forall ((P_25 (-> tptp.nat Bool)) (Xs_106 tptp.list_nat)) (=> (@ tptp.linorder_sorted_nat Xs_106) (@ tptp.linorder_sorted_nat (@ (@ tptp.dropWhile_nat P_25) Xs_106)))))
% 0.51/0.77 (assert (forall ((X_74 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.replic1511538809le_alt tptp.zero_zero_nat) X_74) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((X_74 tptp.nat)) (= (@ (@ tptp.replicate_nat tptp.zero_zero_nat) X_74) tptp.nil_nat)))
% 0.51/0.77 (assert (forall ((N_47 tptp.nat) (X_73 tptp.arrow_475358991le_alt)) (= (= tptp.nil_Ar1286194111le_alt (@ (@ tptp.replic1511538809le_alt N_47) X_73)) (= N_47 tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((N_47 tptp.nat) (X_73 tptp.nat)) (= (= tptp.nil_nat (@ (@ tptp.replicate_nat N_47) X_73)) (= N_47 tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((N_46 tptp.nat) (X_72 tptp.arrow_475358991le_alt)) (= (= (@ (@ tptp.replic1511538809le_alt N_46) X_72) tptp.nil_Ar1286194111le_alt) (= N_46 tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((N_46 tptp.nat) (X_72 tptp.nat)) (= (= (@ (@ tptp.replicate_nat N_46) X_72) tptp.nil_nat) (= N_46 tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((X_71 tptp.arrow_475358991le_alt) (A_86 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_71) tptp.nil_Ar1286194111le_alt))) (let ((_let_2 (@ (@ tptp.sublis2047953604le_alt _let_1) A_86))) (let ((_let_3 (@ (@ tptp.member_nat tptp.zero_zero_nat) A_86))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_Ar1286194111le_alt))))))))
% 0.51/0.77 (assert (forall ((X_71 tptp.nat) (A_86 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.cons_nat X_71) tptp.nil_nat))) (let ((_let_2 (@ (@ tptp.sublist_nat _let_1) A_86))) (let ((_let_3 (@ (@ tptp.member_nat tptp.zero_zero_nat) A_86))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 0.51/0.77 (assert (forall ((P_24 (-> tptp.arrow_475358991le_alt Bool)) (Xs_105 tptp.list_A2115238852le_alt) (Y_34 tptp.arrow_475358991le_alt) (Ys_21 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt Y_34) Ys_21))) (= (= (@ (@ tptp.dropWh1316781920le_alt P_24) Xs_105) _let_1) (and (= Xs_105 (@ (@ tptp.append179082452le_alt (@ (@ tptp.takeWh1696291512le_alt P_24) Xs_105)) _let_1)) (not (@ P_24 Y_34)))))))
% 0.51/0.77 (assert (forall ((Fa_1 (-> tptp.arrow_475358991le_alt tptp.nat))) (= (@ (@ tptp.list_s250295873le_alt Fa_1) tptp.nil_Ar1286194111le_alt) tptp.zero_zero_nat)))
% 0.51/0.77 (assert (forall ((Fa_1 (-> tptp.nat tptp.nat))) (= (@ (@ tptp.list_size_nat Fa_1) tptp.nil_nat) tptp.zero_zero_nat)))
% 0.51/0.77 (assert (forall ((A1_1 tptp.arrow_475358991le_alt) (A2_1 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.listMe78047147le_alt A1_1) A2_1) (or (exists ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt)) (and (= A1_1 X_1) (= A2_1 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)))) (exists ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt) (Y_3 tptp.arrow_475358991le_alt)) (and (= A1_1 X_1) (= A2_1 (@ (@ tptp.cons_A228743023le_alt Y_3) Xs_54)) (@ (@ tptp.listMe78047147le_alt X_1) Xs_54)))))))
% 0.51/0.77 (assert (forall ((X_70 tptp.int)) (= (= tptp.zero_zero_int X_70) (= X_70 tptp.zero_zero_int))))
% 0.51/0.77 (assert (forall ((X_70 tptp.nat)) (= (= tptp.zero_zero_nat X_70) (= X_70 tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((Xs_104 tptp.list_nat)) (=> (not (= Xs_104 tptp.nil_nat)) (= (@ tptp.hd_nat Xs_104) (@ (@ tptp.nth_nat Xs_104) tptp.zero_zero_nat)))))
% 0.51/0.77 (assert (forall ((Xs_104 tptp.list_A2115238852le_alt)) (=> (not (= Xs_104 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.hd_Arr1965683346le_alt Xs_104) (@ (@ tptp.nth_Ar125878976le_alt Xs_104) tptp.zero_zero_nat)))))
% 0.51/0.77 (assert (forall ((P_23 (-> tptp.nat Bool))) (= (@ (@ tptp.takeWhile_nat P_23) tptp.nil_nat) tptp.nil_nat)))
% 0.51/0.77 (assert (forall ((P_23 (-> tptp.arrow_475358991le_alt Bool))) (= (@ (@ tptp.takeWh1696291512le_alt P_23) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((P_22 (-> tptp.arrow_475358991le_alt Bool)) (Xs_103 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_103) (@ tptp.distin236324274le_alt (@ (@ tptp.takeWh1696291512le_alt P_22) Xs_103)))))
% 0.51/0.77 (assert (forall ((P_21 (-> tptp.nat Bool)) (Xs_102 tptp.list_nat)) (=> (@ tptp.linorder_sorted_nat Xs_102) (@ tptp.linorder_sorted_nat (@ (@ tptp.takeWhile_nat P_21) Xs_102)))))
% 0.51/0.77 (assert (forall ((A_85 (-> tptp.nat Bool))) (= (@ (@ tptp.sublist_nat tptp.nil_nat) A_85) tptp.nil_nat)))
% 0.51/0.77 (assert (forall ((A_85 (-> tptp.nat Bool))) (= (@ (@ tptp.sublis2047953604le_alt tptp.nil_Ar1286194111le_alt) A_85) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((I_27 (-> tptp.nat Bool)) (Xs_101 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_101) (@ tptp.distin236324274le_alt (@ (@ tptp.sublis2047953604le_alt Xs_101) I_27)))))
% 0.51/0.77 (assert (forall ((X_69 tptp.nat) (Xs_100 tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X_69) Xs_100)) tptp.zero_zero_nat) X_69)))
% 0.51/0.77 (assert (forall ((X_69 tptp.arrow_475358991le_alt) (Xs_100 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_69) Xs_100)) tptp.zero_zero_nat) X_69)))
% 0.51/0.77 (assert (forall ((Xs_99 tptp.list_nat) (P_20 (-> tptp.nat Bool)) (X_68 tptp.nat)) (let ((_let_1 (@ tptp.cons_nat X_68))) (let ((_let_2 (@ tptp.takeWhile_nat P_20))) (let ((_let_3 (@ _let_2 (@ _let_1 Xs_99)))) (let ((_let_4 (@ P_20 X_68))) (and (=> _let_4 (= _let_3 (@ _let_1 (@ _let_2 Xs_99)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 0.51/0.77 (assert (forall ((Xs_99 tptp.list_A2115238852le_alt) (P_20 (-> tptp.arrow_475358991le_alt Bool)) (X_68 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_68))) (let ((_let_2 (@ tptp.takeWh1696291512le_alt P_20))) (let ((_let_3 (@ _let_2 (@ _let_1 Xs_99)))) (let ((_let_4 (@ P_20 X_68))) (and (=> _let_4 (= _let_3 (@ _let_1 (@ _let_2 Xs_99)))) (=> (not _let_4) (= _let_3 tptp.nil_Ar1286194111le_alt)))))))))
% 0.51/0.77 (assert (forall ((Xs_98 tptp.list_A2115238852le_alt) (L_1 tptp.list_A2115238852le_alt) (P_19 (-> tptp.arrow_475358991le_alt Bool)) (X_67 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.takeWh1696291512le_alt P_19))) (=> (not (@ P_19 X_67)) (= (@ _let_1 (@ (@ tptp.append179082452le_alt Xs_98) (@ (@ tptp.cons_A228743023le_alt X_67) L_1))) (@ _let_1 Xs_98))))))
% 0.51/0.77 (assert (forall ((P_18 (-> tptp.arrow_475358991le_alt Bool)) (Xs_97 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.append179082452le_alt (@ (@ tptp.takeWh1696291512le_alt P_18) Xs_97)) (@ (@ tptp.dropWh1316781920le_alt P_18) Xs_97)) Xs_97)))
% 0.51/0.77 (assert (forall ((Xs_96 tptp.list_nat) (X_66 tptp.nat) (Ys_20 tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.append_nat Xs_96) (@ (@ tptp.cons_nat X_66) Ys_20))) (@ tptp.size_size_list_nat Xs_96)) X_66)))
% 0.51/0.77 (assert (forall ((Xs_96 tptp.list_A2115238852le_alt) (X_66 tptp.arrow_475358991le_alt) (Ys_20 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.append179082452le_alt Xs_96) (@ (@ tptp.cons_A228743023le_alt X_66) Ys_20))) (@ tptp.size_s1858781230le_alt Xs_96)) X_66)))
% 0.51/0.77 (assert (forall ((Y_33 tptp.int) (Xs_95 tptp.list_int)) (let ((_let_1 (@ (@ (@ tptp.foldr_int_int tptp.ord_max_int) Xs_95) Y_33))) (let ((_let_2 (= Xs_95 tptp.nil_int))) (=> (@ tptp.linorder_sorted_int (@ tptp.rev_int Xs_95)) (and (=> _let_2 (= _let_1 Y_33)) (=> (not _let_2) (= _let_1 (@ (@ tptp.ord_max_int (@ (@ tptp.nth_int Xs_95) tptp.zero_zero_nat)) Y_33)))))))))
% 0.51/0.77 (assert (forall ((Y_33 tptp.nat) (Xs_95 tptp.list_nat)) (let ((_let_1 (@ (@ (@ tptp.foldr_nat_nat tptp.ord_max_nat) Xs_95) Y_33))) (let ((_let_2 (= Xs_95 tptp.nil_nat))) (=> (@ tptp.linorder_sorted_nat (@ tptp.rev_nat Xs_95)) (and (=> _let_2 (= _let_1 Y_33)) (=> (not _let_2) (= _let_1 (@ (@ tptp.ord_max_nat (@ (@ tptp.nth_nat Xs_95) tptp.zero_zero_nat)) Y_33)))))))))
% 0.51/0.77 (assert (forall ((Xs_94 tptp.list_A2115238852le_alt) (Ys_19 tptp.list_nat) (P_17 (-> tptp.list_A2115238852le_alt tptp.list_nat Bool))) (=> (@ (@ P_17 tptp.nil_Ar1286194111le_alt) tptp.nil_nat) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt)) (@ (@ P_17 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)) tptp.nil_nat)) (=> (forall ((Y_3 tptp.nat) (Ys_5 tptp.list_nat)) (@ (@ P_17 tptp.nil_Ar1286194111le_alt) (@ (@ tptp.cons_nat Y_3) Ys_5))) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt) (Y_3 tptp.nat) (Ys_5 tptp.list_nat)) (=> (@ (@ P_17 Xs_54) Ys_5) (@ (@ P_17 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)) (@ (@ tptp.cons_nat Y_3) Ys_5)))) (@ (@ P_17 Xs_94) Ys_19)))))))
% 0.51/0.77 (assert (forall ((Xs_94 tptp.list_nat) (Ys_19 tptp.list_A2115238852le_alt) (P_17 (-> tptp.list_nat tptp.list_A2115238852le_alt Bool))) (=> (@ (@ P_17 tptp.nil_nat) tptp.nil_Ar1286194111le_alt) (=> (forall ((X_1 tptp.nat) (Xs_54 tptp.list_nat)) (@ (@ P_17 (@ (@ tptp.cons_nat X_1) Xs_54)) tptp.nil_Ar1286194111le_alt)) (=> (forall ((Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (@ (@ P_17 tptp.nil_nat) (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5))) (=> (forall ((X_1 tptp.nat) (Xs_54 tptp.list_nat) (Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (=> (@ (@ P_17 Xs_54) Ys_5) (@ (@ P_17 (@ (@ tptp.cons_nat X_1) Xs_54)) (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5)))) (@ (@ P_17 Xs_94) Ys_19)))))))
% 0.51/0.77 (assert (forall ((F_5 (-> tptp.arrow_475358991le_alt tptp.option_nat))) (= (@ (@ tptp.map_fi312151301lt_nat F_5) tptp.nil_Ar1286194111le_alt) tptp.nil_nat)))
% 0.51/0.77 (assert (forall ((F_5 (-> tptp.nat tptp.option514678660le_alt))) (= (@ (@ tptp.map_fi1462697295le_alt F_5) tptp.nil_nat) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((R_2 (-> tptp.nat tptp.nat Bool))) (@ (@ (@ tptp.listrelp_nat R_2) tptp.nil_nat) tptp.nil_nat)))
% 0.51/0.77 (assert (forall ((R_2 (-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool))) (@ (@ (@ tptp.listre1213162009le_alt R_2) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((Xs_93 tptp.list_A2115238852le_alt) (Ys_18 tptp.list_A2115238852le_alt) (R_1 (-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool)) (X_65 tptp.arrow_475358991le_alt) (Y_32 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.listre1213162009le_alt R_1))) (=> (@ (@ R_1 X_65) Y_32) (=> (@ (@ _let_1 Xs_93) Ys_18) (@ (@ _let_1 (@ (@ tptp.cons_A228743023le_alt X_65) Xs_93)) (@ (@ tptp.cons_A228743023le_alt Y_32) Ys_18)))))))
% 0.51/0.77 (assert (forall ((Xs_92 tptp.list_nat)) (= (@ (@ tptp.sublist_nat Xs_92) tptp.bot_bot_nat_o) tptp.nil_nat)))
% 0.51/0.77 (assert (forall ((Xs_92 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.sublis2047953604le_alt Xs_92) tptp.bot_bot_nat_o) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((Xs_91 tptp.list_A2115238852le_alt) (Ys_17 tptp.list_A2115238852le_alt)) (=> (not (= (@ tptp.size_s1858781230le_alt Xs_91) (@ tptp.size_s1858781230le_alt Ys_17))) (not (= Xs_91 Ys_17)))))
% 0.51/0.77 (assert (forall ((Xs_90 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rev_nat Xs_90)) (@ tptp.size_size_list_nat Xs_90))))
% 0.51/0.77 (assert (forall ((Xs_90 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ tptp.rev_Ar1106406943le_alt Xs_90)) (@ tptp.size_s1858781230le_alt Xs_90))))
% 0.51/0.77 (assert (forall ((N_45 tptp.nat) (X_64 tptp.arrow_475358991le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ tptp.replic1511538809le_alt N_45) X_64)) N_45)))
% 0.51/0.77 (assert (forall ((Xs_89 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ tptp.rotate335349260le_alt Xs_89)) (@ tptp.size_s1858781230le_alt Xs_89))))
% 0.51/0.77 (assert (forall ((F_4 (-> tptp.nat tptp.nat tptp.nat)) (X_63 tptp.nat) (Xs_88 tptp.list_nat) (A_84 tptp.nat)) (let ((_let_1 (@ tptp.foldr_nat_nat F_4))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat X_63) Xs_88)) A_84) (@ (@ F_4 X_63) (@ (@ _let_1 Xs_88) A_84))))))
% 0.51/0.77 (assert (forall ((F_3 (-> tptp.nat tptp.nat tptp.nat)) (A_83 tptp.nat)) (= (@ (@ (@ tptp.foldr_nat_nat F_3) tptp.nil_nat) A_83) A_83)))
% 0.51/0.77 (assert (forall ((F_2 (-> tptp.nat tptp.nat tptp.nat)) (Xs_87 tptp.list_nat) (Ys_16 tptp.list_nat) (A_82 tptp.nat)) (let ((_let_1 (@ tptp.foldr_nat_nat F_2))) (= (@ (@ _let_1 (@ (@ tptp.append_nat Xs_87) Ys_16)) A_82) (@ (@ _let_1 Xs_87) (@ (@ _let_1 Ys_16) A_82))))))
% 0.51/0.77 (assert (forall ((Xs_86 tptp.list_nat)) (= (= (@ tptp.size_size_list_nat Xs_86) tptp.zero_zero_nat) (= Xs_86 tptp.nil_nat))))
% 0.51/0.77 (assert (forall ((Xs_86 tptp.list_A2115238852le_alt)) (= (= (@ tptp.size_s1858781230le_alt Xs_86) tptp.zero_zero_nat) (= Xs_86 tptp.nil_Ar1286194111le_alt))))
% 0.51/0.77 (assert (= (@ tptp.size_size_list_nat tptp.nil_nat) tptp.zero_zero_nat))
% 0.51/0.77 (assert (= (@ tptp.size_s1858781230le_alt tptp.nil_Ar1286194111le_alt) tptp.zero_zero_nat))
% 0.51/0.77 (assert (forall ((P_16 (-> tptp.list_A2115238852le_alt tptp.list_nat Bool)) (Xs_85 tptp.list_A2115238852le_alt) (Ys_15 tptp.list_nat)) (=> (= (@ tptp.size_s1858781230le_alt Xs_85) (@ tptp.size_size_list_nat Ys_15)) (=> (@ (@ P_16 tptp.nil_Ar1286194111le_alt) tptp.nil_nat) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt) (Y_3 tptp.nat) (Ys_5 tptp.list_nat)) (=> (= (@ tptp.size_s1858781230le_alt Xs_54) (@ tptp.size_size_list_nat Ys_5)) (=> (@ (@ P_16 Xs_54) Ys_5) (@ (@ P_16 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)) (@ (@ tptp.cons_nat Y_3) Ys_5))))) (@ (@ P_16 Xs_85) Ys_15))))))
% 0.51/0.77 (assert (forall ((P_16 (-> tptp.list_nat tptp.list_A2115238852le_alt Bool)) (Xs_85 tptp.list_nat) (Ys_15 tptp.list_A2115238852le_alt)) (=> (= (@ tptp.size_size_list_nat Xs_85) (@ tptp.size_s1858781230le_alt Ys_15)) (=> (@ (@ P_16 tptp.nil_nat) tptp.nil_Ar1286194111le_alt) (=> (forall ((X_1 tptp.nat) (Xs_54 tptp.list_nat) (Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (=> (= (@ tptp.size_size_list_nat Xs_54) (@ tptp.size_s1858781230le_alt Ys_5)) (=> (@ (@ P_16 Xs_54) Ys_5) (@ (@ P_16 (@ (@ tptp.cons_nat X_1) Xs_54)) (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5))))) (@ (@ P_16 Xs_85) Ys_15))))))
% 0.51/0.77 (assert (forall ((P_16 (-> tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt Bool)) (Xs_85 tptp.list_A2115238852le_alt) (Ys_15 tptp.list_A2115238852le_alt)) (=> (= (@ tptp.size_s1858781230le_alt Xs_85) (@ tptp.size_s1858781230le_alt Ys_15)) (=> (@ (@ P_16 tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt) (Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (=> (= (@ tptp.size_s1858781230le_alt Xs_54) (@ tptp.size_s1858781230le_alt Ys_5)) (=> (@ (@ P_16 Xs_54) Ys_5) (@ (@ P_16 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)) (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5))))) (@ (@ P_16 Xs_85) Ys_15))))))
% 0.51/0.77 (assert (forall ((A_81 tptp.int)) (not (@ (@ tptp.member_int A_81) tptp.bot_bot_int_o))))
% 0.51/0.77 (assert (forall ((A_81 tptp.nat)) (not (@ (@ tptp.member_nat A_81) tptp.bot_bot_nat_o))))
% 0.51/0.77 (assert (forall ((X_1 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_1) tptp.bot_bot_o)))
% 0.51/0.77 (assert (forall ((X_62 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_62) tptp.bot_bot_o)))
% 0.51/0.77 (assert (forall ((N_44 tptp.nat)) (exists ((Xs_54 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt Xs_54) N_44))))
% 0.51/0.77 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (A1 tptp.list_nat) (A2 tptp.list_nat)) (= (@ (@ (@ tptp.listrelp_nat R) A1) A2) (or (and (= A1 tptp.nil_nat) (= A2 tptp.nil_nat)) (exists ((X_1 tptp.nat) (Y_3 tptp.nat) (Xs_54 tptp.list_nat) (Ys_5 tptp.list_nat)) (and (= A1 (@ (@ tptp.cons_nat X_1) Xs_54)) (= A2 (@ (@ tptp.cons_nat Y_3) Ys_5)) (@ (@ R X_1) Y_3) (@ (@ (@ tptp.listrelp_nat R) Xs_54) Ys_5)))))))
% 0.51/0.77 (assert (forall ((R (-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool)) (A1 tptp.list_A2115238852le_alt) (A2 tptp.list_A2115238852le_alt)) (= (@ (@ (@ tptp.listre1213162009le_alt R) A1) A2) (or (and (= A1 tptp.nil_Ar1286194111le_alt) (= A2 tptp.nil_Ar1286194111le_alt)) (exists ((X_1 tptp.arrow_475358991le_alt) (Y_3 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (and (= A1 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)) (= A2 (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5)) (@ (@ R X_1) Y_3) (@ (@ (@ tptp.listre1213162009le_alt R) Xs_54) Ys_5)))))))
% 0.51/0.77 (assert (forall ((A_80 tptp.int) (A_79 (-> tptp.int Bool))) (=> (= A_79 tptp.bot_bot_int_o) (not (@ (@ tptp.member_int A_80) A_79)))))
% 0.51/0.77 (assert (forall ((A_80 tptp.nat) (A_79 (-> tptp.nat Bool))) (=> (= A_79 tptp.bot_bot_nat_o) (not (@ (@ tptp.member_nat A_80) A_79)))))
% 0.51/0.77 (assert (forall ((P_15 (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P_15) tptp.bot_bot_nat_o) (forall ((X_1 tptp.nat)) (not (@ P_15 X_1))))))
% 0.51/0.77 (assert (forall ((C_36 tptp.int)) (not (@ (@ tptp.member_int C_36) tptp.bot_bot_int_o))))
% 0.51/0.77 (assert (forall ((C_36 tptp.nat)) (not (@ (@ tptp.member_nat C_36) tptp.bot_bot_nat_o))))
% 0.51/0.77 (assert (forall ((P_14 (-> tptp.nat Bool))) (= (= tptp.bot_bot_nat_o (@ tptp.collect_nat P_14)) (forall ((X_1 tptp.nat)) (not (@ P_14 X_1))))))
% 0.51/0.77 (assert (forall ((A_78 (-> tptp.int Bool))) (= (exists ((X_1 tptp.int)) (@ (@ tptp.member_int X_1) A_78)) (not (= A_78 tptp.bot_bot_int_o)))))
% 0.51/0.77 (assert (forall ((A_78 (-> tptp.nat Bool))) (= (exists ((X_1 tptp.nat)) (@ (@ tptp.member_nat X_1) A_78)) (not (= A_78 tptp.bot_bot_nat_o)))))
% 0.51/0.77 (assert (forall ((A_77 (-> tptp.int Bool))) (= (forall ((X_1 tptp.int)) (not (@ (@ tptp.member_int X_1) A_77))) (= A_77 tptp.bot_bot_int_o))))
% 0.51/0.77 (assert (forall ((A_77 (-> tptp.nat Bool))) (= (forall ((X_1 tptp.nat)) (not (@ (@ tptp.member_nat X_1) A_77))) (= A_77 tptp.bot_bot_nat_o))))
% 0.51/0.77 (assert (= tptp.bot_bot_nat_o (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) false))))
% 0.51/0.77 (assert (forall ((A_76 (-> tptp.int Bool))) (=> (forall ((Y_3 tptp.int)) (not (@ (@ tptp.member_int Y_3) A_76))) (= A_76 tptp.bot_bot_int_o))))
% 0.51/0.77 (assert (forall ((A_76 (-> tptp.nat Bool))) (=> (forall ((Y_3 tptp.nat)) (not (@ (@ tptp.member_nat Y_3) A_76))) (= A_76 tptp.bot_bot_nat_o))))
% 0.51/0.77 (assert (= (@ tptp.linord810813188et_nat tptp.bot_bot_nat_o) tptp.nil_nat))
% 0.51/0.77 (assert (forall ((X_61 tptp.int) (Y_31 tptp.int) (Z_8 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int X_61))) (= (@ (@ tptp.ord_max_int (@ _let_1 Y_31)) Z_8) (@ _let_1 (@ (@ tptp.ord_max_int Y_31) Z_8))))))
% 0.51/0.77 (assert (forall ((X_61 tptp.nat) (Y_31 tptp.nat) (Z_8 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat X_61))) (= (@ (@ tptp.ord_max_nat (@ _let_1 Y_31)) Z_8) (@ _let_1 (@ (@ tptp.ord_max_nat Y_31) Z_8))))))
% 0.51/0.77 (assert (forall ((A_75 tptp.int) (B_47 tptp.int) (C_35 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A_75))) (= (@ (@ tptp.ord_max_int (@ _let_1 B_47)) C_35) (@ _let_1 (@ (@ tptp.ord_max_int B_47) C_35))))))
% 0.51/0.77 (assert (forall ((A_75 tptp.nat) (B_47 tptp.nat) (C_35 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A_75))) (= (@ (@ tptp.ord_max_nat (@ _let_1 B_47)) C_35) (@ _let_1 (@ (@ tptp.ord_max_nat B_47) C_35))))))
% 0.51/0.77 (assert (forall ((X_60 tptp.int) (Y_30 tptp.int) (Z_7 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int X_60))) (let ((_let_2 (@ tptp.ord_max_int Y_30))) (= (@ _let_1 (@ _let_2 Z_7)) (@ _let_2 (@ _let_1 Z_7)))))))
% 0.51/0.77 (assert (forall ((X_60 tptp.nat) (Y_30 tptp.nat) (Z_7 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat X_60))) (let ((_let_2 (@ tptp.ord_max_nat Y_30))) (= (@ _let_1 (@ _let_2 Z_7)) (@ _let_2 (@ _let_1 Z_7)))))))
% 0.51/0.77 (assert (forall ((B_46 tptp.int) (A_74 tptp.int) (C_34 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int B_46))) (let ((_let_2 (@ tptp.ord_max_int A_74))) (= (@ _let_1 (@ _let_2 C_34)) (@ _let_2 (@ _let_1 C_34)))))))
% 0.51/0.77 (assert (forall ((B_46 tptp.nat) (A_74 tptp.nat) (C_34 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat B_46))) (let ((_let_2 (@ tptp.ord_max_nat A_74))) (= (@ _let_1 (@ _let_2 C_34)) (@ _let_2 (@ _let_1 C_34)))))))
% 0.51/0.77 (assert (forall ((A_73 tptp.int)) (= (@ (@ tptp.ord_max_int A_73) A_73) A_73)))
% 0.51/0.77 (assert (forall ((A_73 tptp.nat)) (= (@ (@ tptp.ord_max_nat A_73) A_73) A_73)))
% 0.51/0.77 (assert (forall ((A_72 tptp.int) (B_45 tptp.int)) (= (@ (@ tptp.ord_max_int A_72) B_45) (@ (@ tptp.ord_max_int B_45) A_72))))
% 0.51/0.77 (assert (forall ((A_72 tptp.nat) (B_45 tptp.nat)) (= (@ (@ tptp.ord_max_nat A_72) B_45) (@ (@ tptp.ord_max_nat B_45) A_72))))
% 0.51/0.77 (assert (forall ((X_59 tptp.int) (Y_29 tptp.int)) (= (@ (@ tptp.ord_max_int X_59) Y_29) (@ (@ tptp.ord_max_int Y_29) X_59))))
% 0.51/0.77 (assert (forall ((X_59 tptp.nat) (Y_29 tptp.nat)) (= (@ (@ tptp.ord_max_nat X_59) Y_29) (@ (@ tptp.ord_max_nat Y_29) X_59))))
% 0.51/0.77 (assert (forall ((A_71 tptp.int) (B_44 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A_71))) (let ((_let_2 (@ _let_1 B_44))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.77 (assert (forall ((A_71 tptp.nat) (B_44 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A_71))) (let ((_let_2 (@ _let_1 B_44))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.77 (assert (forall ((X_58 tptp.int) (Y_28 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int X_58))) (let ((_let_2 (@ _let_1 Y_28))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.77 (assert (forall ((X_58 tptp.nat) (Y_28 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat X_58))) (let ((_let_2 (@ _let_1 Y_28))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.77 (assert (forall ((X_57 tptp.int)) (= (@ (@ tptp.ord_max_int X_57) X_57) X_57)))
% 0.51/0.77 (assert (forall ((X_57 tptp.nat)) (= (@ (@ tptp.ord_max_nat X_57) X_57) X_57)))
% 0.51/0.77 (assert (forall ((P_13 (-> tptp.arrow_475358991le_alt Bool)) (Xs_84 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.dropWh1316781920le_alt P_13) Xs_84) (@ (@ tptp.drop_A1346709759le_alt (@ tptp.size_s1858781230le_alt (@ (@ tptp.takeWh1696291512le_alt P_13) Xs_84))) Xs_84))))
% 0.51/0.77 (assert (forall ((P_12 (-> tptp.nat Bool)) (Xs_83 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat (@ (@ tptp.takeWhile_nat P_12) Xs_83)))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_nat Xs_83)) (not (@ P_12 (@ (@ tptp.nth_nat Xs_83) _let_1)))))))
% 0.51/0.77 (assert (forall ((P_12 (-> tptp.arrow_475358991le_alt Bool)) (Xs_83 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt (@ (@ tptp.takeWh1696291512le_alt P_12) Xs_83)))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_s1858781230le_alt Xs_83)) (not (@ P_12 (@ (@ tptp.nth_Ar125878976le_alt Xs_83) _let_1)))))))
% 0.51/0.77 (assert (forall ((J_7 tptp.nat) (P_11 (-> tptp.nat Bool)) (Xs_82 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.takeWhile_nat P_11) Xs_82))) (=> (@ (@ tptp.ord_less_nat J_7) (@ tptp.size_size_list_nat _let_1)) (= (@ (@ tptp.nth_nat _let_1) J_7) (@ (@ tptp.nth_nat Xs_82) J_7))))))
% 0.51/0.77 (assert (forall ((J_7 tptp.nat) (P_11 (-> tptp.arrow_475358991le_alt Bool)) (Xs_82 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.takeWh1696291512le_alt P_11) Xs_82))) (=> (@ (@ tptp.ord_less_nat J_7) (@ tptp.size_s1858781230le_alt _let_1)) (= (@ (@ tptp.nth_Ar125878976le_alt _let_1) J_7) (@ (@ tptp.nth_Ar125878976le_alt Xs_82) J_7))))))
% 0.51/0.77 (assert (forall ((Xs_81 tptp.list_A2115238852le_alt) (X_56 tptp.arrow_475358991le_alt) (Ys_14 tptp.list_A2115238852le_alt) (Y_27 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Xs_81))) (= (@ (@ (@ tptp.list_u62477863le_alt (@ _let_1 (@ (@ tptp.cons_A228743023le_alt X_56) Ys_14))) (@ tptp.size_s1858781230le_alt Xs_81)) Y_27) (@ _let_1 (@ (@ tptp.cons_A228743023le_alt Y_27) Ys_14))))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N_5) N_5)))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_5) tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((Xs_80 tptp.list_A2115238852le_alt) (I_26 tptp.nat) (X_55 tptp.arrow_475358991le_alt) (Y_26 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ (@ tptp.list_u62477863le_alt Xs_80) I_26))) (= (@ (@ (@ tptp.list_u62477863le_alt (@ _let_1 X_55)) I_26) Y_26) (@ _let_1 Y_26)))))
% 0.51/0.77 (assert (forall ((Xs_79 tptp.list_A2115238852le_alt) (X_54 tptp.arrow_475358991le_alt) (X_53 tptp.arrow_475358991le_alt) (I_25 tptp.nat) (I_24 tptp.nat)) (let ((_let_1 (@ tptp.list_u62477863le_alt Xs_79))) (=> (not (= I_25 I_24)) (= (@ (@ (@ tptp.list_u62477863le_alt (@ (@ _let_1 I_25) X_54)) I_24) X_53) (@ (@ (@ tptp.list_u62477863le_alt (@ (@ _let_1 I_24) X_53)) I_25) X_54))))))
% 0.51/0.77 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ (@ P N_5) M))) (=> (=> (@ (@ tptp.ord_less_nat M) N_5) _let_1) (=> (=> (= M N_5) _let_1) (=> (=> (@ (@ tptp.ord_less_nat N_5) M) _let_1) _let_1))))))
% 0.51/0.77 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N_5) M) (not (= M N_5)))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_5) N_5))))
% 0.51/0.77 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (not (= M N_5)) (or (@ (@ tptp.ord_less_nat M) N_5) (@ (@ tptp.ord_less_nat N_5) M)))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_5) N_5))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (=> (not (= N_5 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N_5) (not (= N_5 tptp.zero_zero_nat)))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_5) tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (= (not (= N_5 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_5) tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((X_52 tptp.int)) (not (@ (@ tptp.ord_less_int X_52) X_52))))
% 0.51/0.77 (assert (forall ((X_52 (-> tptp.nat Bool))) (not (@ (@ tptp.ord_less_nat_o X_52) X_52))))
% 0.51/0.77 (assert (forall ((X_52 tptp.nat)) (not (@ (@ tptp.ord_less_nat X_52) X_52))))
% 0.51/0.77 (assert (forall ((X_51 tptp.int) (Y_25 tptp.int)) (= (not (= X_51 Y_25)) (or (@ (@ tptp.ord_less_int X_51) Y_25) (@ (@ tptp.ord_less_int Y_25) X_51)))))
% 0.51/0.77 (assert (forall ((X_51 tptp.nat) (Y_25 tptp.nat)) (= (not (= X_51 Y_25)) (or (@ (@ tptp.ord_less_nat X_51) Y_25) (@ (@ tptp.ord_less_nat Y_25) X_51)))))
% 0.51/0.77 (assert (forall ((X_50 tptp.int) (Y_24 tptp.int)) (= (not (@ (@ tptp.ord_less_int X_50) Y_24)) (or (@ (@ tptp.ord_less_int Y_24) X_50) (= X_50 Y_24)))))
% 0.51/0.77 (assert (forall ((X_50 tptp.nat) (Y_24 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X_50) Y_24)) (or (@ (@ tptp.ord_less_nat Y_24) X_50) (= X_50 Y_24)))))
% 0.51/0.77 (assert (forall ((X_49 tptp.int) (Y_23 tptp.int)) (or (@ (@ tptp.ord_less_int X_49) Y_23) (= X_49 Y_23) (@ (@ tptp.ord_less_int Y_23) X_49))))
% 0.51/0.77 (assert (forall ((X_49 tptp.nat) (Y_23 tptp.nat)) (or (@ (@ tptp.ord_less_nat X_49) Y_23) (= X_49 Y_23) (@ (@ tptp.ord_less_nat Y_23) X_49))))
% 0.51/0.77 (assert (forall ((Y_22 tptp.int) (X_48 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y_22) X_48)) (= (not (@ (@ tptp.ord_less_int X_48) Y_22)) (= X_48 Y_22)))))
% 0.51/0.77 (assert (forall ((Y_22 tptp.nat) (X_48 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y_22) X_48)) (= (not (@ (@ tptp.ord_less_nat X_48) Y_22)) (= X_48 Y_22)))))
% 0.51/0.77 (assert (forall ((X_47 tptp.int) (Y_21 tptp.int)) (=> (not (= X_47 Y_21)) (=> (not (@ (@ tptp.ord_less_int X_47) Y_21)) (@ (@ tptp.ord_less_int Y_21) X_47)))))
% 0.51/0.77 (assert (forall ((X_47 tptp.nat) (Y_21 tptp.nat)) (=> (not (= X_47 Y_21)) (=> (not (@ (@ tptp.ord_less_nat X_47) Y_21)) (@ (@ tptp.ord_less_nat Y_21) X_47)))))
% 0.51/0.77 (assert (forall ((X_46 tptp.int) (Y_20 tptp.int)) (=> (@ (@ tptp.ord_less_int X_46) Y_20) (not (= X_46 Y_20)))))
% 0.51/0.77 (assert (forall ((X_46 (-> tptp.nat Bool)) (Y_20 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o X_46) Y_20) (not (= X_46 Y_20)))))
% 0.51/0.77 (assert (forall ((X_46 tptp.nat) (Y_20 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_46) Y_20) (not (= X_46 Y_20)))))
% 0.51/0.77 (assert (forall ((X_45 tptp.int) (Y_19 tptp.int)) (=> (@ (@ tptp.ord_less_int X_45) Y_19) (not (@ (@ tptp.ord_less_int Y_19) X_45)))))
% 0.51/0.77 (assert (forall ((X_45 (-> tptp.nat Bool)) (Y_19 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o X_45) Y_19) (not (@ (@ tptp.ord_less_nat_o Y_19) X_45)))))
% 0.51/0.77 (assert (forall ((X_45 tptp.nat) (Y_19 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_45) Y_19) (not (@ (@ tptp.ord_less_nat Y_19) X_45)))))
% 0.51/0.77 (assert (forall ((X_44 tptp.int) (Y_18 tptp.int)) (=> (@ (@ tptp.ord_less_int X_44) Y_18) (not (@ (@ tptp.ord_less_int Y_18) X_44)))))
% 0.51/0.77 (assert (forall ((X_44 (-> tptp.nat Bool)) (Y_18 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o X_44) Y_18) (not (@ (@ tptp.ord_less_nat_o Y_18) X_44)))))
% 0.51/0.77 (assert (forall ((X_44 tptp.nat) (Y_18 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_44) Y_18) (not (@ (@ tptp.ord_less_nat Y_18) X_44)))))
% 0.51/0.77 (assert (forall ((X_43 tptp.int) (Y_17 tptp.int)) (=> (@ (@ tptp.ord_less_int X_43) Y_17) (not (= X_43 Y_17)))))
% 0.51/0.77 (assert (forall ((X_43 (-> tptp.nat Bool)) (Y_17 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o X_43) Y_17) (not (= X_43 Y_17)))))
% 0.51/0.77 (assert (forall ((X_43 tptp.nat) (Y_17 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_43) Y_17) (not (= X_43 Y_17)))))
% 0.51/0.77 (assert (forall ((X_42 tptp.int) (Y_16 tptp.int)) (=> (@ (@ tptp.ord_less_int X_42) Y_16) (not (= Y_16 X_42)))))
% 0.51/0.77 (assert (forall ((X_42 (-> tptp.nat Bool)) (Y_16 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o X_42) Y_16) (not (= Y_16 X_42)))))
% 0.51/0.77 (assert (forall ((X_42 tptp.nat) (Y_16 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_42) Y_16) (not (= Y_16 X_42)))))
% 0.51/0.77 (assert (forall ((P_10 Bool) (X_41 tptp.int) (Y_15 tptp.int)) (=> (@ (@ tptp.ord_less_int X_41) Y_15) (=> (@ (@ tptp.ord_less_int Y_15) X_41) P_10))))
% 0.51/0.77 (assert (forall ((P_10 Bool) (X_41 (-> tptp.nat Bool)) (Y_15 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o X_41) Y_15) (=> (@ (@ tptp.ord_less_nat_o Y_15) X_41) P_10))))
% 0.51/0.77 (assert (forall ((P_10 Bool) (X_41 tptp.nat) (Y_15 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_41) Y_15) (=> (@ (@ tptp.ord_less_nat Y_15) X_41) P_10))))
% 0.51/0.77 (assert (forall ((A_70 tptp.int) (B_43 tptp.int)) (=> (@ (@ tptp.ord_less_int A_70) B_43) (not (@ (@ tptp.ord_less_int B_43) A_70)))))
% 0.51/0.77 (assert (forall ((A_70 (-> tptp.nat Bool)) (B_43 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o A_70) B_43) (not (@ (@ tptp.ord_less_nat_o B_43) A_70)))))
% 0.51/0.77 (assert (forall ((A_70 tptp.nat) (B_43 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_70) B_43) (not (@ (@ tptp.ord_less_nat B_43) A_70)))))
% 0.51/0.77 (assert (forall ((B_42 tptp.int) (A_69 tptp.int)) (=> (@ (@ tptp.ord_less_int B_42) A_69) (not (@ (@ tptp.ord_less_int A_69) B_42)))))
% 0.51/0.77 (assert (forall ((B_42 (-> tptp.nat Bool)) (A_69 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o B_42) A_69) (not (@ (@ tptp.ord_less_nat_o A_69) B_42)))))
% 0.51/0.77 (assert (forall ((B_42 tptp.nat) (A_69 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B_42) A_69) (not (@ (@ tptp.ord_less_nat A_69) B_42)))))
% 0.51/0.77 (assert (forall ((C_33 tptp.int) (A_68 tptp.int) (B_41 tptp.int)) (=> (= A_68 B_41) (=> (@ (@ tptp.ord_less_int B_41) C_33) (@ (@ tptp.ord_less_int A_68) C_33)))))
% 0.51/0.77 (assert (forall ((C_33 (-> tptp.nat Bool)) (A_68 (-> tptp.nat Bool)) (B_41 (-> tptp.nat Bool))) (=> (= A_68 B_41) (=> (@ (@ tptp.ord_less_nat_o B_41) C_33) (@ (@ tptp.ord_less_nat_o A_68) C_33)))))
% 0.51/0.77 (assert (forall ((C_33 tptp.nat) (A_68 tptp.nat) (B_41 tptp.nat)) (=> (= A_68 B_41) (=> (@ (@ tptp.ord_less_nat B_41) C_33) (@ (@ tptp.ord_less_nat A_68) C_33)))))
% 0.51/0.77 (assert (forall ((C_32 tptp.int) (A_67 tptp.int) (B_40 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C_32))) (=> (= A_67 B_40) (=> (@ _let_1 B_40) (@ _let_1 A_67))))))
% 0.51/0.77 (assert (forall ((C_32 (-> tptp.nat Bool)) (A_67 (-> tptp.nat Bool)) (B_40 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_nat_o C_32))) (=> (= A_67 B_40) (=> (@ _let_1 B_40) (@ _let_1 A_67))))))
% 0.51/0.77 (assert (forall ((C_32 tptp.nat) (A_67 tptp.nat) (B_40 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C_32))) (=> (= A_67 B_40) (=> (@ _let_1 B_40) (@ _let_1 A_67))))))
% 0.51/0.77 (assert (forall ((C_31 tptp.int) (A_66 tptp.int) (B_39 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A_66))) (=> (@ _let_1 B_39) (=> (= B_39 C_31) (@ _let_1 C_31))))))
% 0.51/0.77 (assert (forall ((C_31 (-> tptp.nat Bool)) (A_66 (-> tptp.nat Bool)) (B_39 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_nat_o A_66))) (=> (@ _let_1 B_39) (=> (= B_39 C_31) (@ _let_1 C_31))))))
% 0.51/0.77 (assert (forall ((C_31 tptp.nat) (A_66 tptp.nat) (B_39 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A_66))) (=> (@ _let_1 B_39) (=> (= B_39 C_31) (@ _let_1 C_31))))))
% 0.51/0.77 (assert (forall ((C_30 tptp.int) (B_38 tptp.int) (A_65 tptp.int)) (=> (@ (@ tptp.ord_less_int B_38) A_65) (=> (= B_38 C_30) (@ (@ tptp.ord_less_int C_30) A_65)))))
% 0.51/0.77 (assert (forall ((C_30 (-> tptp.nat Bool)) (B_38 (-> tptp.nat Bool)) (A_65 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o B_38) A_65) (=> (= B_38 C_30) (@ (@ tptp.ord_less_nat_o C_30) A_65)))))
% 0.51/0.77 (assert (forall ((C_30 tptp.nat) (B_38 tptp.nat) (A_65 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B_38) A_65) (=> (= B_38 C_30) (@ (@ tptp.ord_less_nat C_30) A_65)))))
% 0.51/0.77 (assert (forall ((Z_6 tptp.int) (X_40 tptp.int) (Y_14 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X_40))) (=> (@ _let_1 Y_14) (=> (@ (@ tptp.ord_less_int Y_14) Z_6) (@ _let_1 Z_6))))))
% 0.51/0.77 (assert (forall ((Z_6 (-> tptp.nat Bool)) (X_40 (-> tptp.nat Bool)) (Y_14 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_nat_o X_40))) (=> (@ _let_1 Y_14) (=> (@ (@ tptp.ord_less_nat_o Y_14) Z_6) (@ _let_1 Z_6))))))
% 0.51/0.77 (assert (forall ((Z_6 tptp.nat) (X_40 tptp.nat) (Y_14 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_40))) (=> (@ _let_1 Y_14) (=> (@ (@ tptp.ord_less_nat Y_14) Z_6) (@ _let_1 Z_6))))))
% 0.51/0.77 (assert (forall ((Z_5 tptp.int) (Y_13 tptp.int) (X_39 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z_5))) (=> (@ (@ tptp.ord_less_int Y_13) X_39) (=> (@ _let_1 Y_13) (@ _let_1 X_39))))))
% 0.51/0.77 (assert (forall ((Z_5 (-> tptp.nat Bool)) (Y_13 (-> tptp.nat Bool)) (X_39 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_nat_o Z_5))) (=> (@ (@ tptp.ord_less_nat_o Y_13) X_39) (=> (@ _let_1 Y_13) (@ _let_1 X_39))))))
% 0.51/0.77 (assert (forall ((Z_5 tptp.nat) (Y_13 tptp.nat) (X_39 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z_5))) (=> (@ (@ tptp.ord_less_nat Y_13) X_39) (=> (@ _let_1 Y_13) (@ _let_1 X_39))))))
% 0.51/0.77 (assert (forall ((X_38 tptp.int) (Y_12 tptp.int)) (=> (@ (@ tptp.ord_less_int X_38) Y_12) (not (@ (@ tptp.ord_less_int Y_12) X_38)))))
% 0.51/0.77 (assert (forall ((X_38 (-> tptp.nat Bool)) (Y_12 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o X_38) Y_12) (not (@ (@ tptp.ord_less_nat_o Y_12) X_38)))))
% 0.51/0.77 (assert (forall ((X_38 tptp.nat) (Y_12 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_38) Y_12) (not (@ (@ tptp.ord_less_nat Y_12) X_38)))))
% 0.51/0.77 (assert (forall ((X_37 tptp.int) (Y_11 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X_37) Y_11)) (=> (not (= X_37 Y_11)) (@ (@ tptp.ord_less_int Y_11) X_37)))))
% 0.51/0.77 (assert (forall ((X_37 tptp.nat) (Y_11 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X_37) Y_11)) (=> (not (= X_37 Y_11)) (@ (@ tptp.ord_less_nat Y_11) X_37)))))
% 0.51/0.77 (assert (forall ((Ys_13 tptp.list_A2115238852le_alt) (X_36 tptp.arrow_475358991le_alt) (I_23 tptp.nat) (Xs_78 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_23) (@ tptp.size_s1858781230le_alt Xs_78)) (= (@ (@ (@ tptp.list_u62477863le_alt (@ (@ tptp.append179082452le_alt Xs_78) Ys_13)) I_23) X_36) (@ (@ tptp.append179082452le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_78) I_23) X_36)) Ys_13)))))
% 0.51/0.77 (assert (forall ((X_35 tptp.arrow_475358991le_alt) (J_6 tptp.nat) (I_22 tptp.nat) (Xs_77 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.nth_Ar125878976le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_77) I_22) X_35)) J_6))) (let ((_let_2 (= I_22 J_6))) (=> (@ (@ tptp.ord_less_nat I_22) (@ tptp.size_s1858781230le_alt Xs_77)) (and (=> _let_2 (= _let_1 X_35)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_Ar125878976le_alt Xs_77) J_6)))))))))
% 0.51/0.77 (assert (forall ((X_35 tptp.nat) (J_6 tptp.nat) (I_22 tptp.nat) (Xs_77 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs_77) I_22) X_35)) J_6))) (let ((_let_2 (= I_22 J_6))) (=> (@ (@ tptp.ord_less_nat I_22) (@ tptp.size_size_list_nat Xs_77)) (and (=> _let_2 (= _let_1 X_35)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs_77) J_6)))))))))
% 0.51/0.77 (assert (forall ((X_34 tptp.arrow_475358991le_alt) (I_21 tptp.nat) (Xs_76 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_21) (@ tptp.size_s1858781230le_alt Xs_76)) (= (= (@ (@ (@ tptp.list_u62477863le_alt Xs_76) I_21) X_34) Xs_76) (= (@ (@ tptp.nth_Ar125878976le_alt Xs_76) I_21) X_34)))))
% 0.51/0.77 (assert (forall ((X_34 tptp.nat) (I_21 tptp.nat) (Xs_76 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I_21) (@ tptp.size_size_list_nat Xs_76)) (= (= (@ (@ (@ tptp.list_update_nat Xs_76) I_21) X_34) Xs_76) (= (@ (@ tptp.nth_nat Xs_76) I_21) X_34)))))
% 0.51/0.77 (assert (forall ((X_33 tptp.arrow_475358991le_alt) (I_20 tptp.nat) (Xs_75 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_20) (@ tptp.size_s1858781230le_alt Xs_75)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_75) I_20) X_33)) I_20) X_33))))
% 0.51/0.77 (assert (forall ((X_33 tptp.nat) (I_20 tptp.nat) (Xs_75 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I_20) (@ tptp.size_size_list_nat Xs_75)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs_75) I_20) X_33)) I_20) X_33))))
% 0.51/0.77 (assert (forall ((N_43 tptp.nat) (Xs_74 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat N_43) (@ tptp.size_s1858781230le_alt Xs_74)) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.drop_A1346709759le_alt N_43) Xs_74)) (@ tptp.last_A1217315288le_alt Xs_74)))))
% 0.51/0.77 (assert (forall ((A_64 Bool)) (not (@ (@ tptp.ord_less_o A_64) tptp.bot_bot_o))))
% 0.51/0.77 (assert (forall ((A_64 tptp.nat)) (not (@ (@ tptp.ord_less_nat A_64) tptp.bot_bot_nat))))
% 0.51/0.77 (assert (forall ((A_64 (-> tptp.nat Bool))) (not (@ (@ tptp.ord_less_nat_o A_64) tptp.bot_bot_nat_o))))
% 0.51/0.77 (assert (forall ((A_63 Bool)) (= (not (= A_63 tptp.bot_bot_o)) (@ (@ tptp.ord_less_o tptp.bot_bot_o) A_63))))
% 0.51/0.77 (assert (forall ((A_63 tptp.nat)) (= (not (= A_63 tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A_63))))
% 0.51/0.77 (assert (forall ((A_63 (-> tptp.nat Bool))) (= (not (= A_63 tptp.bot_bot_nat_o)) (@ (@ tptp.ord_less_nat_o tptp.bot_bot_nat_o) A_63))))
% 0.51/0.77 (assert (forall ((Xs_73 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt tptp.zero_zero_nat) Xs_73) Xs_73)))
% 0.51/0.77 (assert (forall ((N_42 tptp.nat)) (= (@ (@ tptp.drop_nat N_42) tptp.nil_nat) tptp.nil_nat)))
% 0.51/0.77 (assert (forall ((N_42 tptp.nat)) (= (@ (@ tptp.drop_A1346709759le_alt N_42) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((Z_4 tptp.int) (X_32 tptp.int) (Y_10 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z_4))) (= (@ _let_1 (@ (@ tptp.ord_max_int X_32) Y_10)) (or (@ _let_1 X_32) (@ _let_1 Y_10))))))
% 0.51/0.77 (assert (forall ((Z_4 tptp.nat) (X_32 tptp.nat) (Y_10 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z_4))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X_32) Y_10)) (or (@ _let_1 X_32) (@ _let_1 Y_10))))))
% 0.51/0.77 (assert (forall ((X_31 tptp.int) (Y_9 tptp.int) (Z_3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X_31) Y_9)) Z_3) (and (@ (@ tptp.ord_less_int X_31) Z_3) (@ (@ tptp.ord_less_int Y_9) Z_3)))))
% 0.51/0.77 (assert (forall ((X_31 tptp.nat) (Y_9 tptp.nat) (Z_3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X_31) Y_9)) Z_3) (and (@ (@ tptp.ord_less_nat X_31) Z_3) (@ (@ tptp.ord_less_nat Y_9) Z_3)))))
% 0.51/0.77 (assert (forall ((B_37 tptp.int) (X_30 tptp.int) (A_62 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X_30))) (=> (@ _let_1 A_62) (@ _let_1 (@ (@ tptp.ord_max_int A_62) B_37))))))
% 0.51/0.77 (assert (forall ((B_37 tptp.nat) (X_30 tptp.nat) (A_62 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_30))) (=> (@ _let_1 A_62) (@ _let_1 (@ (@ tptp.ord_max_nat A_62) B_37))))))
% 0.51/0.77 (assert (forall ((A_61 tptp.int) (X_29 tptp.int) (B_36 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X_29))) (=> (@ _let_1 B_36) (@ _let_1 (@ (@ tptp.ord_max_int A_61) B_36))))))
% 0.51/0.77 (assert (forall ((A_61 tptp.nat) (X_29 tptp.nat) (B_36 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_29))) (=> (@ _let_1 B_36) (@ _let_1 (@ (@ tptp.ord_max_nat A_61) B_36))))))
% 0.51/0.77 (assert (forall ((I_19 tptp.nat) (Xs_72 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_72) (@ tptp.distin236324274le_alt (@ (@ tptp.drop_A1346709759le_alt I_19) Xs_72)))))
% 0.51/0.77 (assert (forall ((N_41 tptp.nat) (Xs_71 tptp.list_nat)) (=> (@ tptp.linorder_sorted_nat Xs_71) (@ tptp.linorder_sorted_nat (@ (@ tptp.drop_nat N_41) Xs_71)))))
% 0.51/0.77 (assert (forall ((Xs_70 tptp.list_nat) (K_7 tptp.nat) (X_28 tptp.nat)) (= (= (@ (@ (@ tptp.list_update_nat Xs_70) K_7) X_28) tptp.nil_nat) (= Xs_70 tptp.nil_nat))))
% 0.51/0.77 (assert (forall ((Xs_70 tptp.list_A2115238852le_alt) (K_7 tptp.nat) (X_28 tptp.arrow_475358991le_alt)) (= (= (@ (@ (@ tptp.list_u62477863le_alt Xs_70) K_7) X_28) tptp.nil_Ar1286194111le_alt) (= Xs_70 tptp.nil_Ar1286194111le_alt))))
% 0.51/0.77 (assert (forall ((I_18 tptp.nat) (V_3 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat tptp.nil_nat) I_18) V_3) tptp.nil_nat)))
% 0.51/0.77 (assert (forall ((I_18 tptp.nat) (V_3 tptp.arrow_475358991le_alt)) (= (@ (@ (@ tptp.list_u62477863le_alt tptp.nil_Ar1286194111le_alt) I_18) V_3) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((I_17 tptp.nat) (Y_8 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat tptp.nil_nat) I_17) Y_8) tptp.nil_nat)))
% 0.51/0.77 (assert (forall ((I_17 tptp.nat) (Y_8 tptp.arrow_475358991le_alt)) (= (@ (@ (@ tptp.list_u62477863le_alt tptp.nil_Ar1286194111le_alt) I_17) Y_8) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((Xs_69 tptp.list_A2115238852le_alt) (I_16 tptp.nat) (X_27 tptp.arrow_475358991le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_69) I_16) X_27)) (@ tptp.size_s1858781230le_alt Xs_69))))
% 0.51/0.77 (assert (forall ((Xs_68 tptp.list_A2115238852le_alt) (I_15 tptp.nat)) (= (@ (@ (@ tptp.list_u62477863le_alt Xs_68) I_15) (@ (@ tptp.nth_Ar125878976le_alt Xs_68) I_15)) Xs_68)))
% 0.51/0.77 (assert (forall ((Xs_68 tptp.list_nat) (I_15 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs_68) I_15) (@ (@ tptp.nth_nat Xs_68) I_15)) Xs_68)))
% 0.51/0.77 (assert (forall ((Xs_67 tptp.list_A2115238852le_alt) (X_26 tptp.arrow_475358991le_alt) (I_14 tptp.nat) (J_5 tptp.nat)) (=> (not (= I_14 J_5)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_67) I_14) X_26)) J_5) (@ (@ tptp.nth_Ar125878976le_alt Xs_67) J_5)))))
% 0.51/0.77 (assert (forall ((Xs_67 tptp.list_nat) (X_26 tptp.nat) (I_14 tptp.nat) (J_5 tptp.nat)) (=> (not (= I_14 J_5)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs_67) I_14) X_26)) J_5) (@ (@ tptp.nth_nat Xs_67) J_5)))))
% 0.51/0.77 (assert (forall ((N_40 tptp.nat) (Xs_66 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.drop_A1346709759le_alt N_40))) (= (@ _let_1 (@ tptp.butlas274947851le_alt Xs_66)) (@ tptp.butlas274947851le_alt (@ _let_1 Xs_66))))))
% 0.51/0.77 (assert (forall ((N_39 tptp.nat) (Xs_65 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.drop_A1346709759le_alt N_39))) (= (@ tptp.butlas274947851le_alt (@ _let_1 Xs_65)) (@ _let_1 (@ tptp.butlas274947851le_alt Xs_65))))))
% 0.51/0.77 (assert (forall ((N_38 tptp.nat) (Xs_64 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.drop_A1346709759le_alt N_38))) (= (@ tptp.tl_Arr465451158le_alt (@ _let_1 Xs_64)) (@ _let_1 (@ tptp.tl_Arr465451158le_alt Xs_64))))))
% 0.51/0.77 (assert (forall ((N_37 tptp.nat) (Xs_63 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.drop_A1346709759le_alt N_37))) (= (@ _let_1 (@ tptp.tl_Arr465451158le_alt Xs_63)) (@ tptp.tl_Arr465451158le_alt (@ _let_1 Xs_63))))))
% 0.51/0.77 (assert (forall ((N_36 tptp.nat) (Xs_62 tptp.list_nat)) (=> (not (= Xs_62 tptp.nil_nat)) (=> (@ (@ tptp.ord_less_nat N_36) (@ tptp.size_size_list_nat Xs_62)) (= (@ tptp.hd_nat (@ (@ tptp.drop_nat N_36) Xs_62)) (@ (@ tptp.nth_nat Xs_62) N_36))))))
% 0.51/0.77 (assert (forall ((N_36 tptp.nat) (Xs_62 tptp.list_A2115238852le_alt)) (=> (not (= Xs_62 tptp.nil_Ar1286194111le_alt)) (=> (@ (@ tptp.ord_less_nat N_36) (@ tptp.size_s1858781230le_alt Xs_62)) (= (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.drop_A1346709759le_alt N_36) Xs_62)) (@ (@ tptp.nth_Ar125878976le_alt Xs_62) N_36))))))
% 0.51/0.77 (assert (forall ((N_35 tptp.nat) (Xs_61 tptp.list_nat) (Y_7 tptp.nat) (Ys_12 tptp.list_nat)) (=> (= (@ (@ tptp.drop_nat N_35) Xs_61) (@ (@ tptp.cons_nat Y_7) Ys_12)) (= (@ (@ tptp.nth_nat Xs_61) N_35) Y_7))))
% 0.51/0.77 (assert (forall ((N_35 tptp.nat) (Xs_61 tptp.list_A2115238852le_alt) (Y_7 tptp.arrow_475358991le_alt) (Ys_12 tptp.list_A2115238852le_alt)) (=> (= (@ (@ tptp.drop_A1346709759le_alt N_35) Xs_61) (@ (@ tptp.cons_A228743023le_alt Y_7) Ys_12)) (= (@ (@ tptp.nth_Ar125878976le_alt Xs_61) N_35) Y_7))))
% 0.51/0.77 (assert (forall ((Xs_60 tptp.list_A2115238852le_alt) (Ys_11 tptp.list_A2115238852le_alt)) (= (= Xs_60 Ys_11) (and (= (@ tptp.size_s1858781230le_alt Xs_60) (@ tptp.size_s1858781230le_alt Ys_11)) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_s1858781230le_alt Xs_60)) (= (@ (@ tptp.nth_Ar125878976le_alt Xs_60) I_4) (@ (@ tptp.nth_Ar125878976le_alt Ys_11) I_4))))))))
% 0.51/0.77 (assert (forall ((Xs_60 tptp.list_nat) (Ys_11 tptp.list_nat)) (= (= Xs_60 Ys_11) (and (= (@ tptp.size_size_list_nat Xs_60) (@ tptp.size_size_list_nat Ys_11)) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_size_list_nat Xs_60)) (= (@ (@ tptp.nth_nat Xs_60) I_4) (@ (@ tptp.nth_nat Ys_11) I_4))))))))
% 0.51/0.77 (assert (forall ((X_25 tptp.arrow_475358991le_alt) (Xs_59 tptp.list_A2115238852le_alt) (Y_6 tptp.arrow_475358991le_alt)) (= (@ (@ (@ tptp.list_u62477863le_alt (@ (@ tptp.cons_A228743023le_alt X_25) Xs_59)) tptp.zero_zero_nat) Y_6) (@ (@ tptp.cons_A228743023le_alt Y_6) Xs_59))))
% 0.51/0.77 (assert (forall ((X_24 tptp.nat) (I_13 tptp.nat) (N_34 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_13) N_34) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N_34) X_24)) I_13) X_24))))
% 0.51/0.77 (assert (forall ((X_24 tptp.arrow_475358991le_alt) (I_13 tptp.nat) (N_34 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_13) N_34) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.replic1511538809le_alt N_34) X_24)) I_13) X_24))))
% 0.51/0.77 (assert (forall ((Xs_58 tptp.list_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs_58)) (not (= Xs_58 tptp.nil_nat)))))
% 0.51/0.77 (assert (forall ((Xs_58 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s1858781230le_alt Xs_58)) (not (= Xs_58 tptp.nil_Ar1286194111le_alt)))))
% 0.51/0.77 (assert (forall ((Xs_57 tptp.list_nat)) (= (@ tptp.distinct_nat Xs_57) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_size_list_nat Xs_57)) (forall ((J_2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs_57))) (=> (@ (@ tptp.ord_less_nat J_2) (@ tptp.size_size_list_nat Xs_57)) (=> (not (= I_4 J_2)) (not (= (@ _let_1 I_4) (@ _let_1 J_2))))))))))))
% 0.51/0.77 (assert (forall ((Xs_57 tptp.list_A2115238852le_alt)) (= (@ tptp.distin236324274le_alt Xs_57) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_s1858781230le_alt Xs_57)) (forall ((J_2 tptp.nat)) (let ((_let_1 (@ tptp.nth_Ar125878976le_alt Xs_57))) (=> (@ (@ tptp.ord_less_nat J_2) (@ tptp.size_s1858781230le_alt Xs_57)) (=> (not (= I_4 J_2)) (not (= (@ _let_1 I_4) (@ _let_1 J_2))))))))))))
% 0.51/0.77 (assert (forall ((J_4 tptp.nat) (I_12 tptp.nat) (Xs_56 tptp.list_nat)) (let ((_let_1 (@ tptp.nth_nat Xs_56))) (let ((_let_2 (@ tptp.size_size_list_nat Xs_56))) (=> (@ tptp.distinct_nat Xs_56) (=> (@ (@ tptp.ord_less_nat I_12) _let_2) (=> (@ (@ tptp.ord_less_nat J_4) _let_2) (= (= (@ _let_1 I_12) (@ _let_1 J_4)) (= I_12 J_4)))))))))
% 0.51/0.77 (assert (forall ((J_4 tptp.nat) (I_12 tptp.nat) (Xs_56 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.nth_Ar125878976le_alt Xs_56))) (let ((_let_2 (@ tptp.size_s1858781230le_alt Xs_56))) (=> (@ tptp.distin236324274le_alt Xs_56) (=> (@ (@ tptp.ord_less_nat I_12) _let_2) (=> (@ (@ tptp.ord_less_nat J_4) _let_2) (= (= (@ _let_1 I_12) (@ _let_1 J_4)) (= I_12 J_4)))))))))
% 0.51/0.77 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (= (@ (@ tptp.ord_max_nat N_5) tptp.zero_zero_nat) N_5)))
% 0.51/0.77 (assert (forall ((Xs_55 tptp.list_A2115238852le_alt) (Ys_10 tptp.list_A2115238852le_alt)) (=> (= (@ tptp.size_s1858781230le_alt Xs_55) (@ tptp.size_s1858781230le_alt Ys_10)) (=> (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_s1858781230le_alt Xs_55)) (= (@ (@ tptp.nth_Ar125878976le_alt Xs_55) I_4) (@ (@ tptp.nth_Ar125878976le_alt Ys_10) I_4)))) (= Xs_55 Ys_10)))))
% 0.51/0.77 (assert (forall ((Xs_55 tptp.list_nat) (Ys_10 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs_55) (@ tptp.size_size_list_nat Ys_10)) (=> (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_size_list_nat Xs_55)) (= (@ (@ tptp.nth_nat Xs_55) I_4) (@ (@ tptp.nth_nat Ys_10) I_4)))) (= Xs_55 Ys_10)))))
% 0.51/0.77 (assert (forall ((P_9 (-> tptp.nat tptp.arrow_475358991le_alt Bool)) (K_6 tptp.nat)) (= (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) K_6) (@ tptp.ex2 (@ P_9 I_4)))) (exists ((Xs_54 tptp.list_A2115238852le_alt)) (and (= (@ tptp.size_s1858781230le_alt Xs_54) K_6) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) K_6) (@ (@ P_9 I_4) (@ (@ tptp.nth_Ar125878976le_alt Xs_54) I_4)))))))))
% 0.51/0.77 (assert (forall ((P_9 (-> tptp.nat tptp.nat Bool)) (K_6 tptp.nat)) (= (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) K_6) (@ tptp.ex1 (@ P_9 I_4)))) (exists ((Xs_54 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs_54) K_6) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) K_6) (@ (@ P_9 I_4) (@ (@ tptp.nth_nat Xs_54) I_4)))))))))
% 0.51/0.77 (assert (forall ((J_3 tptp.nat) (P_8 (-> tptp.nat Bool)) (Xs_53 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.dropWhile_nat P_8) Xs_53))) (=> (@ (@ tptp.ord_less_nat J_3) (@ tptp.size_size_list_nat _let_1)) (= (@ (@ tptp.nth_nat _let_1) J_3) (@ (@ tptp.nth_nat Xs_53) (@ (@ tptp.plus_plus_nat J_3) (@ tptp.size_size_list_nat (@ (@ tptp.takeWhile_nat P_8) Xs_53)))))))))
% 0.51/0.77 (assert (forall ((J_3 tptp.nat) (P_8 (-> tptp.arrow_475358991le_alt Bool)) (Xs_53 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.dropWh1316781920le_alt P_8) Xs_53))) (=> (@ (@ tptp.ord_less_nat J_3) (@ tptp.size_s1858781230le_alt _let_1)) (= (@ (@ tptp.nth_Ar125878976le_alt _let_1) J_3) (@ (@ tptp.nth_Ar125878976le_alt Xs_53) (@ (@ tptp.plus_plus_nat J_3) (@ tptp.size_s1858781230le_alt (@ (@ tptp.takeWh1696291512le_alt P_8) Xs_53)))))))))
% 0.51/0.77 (assert (forall ((I_11 tptp.nat) (Xs_52 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I_11) (@ tptp.size_size_list_nat Xs_52)) (= (@ (@ tptp.cons_nat (@ (@ tptp.nth_nat Xs_52) I_11)) (@ (@ tptp.drop_nat (@ tptp.suc I_11)) Xs_52)) (@ (@ tptp.drop_nat I_11) Xs_52)))))
% 0.51/0.77 (assert (forall ((I_11 tptp.nat) (Xs_52 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_11) (@ tptp.size_s1858781230le_alt Xs_52)) (= (@ (@ tptp.cons_A228743023le_alt (@ (@ tptp.nth_Ar125878976le_alt Xs_52) I_11)) (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc I_11)) Xs_52)) (@ (@ tptp.drop_A1346709759le_alt I_11) Xs_52)))))
% 0.51/0.77 (assert (forall ((P_7 (-> tptp.arrow_475358991le_alt Bool)) (Xs_51 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.list_e1252802557le_alt P_7) Xs_51) (exists ((N_7 tptp.nat)) (and (@ (@ tptp.ord_less_nat N_7) (@ tptp.size_s1858781230le_alt Xs_51)) (@ P_7 (@ (@ tptp.nth_Ar125878976le_alt Xs_51) N_7)))))))
% 0.51/0.77 (assert (forall ((P_7 (-> tptp.nat Bool)) (Xs_51 tptp.list_nat)) (= (@ (@ tptp.list_ex_nat P_7) Xs_51) (exists ((N_7 tptp.nat)) (and (@ (@ tptp.ord_less_nat N_7) (@ tptp.size_size_list_nat Xs_51)) (@ P_7 (@ (@ tptp.nth_nat Xs_51) N_7)))))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (@ (@ tptp.ord_less_nat N_5) (@ tptp.suc N_5))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N_5) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N_5)))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N_5))))
% 0.51/0.77 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (K_3 tptp.nat) (N_5 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) K_3) (@ (@ tptp.plus_plus_nat N_5) K_3)) (= M N_5))))
% 0.51/0.77 (assert (forall ((K_3 tptp.nat) (M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K_3))) (= (= (@ _let_1 M) (@ _let_1 N_5)) (= M N_5)))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat) (K_3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 N_5)) K_3) (@ _let_1 (@ (@ tptp.plus_plus_nat N_5) K_3))))))
% 0.51/0.77 (assert (forall ((Nat_3 tptp.nat) (Nat_2 tptp.nat)) (= (= (@ tptp.suc Nat_3) (@ tptp.suc Nat_2)) (= Nat_3 Nat_2))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N_5) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N_5)))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N_5) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N_5)))))
% 0.51/0.77 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (let ((_let_2 (@ tptp.plus_plus_nat Y))) (= (@ _let_1 (@ _let_2 Z_1)) (@ _let_2 (@ _let_1 Z_1)))))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N_5)) (@ tptp.suc (@ _let_1 N_5))))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N_5) (@ (@ tptp.plus_plus_nat N_5) M))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N_5) (exists ((K_5 tptp.nat)) (= N_5 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_5)))))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (not (= (@ tptp.suc N_5) N_5))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (not (= N_5 (@ tptp.suc N_5)))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N_5) _let_1) (or (and (= M _let_1) (= N_5 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N_5 _let_1)))))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N_5)) (or (and (= M _let_1) (= N_5 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N_5 _let_1)))))))
% 0.51/0.77 (assert (forall ((B_35 tptp.nat) (A_60 tptp.nat) (C_29 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B_35) A_60) (@ (@ tptp.plus_plus_nat C_29) A_60)) (= B_35 C_29))))
% 0.51/0.77 (assert (forall ((B_35 tptp.int) (A_60 tptp.int) (C_29 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B_35) A_60) (@ (@ tptp.plus_plus_int C_29) A_60)) (= B_35 C_29))))
% 0.51/0.77 (assert (forall ((A_59 tptp.nat) (B_34 tptp.nat) (C_28 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_59))) (=> (= (@ _let_1 B_34) (@ _let_1 C_28)) (= B_34 C_28)))))
% 0.51/0.77 (assert (forall ((A_59 tptp.int) (B_34 tptp.int) (C_28 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_59))) (=> (= (@ _let_1 B_34) (@ _let_1 C_28)) (= B_34 C_28)))))
% 0.51/0.77 (assert (forall ((A_58 tptp.nat) (B_33 tptp.nat) (C_27 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_58))) (=> (= (@ _let_1 B_33) (@ _let_1 C_27)) (= B_33 C_27)))))
% 0.51/0.77 (assert (forall ((A_58 tptp.int) (B_33 tptp.int) (C_27 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_58))) (=> (= (@ _let_1 B_33) (@ _let_1 C_27)) (= B_33 C_27)))))
% 0.51/0.77 (assert (forall ((B_32 tptp.nat) (A_57 tptp.nat) (C_26 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B_32) A_57) (@ (@ tptp.plus_plus_nat C_26) A_57)) (= B_32 C_26))))
% 0.51/0.77 (assert (forall ((B_32 tptp.int) (A_57 tptp.int) (C_26 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B_32) A_57) (@ (@ tptp.plus_plus_int C_26) A_57)) (= B_32 C_26))))
% 0.51/0.77 (assert (forall ((A_56 tptp.nat) (B_31 tptp.nat) (C_25 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_56))) (= (= (@ _let_1 B_31) (@ _let_1 C_25)) (= B_31 C_25)))))
% 0.51/0.77 (assert (forall ((A_56 tptp.int) (B_31 tptp.int) (C_25 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_56))) (= (= (@ _let_1 B_31) (@ _let_1 C_25)) (= B_31 C_25)))))
% 0.51/0.77 (assert (forall ((A_55 tptp.nat) (B_30 tptp.nat) (C_24 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_55))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_30)) C_24) (@ _let_1 (@ (@ tptp.plus_plus_nat B_30) C_24))))))
% 0.51/0.77 (assert (forall ((A_55 tptp.int) (B_30 tptp.int) (C_24 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_55))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_30)) C_24) (@ _let_1 (@ (@ tptp.plus_plus_int B_30) C_24))))))
% 0.51/0.77 (assert (forall ((A_54 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_54) tptp.zero_zero_nat) A_54)))
% 0.51/0.77 (assert (forall ((A_54 tptp.int)) (= (@ (@ tptp.plus_plus_int A_54) tptp.zero_zero_int) A_54)))
% 0.51/0.77 (assert (forall ((A_53 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_53) tptp.zero_zero_nat) A_53)))
% 0.51/0.77 (assert (forall ((A_53 tptp.int)) (= (@ (@ tptp.plus_plus_int A_53) tptp.zero_zero_int) A_53)))
% 0.51/0.77 (assert (forall ((A_52 tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A_52) A_52)) (= A_52 tptp.zero_zero_int))))
% 0.51/0.77 (assert (forall ((A_51 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_51) A_51)))
% 0.51/0.77 (assert (forall ((A_51 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_51) A_51)))
% 0.51/0.77 (assert (forall ((A_50 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_50) A_50)))
% 0.51/0.77 (assert (forall ((A_50 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_50) A_50)))
% 0.51/0.77 (assert (forall ((C_23 tptp.nat) (A_49 tptp.nat) (B_29 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_23))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A_49)) (@ _let_1 B_29)) (@ (@ tptp.ord_less_nat A_49) B_29)))))
% 0.51/0.77 (assert (forall ((C_23 tptp.int) (A_49 tptp.int) (B_29 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_23))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A_49)) (@ _let_1 B_29)) (@ (@ tptp.ord_less_int A_49) B_29)))))
% 0.51/0.77 (assert (forall ((A_48 tptp.nat) (C_22 tptp.nat) (B_28 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_48) C_22)) (@ (@ tptp.plus_plus_nat B_28) C_22)) (@ (@ tptp.ord_less_nat A_48) B_28))))
% 0.51/0.77 (assert (forall ((A_48 tptp.int) (C_22 tptp.int) (B_28 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_48) C_22)) (@ (@ tptp.plus_plus_int B_28) C_22)) (@ (@ tptp.ord_less_int A_48) B_28))))
% 0.51/0.77 (assert (forall ((C_21 tptp.nat) (D_6 tptp.nat) (A_47 tptp.nat) (B_27 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_47) B_27) (=> (@ (@ tptp.ord_less_nat C_21) D_6) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_47) C_21)) (@ (@ tptp.plus_plus_nat B_27) D_6))))))
% 0.51/0.77 (assert (forall ((C_21 tptp.int) (D_6 tptp.int) (A_47 tptp.int) (B_27 tptp.int)) (=> (@ (@ tptp.ord_less_int A_47) B_27) (=> (@ (@ tptp.ord_less_int C_21) D_6) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_47) C_21)) (@ (@ tptp.plus_plus_int B_27) D_6))))))
% 0.51/0.77 (assert (forall ((C_20 tptp.nat) (A_46 tptp.nat) (B_26 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_20))) (=> (@ (@ tptp.ord_less_nat A_46) B_26) (@ (@ tptp.ord_less_nat (@ _let_1 A_46)) (@ _let_1 B_26))))))
% 0.51/0.77 (assert (forall ((C_20 tptp.int) (A_46 tptp.int) (B_26 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_20))) (=> (@ (@ tptp.ord_less_int A_46) B_26) (@ (@ tptp.ord_less_int (@ _let_1 A_46)) (@ _let_1 B_26))))))
% 0.51/0.77 (assert (forall ((C_19 tptp.nat) (A_45 tptp.nat) (B_25 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_45) B_25) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_45) C_19)) (@ (@ tptp.plus_plus_nat B_25) C_19)))))
% 0.51/0.77 (assert (forall ((C_19 tptp.int) (A_45 tptp.int) (B_25 tptp.int)) (=> (@ (@ tptp.ord_less_int A_45) B_25) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_45) C_19)) (@ (@ tptp.plus_plus_int B_25) C_19)))))
% 0.51/0.77 (assert (forall ((C_18 tptp.nat) (A_44 tptp.nat) (B_24 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_18))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A_44)) (@ _let_1 B_24)) (@ (@ tptp.ord_less_nat A_44) B_24)))))
% 0.51/0.77 (assert (forall ((C_18 tptp.int) (A_44 tptp.int) (B_24 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_18))) (= (@ (@ tptp.ord_less_int (@ _let_1 A_44)) (@ _let_1 B_24)) (@ (@ tptp.ord_less_int A_44) B_24)))))
% 0.51/0.77 (assert (forall ((A_43 tptp.nat) (C_17 tptp.nat) (B_23 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_43) C_17)) (@ (@ tptp.plus_plus_nat B_23) C_17)) (@ (@ tptp.ord_less_nat A_43) B_23))))
% 0.51/0.77 (assert (forall ((A_43 tptp.int) (C_17 tptp.int) (B_23 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_43) C_17)) (@ (@ tptp.plus_plus_int B_23) C_17)) (@ (@ tptp.ord_less_int A_43) B_23))))
% 0.51/0.77 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.51/0.77 (assert (forall ((Nat_2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat_2)))))
% 0.51/0.77 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((Nat_1 tptp.nat)) (not (= (@ tptp.suc Nat_1) tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.51/0.77 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N_5)) (@ (@ tptp.ord_less_nat N_5) (@ tptp.suc M)))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N_5)) (or (@ _let_1 N_5) (= M N_5))))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N_5)) (@ (@ tptp.ord_less_nat M) N_5))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N_5))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N_5 M))))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N_5))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N_5))))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N_5) (@ _let_1 (@ tptp.suc N_5))))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N_5) (=> (not (= _let_1 N_5)) (@ (@ tptp.ord_less_nat _let_1) N_5))))))
% 0.51/0.77 (assert (forall ((K_3 tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K_3) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K_3)))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N_5)) (=> (not (@ _let_1 N_5)) (= M N_5))))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N_5) (@ (@ tptp.ord_less_nat M) N_5))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N_5)) (@ (@ tptp.ord_less_nat M) N_5))))
% 0.51/0.77 (assert (forall ((A_42 (-> tptp.nat Bool))) (not (@ (@ tptp.ord_less_nat_o A_42) tptp.bot_bot_nat_o))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N_5) N_5)))
% 0.51/0.77 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N_5) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N_5 tptp.zero_zero_nat)))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N_5) M) (= N_5 tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 0.51/0.77 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 0.51/0.77 (assert (forall ((K_3 tptp.nat) (M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K_3))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N_5)) (@ (@ tptp.ord_less_nat M) N_5)))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 0.51/0.77 (assert (forall ((K_3 tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K_3)) (@ (@ tptp.plus_plus_nat J) K_3)))))
% 0.51/0.77 (assert (forall ((K_3 tptp.nat) (L tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K_3) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K_3)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat) (K_3 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat K_3) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K_3) N_5)) (@ (@ tptp.ord_less_nat M) N_5)))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (J tptp.nat) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K_3) (@ (@ tptp.ord_less_nat I) K_3))))
% 0.51/0.77 (assert (forall ((X_23 tptp.nat) (Y_5 tptp.nat) (Z_2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X_23) Y_5)) Z_2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X_23) Z_2)) (@ (@ tptp.plus_plus_nat Y_5) Z_2)))))
% 0.51/0.77 (assert (forall ((X_23 tptp.int) (Y_5 tptp.int) (Z_2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X_23) Y_5)) Z_2) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X_23) Z_2)) (@ (@ tptp.plus_plus_int Y_5) Z_2)))))
% 0.51/0.77 (assert (forall ((N_33 tptp.nat) (M_4 tptp.nat) (Xs_50 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt N_33) (@ (@ tptp.drop_A1346709759le_alt M_4) Xs_50)) (@ (@ tptp.drop_A1346709759le_alt (@ (@ tptp.plus_plus_nat N_33) M_4)) Xs_50))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N_5)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N_5)))))
% 0.51/0.77 (assert (forall ((A_41 tptp.arrow_475358991le_alt) (List_1 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ tptp.cons_A228743023le_alt A_41) List_1)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1858781230le_alt List_1)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.51/0.77 (assert (forall ((Fa (-> tptp.arrow_475358991le_alt tptp.nat)) (A_40 tptp.arrow_475358991le_alt) (List tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.list_s250295873le_alt Fa))) (= (@ _let_1 (@ (@ tptp.cons_A228743023le_alt A_40) List)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ Fa A_40)) (@ _let_1 List))) (@ tptp.suc tptp.zero_zero_nat))))))
% 0.51/0.77 (assert (forall ((P_6 (-> tptp.arrow_475358991le_alt Bool)) (X_22 tptp.arrow_475358991le_alt) (Xs_49 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.list_e1252802557le_alt P_6))) (= (@ _let_1 (@ (@ tptp.cons_A228743023le_alt X_22) Xs_49)) (or (@ P_6 X_22) (@ _let_1 Xs_49))))))
% 0.51/0.77 (assert (forall ((P_5 (-> tptp.nat Bool))) (not (@ (@ tptp.list_ex_nat P_5) tptp.nil_nat))))
% 0.51/0.77 (assert (forall ((P_5 (-> tptp.arrow_475358991le_alt Bool))) (not (@ (@ tptp.list_e1252802557le_alt P_5) tptp.nil_Ar1286194111le_alt))))
% 0.51/0.77 (assert (forall ((P_4 (-> tptp.arrow_475358991le_alt Bool)) (Xs_48 tptp.list_A2115238852le_alt) (Ys_9 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.list_e1252802557le_alt P_4))) (= (@ _let_1 (@ (@ tptp.append179082452le_alt Xs_48) Ys_9)) (or (@ _let_1 Xs_48) (@ _let_1 Ys_9))))))
% 0.51/0.77 (assert (forall ((A_39 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A_39) A_39)) (@ _let_1 A_39)))))
% 0.51/0.77 (assert (forall ((A_38 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_38) A_38)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_38) tptp.zero_zero_int))))
% 0.51/0.77 (assert (forall ((B_22 tptp.nat) (A_37 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_37) (=> (@ _let_1 B_22) (@ _let_1 (@ (@ tptp.plus_plus_nat A_37) B_22)))))))
% 0.51/0.77 (assert (forall ((B_22 tptp.int) (A_37 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A_37) (=> (@ _let_1 B_22) (@ _let_1 (@ (@ tptp.plus_plus_int A_37) B_22)))))))
% 0.51/0.77 (assert (forall ((B_21 tptp.nat) (A_36 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_36) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B_21) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_36) B_21)) tptp.zero_zero_nat)))))
% 0.51/0.77 (assert (forall ((B_21 tptp.int) (A_36 tptp.int)) (=> (@ (@ tptp.ord_less_int A_36) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B_21) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_36) B_21)) tptp.zero_zero_int)))))
% 0.51/0.77 (assert (forall ((P_3 (-> tptp.nat Bool)) (Xs_47 tptp.list_nat)) (let ((_let_1 (@ tptp.list_ex_nat P_3))) (= (@ _let_1 (@ tptp.rev_nat Xs_47)) (@ _let_1 Xs_47)))))
% 0.51/0.77 (assert (forall ((P_3 (-> tptp.arrow_475358991le_alt Bool)) (Xs_47 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.list_e1252802557le_alt P_3))) (= (@ _let_1 (@ tptp.rev_Ar1106406943le_alt Xs_47)) (@ _let_1 Xs_47)))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (exists ((M_1 tptp.nat)) (= N_5 (@ tptp.suc M_1))))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (= (@ (@ tptp.ord_less_nat N_5) (@ tptp.suc tptp.zero_zero_nat)) (= N_5 tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N_5)) (or (= M tptp.zero_zero_nat) (exists ((J_2 tptp.nat)) (and (= M (@ tptp.suc J_2)) (@ (@ tptp.ord_less_nat J_2) N_5)))))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N_5)) (or (@ _let_1 M) (@ _let_1 N_5))))))
% 0.51/0.77 (assert (forall ((X_21 tptp.nat) (Xs_46 tptp.list_nat) (N_32 tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X_21) Xs_46)) (@ tptp.suc N_32)) (@ (@ tptp.nth_nat Xs_46) N_32))))
% 0.51/0.77 (assert (forall ((X_21 tptp.arrow_475358991le_alt) (Xs_46 tptp.list_A2115238852le_alt) (N_32 tptp.nat)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_21) Xs_46)) (@ tptp.suc N_32)) (@ (@ tptp.nth_Ar125878976le_alt Xs_46) N_32))))
% 0.51/0.77 (assert (forall ((Xs_45 tptp.list_A2115238852le_alt) (Ys_8 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ tptp.append179082452le_alt Xs_45) Ys_8)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1858781230le_alt Xs_45)) (@ tptp.size_s1858781230le_alt Ys_8)))))
% 0.51/0.77 (assert (forall ((N_31 tptp.nat) (X_20 tptp.arrow_475358991le_alt) (Xs_44 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc N_31)) (@ (@ tptp.cons_A228743023le_alt X_20) Xs_44)) (@ (@ tptp.drop_A1346709759le_alt N_31) Xs_44))))
% 0.51/0.77 (assert (forall ((X_19 tptp.arrow_475358991le_alt) (Xs_43 tptp.list_A2115238852le_alt) (I_10 tptp.nat) (Y_4 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_19))) (= (@ (@ (@ tptp.list_u62477863le_alt (@ _let_1 Xs_43)) (@ tptp.suc I_10)) Y_4) (@ _let_1 (@ (@ (@ tptp.list_u62477863le_alt Xs_43) I_10) Y_4))))))
% 0.51/0.77 (assert (forall ((N_30 tptp.nat) (X_18 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.replic1511538809le_alt (@ tptp.suc N_30)) X_18) (@ (@ tptp.cons_A228743023le_alt X_18) (@ (@ tptp.replic1511538809le_alt N_30) X_18)))))
% 0.51/0.77 (assert (forall ((N_29 tptp.nat) (M_3 tptp.nat) (X_17 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.replic1511538809le_alt (@ (@ tptp.plus_plus_nat N_29) M_3)) X_17) (@ (@ tptp.append179082452le_alt (@ (@ tptp.replic1511538809le_alt N_29) X_17)) (@ (@ tptp.replic1511538809le_alt M_3) X_17)))))
% 0.51/0.77 (assert (forall ((N_28 tptp.nat) (Xs_42 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc N_28)) Xs_42) (@ (@ tptp.drop_A1346709759le_alt N_28) (@ tptp.tl_Arr465451158le_alt Xs_42)))))
% 0.51/0.77 (assert (forall ((Xs_41 tptp.list_A2115238852le_alt) (Ys_7 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ tptp.splice1520898450le_alt Xs_41) Ys_7)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1858781230le_alt Xs_41)) (@ tptp.size_s1858781230le_alt Ys_7)))))
% 0.51/0.77 (assert (forall ((Xs_40 tptp.list_nat) (Ys_6 tptp.list_nat) (N_27 tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.append_nat Xs_40) Ys_6)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat Xs_40)) N_27)) (@ (@ tptp.nth_nat Ys_6) N_27))))
% 0.51/0.77 (assert (forall ((Xs_40 tptp.list_A2115238852le_alt) (Ys_6 tptp.list_A2115238852le_alt) (N_27 tptp.nat)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.append179082452le_alt Xs_40) Ys_6)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1858781230le_alt Xs_40)) N_27)) (@ (@ tptp.nth_Ar125878976le_alt Ys_6) N_27))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N_5) (exists ((K_5 tptp.nat)) (= N_5 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_5)))))))
% 0.51/0.77 (assert (forall ((Xs_39 tptp.list_A2115238852le_alt) (N_26 tptp.nat)) (= (= (@ tptp.size_s1858781230le_alt Xs_39) (@ tptp.suc N_26)) (exists ((Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (and (= Xs_39 (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5)) (= (@ tptp.size_s1858781230le_alt Ys_5) N_26))))))
% 0.51/0.77 (assert (forall ((N_25 tptp.nat) (Xs_38 tptp.list_A2115238852le_alt)) (= (= (@ tptp.suc N_25) (@ tptp.size_s1858781230le_alt Xs_38)) (exists ((Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (and (= Xs_38 (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5)) (= (@ tptp.size_s1858781230le_alt Ys_5) N_25))))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K_5 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_5) (= (@ (@ tptp.plus_plus_nat I) K_5) J))))))
% 0.51/0.77 (assert (forall ((C_16 tptp.int) (A_35 (-> tptp.int Bool)) (B_20 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_16))) (=> (@ (@ tptp.ord_less_int_o A_35) B_20) (=> (@ _let_1 A_35) (@ _let_1 B_20))))))
% 0.51/0.77 (assert (forall ((C_16 tptp.nat) (A_35 (-> tptp.nat Bool)) (B_20 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_16))) (=> (@ (@ tptp.ord_less_nat_o A_35) B_20) (=> (@ _let_1 A_35) (@ _let_1 B_20))))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (exists ((M_1 tptp.nat)) (= N_5 (@ tptp.suc M_1))))))
% 0.51/0.77 (assert (forall ((N_24 tptp.nat) (N_23 tptp.nat) (F_1 (-> tptp.nat tptp.nat))) (=> (forall ((N_7 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F_1 N_7)) (@ F_1 (@ tptp.suc N_7)))) (=> (@ (@ tptp.ord_less_nat N_24) N_23) (@ (@ tptp.ord_less_nat (@ F_1 N_24)) (@ F_1 N_23))))))
% 0.51/0.77 (assert (forall ((N_22 tptp.nat) (M_2 tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((N_7 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N_7)) (@ F (@ tptp.suc N_7)))) (= (@ (@ tptp.ord_less_nat (@ F N_22)) (@ F M_2)) (@ (@ tptp.ord_less_nat N_22) M_2)))))
% 0.51/0.77 (assert (forall ((A_34 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_34) A_34)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_34) tptp.zero_zero_int))))
% 0.51/0.77 (assert (forall ((B_19 tptp.int) (C_15 tptp.int) (A_33 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B_19))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_33) (=> (@ _let_1 C_15) (@ _let_1 (@ (@ tptp.plus_plus_int A_33) C_15)))))))
% 0.51/0.77 (assert (forall ((B_19 tptp.nat) (C_15 tptp.nat) (A_33 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B_19))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_33) (=> (@ _let_1 C_15) (@ _let_1 (@ (@ tptp.plus_plus_nat A_33) C_15)))))))
% 0.51/0.77 (assert (forall ((A_32 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A_32) A_32) tptp.zero_zero_int) (= A_32 tptp.zero_zero_int))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K_3) (=> (not (= K_3 (@ tptp.suc I))) (not (forall ((J_2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_2) (not (= K_3 (@ tptp.suc J_2))))))))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K_3) (not (forall ((J_2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_2) (not (= K_3 (@ tptp.suc J_2)))))))))
% 0.51/0.77 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat tptp.nat)) (not (= Y (@ tptp.suc Nat))))))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (=> (not (= N_5 tptp.zero_zero_nat)) (exists ((M_1 tptp.nat)) (= N_5 (@ tptp.suc M_1))))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N_7 tptp.nat)) (=> (@ P N_7) (@ P (@ tptp.suc N_7)))) (@ P N_5)))))
% 0.51/0.77 (assert (forall ((P (-> tptp.nat Bool)) (K_3 tptp.nat)) (=> (@ P K_3) (=> (forall ((N_7 tptp.nat)) (=> (@ P (@ tptp.suc N_7)) (@ P N_7))) (@ P tptp.zero_zero_nat)))))
% 0.51/0.77 (assert (forall ((N_21 tptp.nat) (Xs_37 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat N_21) (@ tptp.size_s1858781230le_alt Xs_37)) (= (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt N_21) Xs_37)) (@ (@ tptp.cons_A228743023le_alt (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.drop_A1346709759le_alt N_21) Xs_37))) tptp.nil_Ar1286194111le_alt)) (@ (@ tptp.take_A614047655le_alt (@ tptp.suc N_21)) Xs_37)))))
% 0.51/0.77 (assert (forall ((N_20 tptp.nat) (Xs_36 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.take_A614047655le_alt N_20) (@ tptp.tl_Arr465451158le_alt Xs_36)) (@ tptp.tl_Arr465451158le_alt (@ (@ tptp.take_A614047655le_alt (@ tptp.suc N_20)) Xs_36)))))
% 0.51/0.77 (assert (forall ((N_19 tptp.nat)) (= (@ (@ tptp.take_A614047655le_alt N_19) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((I_9 tptp.nat) (Xs_35 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_35) (@ tptp.distin236324274le_alt (@ (@ tptp.take_A614047655le_alt I_9) Xs_35)))))
% 0.51/0.77 (assert (forall ((P_2 (-> tptp.arrow_475358991le_alt Bool)) (Xs_34 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.takeWh1696291512le_alt P_2) Xs_34))) (= _let_1 (@ (@ tptp.take_A614047655le_alt (@ tptp.size_s1858781230le_alt _let_1)) Xs_34)))))
% 0.51/0.77 (assert (forall ((N_18 tptp.nat) (Xs_33 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt N_18) Xs_33)) (@ (@ tptp.drop_A1346709759le_alt N_18) Xs_33)) Xs_33)))
% 0.51/0.77 (assert (forall ((N_17 tptp.nat) (X_16 tptp.arrow_475358991le_alt) (Xs_32 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_16))) (= (@ (@ tptp.take_A614047655le_alt (@ tptp.suc N_17)) (@ _let_1 Xs_32)) (@ _let_1 (@ (@ tptp.take_A614047655le_alt N_17) Xs_32))))))
% 0.51/0.77 (assert (forall ((N_16 tptp.nat) (Xs_31 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.take_A614047655le_alt N_16) Xs_31) tptp.nil_Ar1286194111le_alt) (or (= N_16 tptp.zero_zero_nat) (= Xs_31 tptp.nil_Ar1286194111le_alt)))))
% 0.51/0.77 (assert (forall ((Xs_30 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.take_A614047655le_alt tptp.zero_zero_nat) Xs_30) tptp.nil_Ar1286194111le_alt)))
% 0.51/0.77 (assert (forall ((Xs_29 tptp.list_A2115238852le_alt) (Ys_4 tptp.list_A2115238852le_alt) (Zs tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt Xs_29))) (= (= (@ (@ tptp.append179082452le_alt Xs_29) Ys_4) Zs) (and (= Xs_29 (@ (@ tptp.take_A614047655le_alt _let_1) Zs)) (= Ys_4 (@ (@ tptp.drop_A1346709759le_alt _let_1) Zs)))))))
% 0.51/0.77 (assert (forall ((I_8 tptp.nat) (J_1 tptp.nat) (Xs_28 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.plus_plus_nat I_8) J_1)) Xs_28) (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt I_8) Xs_28)) (@ (@ tptp.take_A614047655le_alt J_1) (@ (@ tptp.drop_A1346709759le_alt I_8) Xs_28))))))
% 0.51/0.77 (assert (forall ((N_15 tptp.nat) (Xs_27 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.take_A614047655le_alt N_15))) (=> (@ (@ tptp.ord_less_nat N_15) (@ tptp.size_s1858781230le_alt Xs_27)) (= (@ _let_1 (@ tptp.butlas274947851le_alt Xs_27)) (@ _let_1 Xs_27))))))
% 0.51/0.77 (assert (forall ((N_14 tptp.nat) (Xs_26 tptp.list_A2115238852le_alt)) (=> (not (= Xs_26 tptp.nil_Ar1286194111le_alt)) (= (@ (@ tptp.take_A614047655le_alt (@ tptp.suc N_14)) Xs_26) (@ (@ tptp.cons_A228743023le_alt (@ tptp.hd_Arr1965683346le_alt Xs_26)) (@ (@ tptp.take_A614047655le_alt N_14) (@ tptp.tl_Arr465451158le_alt Xs_26)))))))
% 0.51/0.77 (assert (forall ((I_7 tptp.nat) (Xs_25 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_7) (@ tptp.size_s1858781230le_alt Xs_25)) (= (@ (@ tptp.take_A614047655le_alt (@ tptp.suc I_7)) Xs_25) (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt I_7) Xs_25)) (@ (@ tptp.cons_A228743023le_alt (@ (@ tptp.nth_Ar125878976le_alt Xs_25) I_7)) tptp.nil_Ar1286194111le_alt))))))
% 0.51/0.77 (assert (forall ((I_6 tptp.nat) (Xs_24 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_6) (@ tptp.size_s1858781230le_alt Xs_24)) (= Xs_24 (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt I_6) Xs_24)) (@ (@ tptp.cons_A228743023le_alt (@ (@ tptp.nth_Ar125878976le_alt Xs_24) I_6)) (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc I_6)) Xs_24)))))))
% 0.51/0.77 (assert (forall ((A_31 tptp.arrow_475358991le_alt) (I_5 tptp.nat) (Xs_23 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_5) (@ tptp.size_s1858781230le_alt Xs_23)) (= (@ (@ (@ tptp.list_u62477863le_alt Xs_23) I_5) A_31) (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt I_5) Xs_23)) (@ (@ tptp.cons_A228743023le_alt A_31) (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc I_5)) Xs_23)))))))
% 0.51/0.77 (assert (forall ((P_1 (-> tptp.arrow_475358991le_alt Bool)) (Xs_22 tptp.list_A2115238852le_alt) (N_13 tptp.nat)) (=> (forall ((I_4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_4))) (=> (@ _let_1 N_13) (=> (@ _let_1 (@ tptp.size_s1858781230le_alt Xs_22)) (@ P_1 (@ (@ tptp.nth_Ar125878976le_alt Xs_22) I_4)))))) (=> (=> (@ (@ tptp.ord_less_nat N_13) (@ tptp.size_s1858781230le_alt Xs_22)) (not (@ P_1 (@ (@ tptp.nth_Ar125878976le_alt Xs_22) N_13)))) (= (@ (@ tptp.takeWh1696291512le_alt P_1) Xs_22) (@ (@ tptp.take_A614047655le_alt N_13) Xs_22))))))
% 0.51/0.77 (assert (forall ((Z_1 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z_1))))))
% 0.51/0.77 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z_1) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z_1))))))
% 0.51/0.77 (assert (forall ((A_30 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_30) A_30)))
% 0.51/0.77 (assert (forall ((A_30 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_30) A_30)))
% 0.51/0.77 (assert (forall ((A_29 tptp.int)) (= (@ (@ tptp.plus_plus_int A_29) tptp.zero_zero_int) A_29)))
% 0.51/0.77 (assert (forall ((A_29 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_29) tptp.zero_zero_nat) A_29)))
% 0.51/0.77 (assert (forall ((A_28 tptp.int) (B_18 tptp.int) (C_14 tptp.int) (D_5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_28))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_18)) (@ (@ tptp.plus_plus_int C_14) D_5)) (@ (@ tptp.plus_plus_int (@ _let_1 C_14)) (@ (@ tptp.plus_plus_int B_18) D_5))))))
% 0.51/0.77 (assert (forall ((A_28 tptp.nat) (B_18 tptp.nat) (C_14 tptp.nat) (D_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_28))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_18)) (@ (@ tptp.plus_plus_nat C_14) D_5)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_14)) (@ (@ tptp.plus_plus_nat B_18) D_5))))))
% 0.51/0.77 (assert (forall ((A_27 tptp.int) (B_17 tptp.int) (C_13 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_27))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_17)) C_13) (@ (@ tptp.plus_plus_int (@ _let_1 C_13)) B_17)))))
% 0.51/0.77 (assert (forall ((A_27 tptp.nat) (B_17 tptp.nat) (C_13 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_27))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_17)) C_13) (@ (@ tptp.plus_plus_nat (@ _let_1 C_13)) B_17)))))
% 0.51/0.77 (assert (forall ((A_26 tptp.int) (B_16 tptp.int) (C_12 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_26))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_16)) C_12) (@ _let_1 (@ (@ tptp.plus_plus_int B_16) C_12))))))
% 0.51/0.77 (assert (forall ((A_26 tptp.nat) (B_16 tptp.nat) (C_12 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_26))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_16)) C_12) (@ _let_1 (@ (@ tptp.plus_plus_nat B_16) C_12))))))
% 0.51/0.77 (assert (forall ((A_25 tptp.int) (C_11 tptp.int) (D_4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_25))) (= (@ _let_1 (@ (@ tptp.plus_plus_int C_11) D_4)) (@ (@ tptp.plus_plus_int (@ _let_1 C_11)) D_4)))))
% 0.51/0.77 (assert (forall ((A_25 tptp.nat) (C_11 tptp.nat) (D_4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_25))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat C_11) D_4)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_11)) D_4)))))
% 0.51/0.77 (assert (forall ((A_24 tptp.int) (C_10 tptp.int) (D_3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_24))) (let ((_let_2 (@ tptp.plus_plus_int C_10))) (= (@ _let_1 (@ _let_2 D_3)) (@ _let_2 (@ _let_1 D_3)))))))
% 0.51/0.77 (assert (forall ((A_24 tptp.nat) (C_10 tptp.nat) (D_3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_24))) (let ((_let_2 (@ tptp.plus_plus_nat C_10))) (= (@ _let_1 (@ _let_2 D_3)) (@ _let_2 (@ _let_1 D_3)))))))
% 0.51/0.77 (assert (forall ((A_23 tptp.int) (C_9 tptp.int)) (= (@ (@ tptp.plus_plus_int A_23) C_9) (@ (@ tptp.plus_plus_int C_9) A_23))))
% 0.51/0.77 (assert (forall ((A_23 tptp.nat) (C_9 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_23) C_9) (@ (@ tptp.plus_plus_nat C_9) A_23))))
% 0.51/0.77 (assert (forall ((B_15 tptp.int) (A_22 tptp.int)) (= (= B_15 (@ (@ tptp.plus_plus_int B_15) A_22)) (= A_22 tptp.zero_zero_int))))
% 0.51/0.77 (assert (forall ((B_15 tptp.nat) (A_22 tptp.nat)) (= (= B_15 (@ (@ tptp.plus_plus_nat B_15) A_22)) (= A_22 tptp.zero_zero_nat))))
% 0.51/0.77 (assert (forall ((N_12 tptp.nat) (Xs_21 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt Xs_21))) (=> (@ (@ tptp.ord_less_nat N_12) _let_1) (= (@ (@ tptp.nth_Ar125878976le_alt (@ tptp.rev_Ar1106406943le_alt Xs_21)) N_12) (@ (@ tptp.nth_Ar125878976le_alt Xs_21) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N_12))))))))
% 0.51/0.77 (assert (forall ((I_3 tptp.nat) (K_4 tptp.nat) (X_15 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt I_3) (@ (@ tptp.replic1511538809le_alt K_4) X_15)) (@ (@ tptp.replic1511538809le_alt (@ (@ tptp.minus_minus_nat K_4) I_3)) X_15))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (K_3 tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K_3)) (@ (@ tptp.plus_plus_nat N_5) K_3)) (@ (@ tptp.minus_minus_nat M) N_5))))
% 0.51/0.77 (assert (forall ((K_3 tptp.nat) (M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K_3))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N_5)) (@ (@ tptp.minus_minus_nat M) N_5)))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (J tptp.nat) (K_3 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K_3) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K_3))))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N_5) M)) N_5) M)))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N_5)) N_5) M)))
% 0.51/0.77 (assert (forall ((A_21 tptp.int) (B_14 tptp.int) (C_8 tptp.int) (D_2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_21) B_14) (@ (@ tptp.minus_minus_int C_8) D_2)) (= (@ (@ tptp.ord_less_int A_21) B_14) (@ (@ tptp.ord_less_int C_8) D_2)))))
% 0.51/0.77 (assert (forall ((A_20 tptp.int) (B_13 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_20) B_13)) B_13) A_20)))
% 0.51/0.77 (assert (forall ((A_19 tptp.int) (B_12 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_19) B_12)) B_12) A_19)))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat) (J tptp.nat) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K_3) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N_5)) K_3))))
% 0.51/0.77 (assert (forall ((L tptp.nat) (M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N_5) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N_5)) (@ _let_1 M))))))))
% 0.51/0.77 (assert (forall ((A_18 tptp.int) (B_11 tptp.int)) (= (@ (@ tptp.ord_less_int A_18) B_11) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A_18) B_11)) tptp.zero_zero_int))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N_5) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N_5)) M))))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N_5) M)) (@ (@ tptp.ord_less_nat M) N_5))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N_5)) (@ tptp.suc M))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N_5) (@ (@ tptp.plus_plus_nat N_5) M)) tptp.zero_zero_nat)))
% 0.51/0.77 (assert (forall ((I tptp.nat) (J tptp.nat) (K_3 tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K_3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K_3)) J))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N_5)) (= (@ (@ tptp.plus_plus_nat N_5) (@ (@ tptp.minus_minus_nat M) N_5)) M))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (J tptp.nat) (K_3 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K_3) (@ (@ tptp.minus_minus_nat (@ _let_1 K_3)) J)))))
% 0.51/0.77 (assert (forall ((X_14 tptp.int) (Y_2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X_14) Y_2)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X_14) Z)) (@ (@ tptp.minus_minus_int Y_2) Z)))))
% 0.51/0.77 (assert (forall ((A_17 tptp.int) (B_10 tptp.int) (C_7 tptp.int) (D_1 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_17) B_10) (@ (@ tptp.minus_minus_int C_7) D_1)) (= (= A_17 B_10) (= C_7 D_1)))))
% 0.51/0.77 (assert (forall ((A_16 tptp.int)) (= (@ (@ tptp.minus_minus_int A_16) tptp.zero_zero_int) A_16)))
% 0.51/0.77 (assert (forall ((A_15 tptp.int)) (= (@ (@ tptp.minus_minus_int A_15) A_15) tptp.zero_zero_int)))
% 0.51/0.77 (assert (forall ((A_14 tptp.int) (B_9 tptp.int)) (= (= A_14 B_9) (= (@ (@ tptp.minus_minus_int A_14) B_9) tptp.zero_zero_int))))
% 0.51/0.77 (assert (forall ((A_13 tptp.int) (B_8 tptp.int)) (= (= (@ (@ tptp.minus_minus_int A_13) B_8) tptp.zero_zero_int) (= A_13 B_8))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N_5) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N_5) M) tptp.zero_zero_nat) (= M N_5)))))
% 0.51/0.77 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 0.51/0.77 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N_5) tptp.zero_zero_nat)))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N_5)) (@ (@ tptp.minus_minus_nat M) N_5))))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat) (K_3 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N_5)) (@ tptp.suc K_3)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N_5)) K_3))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N_5) M)) M) (@ (@ tptp.ord_max_nat N_5) M))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N_5) (@ tptp.suc I))) N_5))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N_5) (@ tptp.suc tptp.zero_zero_nat))) N_5))))
% 0.51/0.77 (assert (forall ((P (-> tptp.nat Bool)) (A_12 tptp.nat) (B_7 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A_12) B_7)) (and (=> (@ (@ tptp.ord_less_nat A_12) B_7) (@ P tptp.zero_zero_nat)) (forall ((D tptp.nat)) (=> (= A_12 (@ (@ tptp.plus_plus_nat B_7) D)) (@ P D)))))))
% 0.51/0.77 (assert (forall ((P (-> tptp.nat Bool)) (A_12 tptp.nat) (B_7 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A_12) B_7)) (not (or (and (@ (@ tptp.ord_less_nat A_12) B_7) (not (@ P tptp.zero_zero_nat))) (exists ((D tptp.nat)) (and (= A_12 (@ (@ tptp.plus_plus_nat B_7) D)) (not (@ P D)))))))))
% 0.51/0.77 (assert (forall ((N_11 tptp.nat) (Xs_20 tptp.list_A2115238852le_alt) (Ys_3 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.take_A614047655le_alt N_11))) (= (@ _let_1 (@ (@ tptp.append179082452le_alt Xs_20) Ys_3)) (@ (@ tptp.append179082452le_alt (@ _let_1 Xs_20)) (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat N_11) (@ tptp.size_s1858781230le_alt Xs_20))) Ys_3))))))
% 0.51/0.77 (assert (forall ((N_10 tptp.nat) (Xs_19 tptp.list_A2115238852le_alt) (Ys_2 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.drop_A1346709759le_alt N_10))) (= (@ _let_1 (@ (@ tptp.append179082452le_alt Xs_19) Ys_2)) (@ (@ tptp.append179082452le_alt (@ _let_1 Xs_19)) (@ (@ tptp.drop_A1346709759le_alt (@ (@ tptp.minus_minus_nat N_10) (@ tptp.size_s1858781230le_alt Xs_19))) Ys_2))))))
% 0.51/0.77 (assert (forall ((Ys_1 tptp.list_A2115238852le_alt) (N_9 tptp.nat) (Xs_18 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt Xs_18))) (let ((_let_2 (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.append179082452le_alt Xs_18) Ys_1)) N_9))) (let ((_let_3 (@ (@ tptp.ord_less_nat N_9) _let_1))) (and (=> _let_3 (= _let_2 (@ (@ tptp.nth_Ar125878976le_alt Xs_18) N_9))) (=> (not _let_3) (= _let_2 (@ (@ tptp.nth_Ar125878976le_alt Ys_1) (@ (@ tptp.minus_minus_nat N_9) _let_1))))))))))
% 0.51/0.77 (assert (forall ((Ys tptp.list_A2115238852le_alt) (X_13 tptp.arrow_475358991le_alt) (N_8 tptp.nat) (Xs_17 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt Xs_17))) (let ((_let_2 (@ tptp.append179082452le_alt Xs_17))) (let ((_let_3 (@ (@ (@ tptp.list_u62477863le_alt (@ _let_2 Ys)) N_8) X_13))) (let ((_let_4 (@ (@ tptp.ord_less_nat N_8) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.append179082452le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_17) N_8) X_13)) Ys))) (=> (not _let_4) (= _let_3 (@ _let_2 (@ (@ (@ tptp.list_u62477863le_alt Ys) (@ (@ tptp.minus_minus_nat N_8) _let_1)) X_13)))))))))))
% 0.51/0.77 (assert (forall ((I_2 tptp.nat) (Xs_16 tptp.list_A2115238852le_alt)) (= (@ tptp.rev_Ar1106406943le_alt (@ (@ tptp.drop_A1346709759le_alt I_2) Xs_16)) (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_16)) I_2)) (@ tptp.rev_Ar1106406943le_alt Xs_16)))))
% 0.51/0.77 (assert (forall ((I_1 tptp.nat) (Xs_15 tptp.list_A2115238852le_alt)) (= (@ tptp.rev_Ar1106406943le_alt (@ (@ tptp.take_A614047655le_alt I_1) Xs_15)) (@ (@ tptp.drop_A1346709759le_alt (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_15)) I_1)) (@ tptp.rev_Ar1106406943le_alt Xs_15)))))
% 0.51/0.77 (assert (forall ((I tptp.nat) (P (-> tptp.nat Bool)) (K_3 tptp.nat)) (=> (@ P K_3) (=> (forall ((N_7 tptp.nat)) (=> (@ P (@ tptp.suc N_7)) (@ P N_7))) (@ P (@ (@ tptp.minus_minus_nat K_3) I))))))
% 0.51/0.77 (assert (forall ((X_12 tptp.arrow_475358991le_alt) (K_2 tptp.nat) (Xs_14 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.last_A1217315288le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_14) K_2) X_12)))) (let ((_let_2 (= K_2 (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_14)) tptp.one_one_nat)))) (=> (not (= Xs_14 tptp.nil_Ar1286194111le_alt)) (and (=> _let_2 (= _let_1 X_12)) (=> (not _let_2) (= _let_1 (@ tptp.last_A1217315288le_alt Xs_14)))))))))
% 0.51/0.77 (assert (forall ((A_11 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o tptp.bot_bot_nat_o) A_11) tptp.bot_bot_nat_o)))
% 0.51/0.77 (assert (forall ((A_10 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_10) tptp.bot_bot_nat_o) A_10)))
% 0.51/0.77 (assert (forall ((A_9 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_9) A_9) tptp.bot_bot_nat_o)))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N_5)) tptp.one_one_nat) N_5)))
% 0.51/0.77 (assert (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N_5)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N_5)))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (= (@ tptp.suc N_5) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) N_5))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (= (@ tptp.suc N_5) (@ (@ tptp.plus_plus_nat N_5) tptp.one_one_nat))))
% 0.51/0.77 (assert (forall ((X_11 tptp.arrow_475358991le_alt) (Xs_13 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt tptp.one_one_nat) (@ (@ tptp.cons_A228743023le_alt X_11) Xs_13)) Xs_13)))
% 0.51/0.77 (assert (forall ((X_10 tptp.nat)) (= (= tptp.one_one_nat X_10) (= X_10 tptp.one_one_nat))))
% 0.51/0.77 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 0.51/0.77 (assert (forall ((A_8 tptp.nat)) (@ (@ tptp.ord_less_nat A_8) (@ (@ tptp.plus_plus_nat A_8) tptp.one_one_nat))))
% 0.51/0.77 (assert (forall ((A_8 tptp.int)) (@ (@ tptp.ord_less_int A_8) (@ (@ tptp.plus_plus_int A_8) tptp.one_one_int))))
% 0.51/0.77 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 0.51/0.77 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 0.51/0.77 (assert (not (= tptp.one_one_nat tptp.zero_zero_nat)))
% 0.51/0.77 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 0.51/0.77 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 0.51/0.77 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 0.51/0.77 (assert (forall ((X_9 tptp.arrow_475358991le_alt) (Xs_12 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_9))) (= (@ (@ tptp.take_A614047655le_alt tptp.one_one_nat) (@ _let_1 Xs_12)) (@ _let_1 tptp.nil_Ar1286194111le_alt)))))
% 0.51/0.77 (assert (forall ((Xs_11 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ tptp.butlas274947851le_alt Xs_11)) (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_11)) tptp.one_one_nat))))
% 0.51/0.77 (assert (forall ((Xs_10 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ tptp.tl_Arr465451158le_alt Xs_10)) (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_10)) tptp.one_one_nat))))
% 0.51/0.77 (assert (forall ((N_6 tptp.nat) (Xs_9 tptp.list_A2115238852le_alt)) (= (@ tptp.tl_Arr465451158le_alt (@ (@ tptp.take_A614047655le_alt N_6) Xs_9)) (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat N_6) tptp.one_one_nat)) (@ tptp.tl_Arr465451158le_alt Xs_9)))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (= N_5 (@ tptp.suc (@ (@ tptp.minus_minus_nat N_5) tptp.one_one_nat))))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N_5) tptp.one_one_nat)) N_5))))
% 0.51/0.77 (assert (forall ((N_5 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N_5))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 N_5)) (=> (not _let_2) (= _let_1 (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N_5)))))))))
% 0.51/0.77 (assert (forall ((X_8 tptp.arrow_475358991le_alt) (Xs_8 tptp.list_A2115238852le_alt) (N_4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_8) Xs_8)) N_4))) (let ((_let_2 (= N_4 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X_8)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_Ar125878976le_alt Xs_8) (@ (@ tptp.minus_minus_nat N_4) tptp.one_one_nat)))))))))
% 0.51/0.77 (assert (forall ((X_7 tptp.arrow_475358991le_alt) (Xs_7 tptp.list_A2115238852le_alt) (N_3 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_7) Xs_7))) (let ((_let_2 (@ (@ tptp.drop_A1346709759le_alt N_3) _let_1))) (let ((_let_3 (= N_3 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.drop_A1346709759le_alt (@ (@ tptp.minus_minus_nat N_3) tptp.one_one_nat)) Xs_7)))))))))
% 0.51/0.77 (assert (forall ((Xs_6 tptp.list_A2115238852le_alt)) (= (@ tptp.butlas274947851le_alt Xs_6) (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_6)) tptp.one_one_nat)) Xs_6))))
% 0.51/0.77 (assert (forall ((X_6 tptp.arrow_475358991le_alt) (K_1 tptp.nat) (Xs_5 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.butlas274947851le_alt Xs_5))) (let ((_let_2 (@ tptp.butlas274947851le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_5) K_1) X_6)))) (let ((_let_3 (= K_1 (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_5)) tptp.one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ tptp.list_u62477863le_alt _let_1) K_1) X_6)))))))))
% 0.51/0.77 (assert (forall ((X_5 tptp.arrow_475358991le_alt) (N_2 tptp.nat)) (=> (not (= N_2 tptp.zero_zero_nat)) (= (@ tptp.tl_Arr465451158le_alt (@ (@ tptp.replic1511538809le_alt N_2) X_5)) (@ (@ tptp.replic1511538809le_alt (@ (@ tptp.minus_minus_nat N_2) tptp.one_one_nat)) X_5)))))
% 0.51/0.77 (assert (forall ((X_4 tptp.arrow_475358991le_alt) (Xs_4 tptp.list_A2115238852le_alt) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_1) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_4) Xs_4)) N_1) (@ (@ tptp.nth_Ar125878976le_alt Xs_4) (@ (@ tptp.minus_minus_nat N_1) tptp.one_one_nat))))))
% 0.51/0.77 (assert (forall ((X_3 tptp.arrow_475358991le_alt) (Xs_3 tptp.list_A2115238852le_alt) (N tptp.nat)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_3))) (let ((_let_2 (@ (@ tptp.take_A614047655le_alt N) (@ _let_1 Xs_3)))) (let ((_let_3 (= N tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.nil_Ar1286194111le_alt)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Xs_3))))))))))
% 0.51/0.77 (assert (forall ((Y_1 tptp.arrow_475358991le_alt) (K tptp.nat) (Xs_2 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt Xs_2))) (=> (@ (@ tptp.ord_less_nat K) _let_1) (= (@ tptp.rev_Ar1106406943le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_2) K) Y_1)) (@ (@ (@ tptp.list_u62477863le_alt (@ tptp.rev_Ar1106406943le_alt Xs_2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat _let_1) K)) tptp.one_one_nat)) Y_1))))))
% 0.51/0.77 (assert (forall ((Xs_1 tptp.list_A2115238852le_alt)) (=> (not (= Xs_1 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.last_A1217315288le_alt Xs_1) (@ (@ tptp.nth_Ar125878976le_alt Xs_1) (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_1)) tptp.one_one_nat))))))
% 0.51/0.77 (assert (forall ((X_2 tptp.arrow_475358991le_alt) (Xs tptp.list_A2115238852le_alt) (V_2 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_2))) (let ((_let_2 (@ tptp.cons_A228743023le_alt X_2))) (let ((_let_3 (@ (@ tptp.take_A614047655le_alt _let_1) (@ _let_2 Xs)))) (let ((_let_4 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 tptp.nil_Ar1286194111le_alt)) (=> (not _let_4) (= _let_3 (@ _let_2 (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat)) Xs)))))))))))
% 0.51/0.77 (assert (forall ((A_7 tptp.int)) (=> (@ (@ tptp.member_int A_7) tptp.ring_1_Ints_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A_7)) A_7)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_7) tptp.zero_zero_int)))))
% 0.51/0.77 (assert (forall ((C_6 tptp.nat) (A_6 (-> tptp.nat Bool)) (B_6 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_6))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_6) B_6)) (not (=> (@ _let_1 A_6) (@ _let_1 B_6)))))))
% 159.65/160.01 (assert (forall ((B_5 (-> tptp.nat Bool)) (C_5 tptp.nat) (A_5 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_5))) (=> (@ _let_1 A_5) (=> (not (@ _let_1 B_5)) (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_5) B_5)))))))
% 159.65/160.01 (assert (forall ((B_4 tptp.int) (A_4 tptp.int)) (=> (@ (@ tptp.member_int A_4) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B_4) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int A_4) B_4)) tptp.ring_1_Ints_int)))))
% 159.65/160.01 (assert (forall ((V_1 tptp.int) (W_1 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.minus_minus_int V_1) W_1)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int V_1)) (@ tptp.number_number_of_int W_1)))))
% 159.65/160.01 (assert (forall ((V tptp.int) (W tptp.int) (C_4 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int W)) C_4)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V) W))) C_4))))
% 159.65/160.01 (assert (forall ((C_3 tptp.nat) (A_3 (-> tptp.nat Bool)) (B_3 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_3))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_3) B_3)) (not (@ _let_1 B_3))))))
% 159.65/160.01 (assert (forall ((C_2 tptp.nat) (A_2 (-> tptp.nat Bool)) (B_2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_2) B_2)) (@ _let_1 A_2)))))
% 159.65/160.01 (assert (forall ((C_1 tptp.nat) (A_1 (-> tptp.nat Bool)) (B_1 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_1))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_1) B_1)) (and (@ _let_1 A_1) (not (@ _let_1 B_1)))))))
% 159.65/160.01 (assert (forall ((A (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A) B) (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X_1))) (and (@ _let_1 A) (not (@ _let_1 B)))))))))
% 159.65/160.01 (assert (forall ((X tptp.list_A2115238852le_alt) (Y tptp.list_A2115238852le_alt)) (or (not (@ (@ tptp.fequal781288069le_alt X) Y)) (= X Y))))
% 159.65/160.01 (assert (forall ((X tptp.list_A2115238852le_alt) (Y tptp.list_A2115238852le_alt)) (or (not (= X Y)) (@ (@ tptp.fequal781288069le_alt X) Y))))
% 159.65/160.01 (assert (not (= tptp.a tptp.b)))
% 159.65/160.01 (assert (not (exists ((C tptp.arrow_475358991le_alt)) (@ tptp.distin236324274le_alt (@ (@ tptp.cons_A228743023le_alt tptp.a) (@ (@ tptp.cons_A228743023le_alt tptp.b) (@ (@ tptp.cons_A228743023le_alt C) tptp.nil_Ar1286194111le_alt)))))))
% 159.65/160.01 (set-info :filename cvc5---1.0.5_19231)
% 159.65/160.01 (check-sat-assuming ( true ))
% 159.65/160.01 ------- get file name : TPTP file name is SCT169^2
% 159.65/160.01 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19231.smt2...
% 159.65/160.01 --- Run --ho-elim --full-saturate-quant at 10...
% 159.65/160.01 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 159.65/160.01 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 159.65/160.01 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 159.65/160.01 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 159.65/160.01 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 159.65/160.01 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 159.65/160.01 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 159.65/160.01 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 159.65/160.01 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 159.65/160.01 % SZS status Theorem for SCT169^2
% 159.65/160.01 % SZS output start Proof for SCT169^2
% 159.65/160.01 (
% 159.65/160.01 (let ((_let_1 (not (exists ((C tptp.arrow_475358991le_alt)) (@ tptp.distin236324274le_alt (@ (@ tptp.cons_A228743023le_alt tptp.a) (@ (@ tptp.cons_A228743023le_alt tptp.b) (@ (@ tptp.cons_A228743023le_alt C) tptp.nil_Ar1286194111le_alt)))))))) (let ((_let_2 (= tptp.a tptp.b))) (let ((_let_3 (not _let_2))) (let ((_let_4 (forall ((Xs_1 tptp.list_A2115238852le_alt)) (=> (not (= Xs_1 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.last_A1217315288le_alt Xs_1) (@ (@ tptp.nth_Ar125878976le_alt Xs_1) (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_1)) tptp.one_one_nat))))))) (let ((_let_5 (forall ((X_3 tptp.arrow_475358991le_alt) (Xs_3 tptp.list_A2115238852le_alt) (N tptp.nat)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_3))) (let ((_let_2 (@ (@ tptp.take_A614047655le_alt N) (@ _let_1 Xs_3)))) (let ((_let_3 (= N tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.nil_Ar1286194111le_alt)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Xs_3))))))))))) (let ((_let_6 (forall ((Xs_6 tptp.list_A2115238852le_alt)) (= (@ tptp.butlas274947851le_alt Xs_6) (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_6)) tptp.one_one_nat)) Xs_6))))) (let ((_let_7 (forall ((X_7 tptp.arrow_475358991le_alt) (Xs_7 tptp.list_A2115238852le_alt) (N_3 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_7) Xs_7))) (let ((_let_2 (@ (@ tptp.drop_A1346709759le_alt N_3) _let_1))) (let ((_let_3 (= N_3 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.drop_A1346709759le_alt (@ (@ tptp.minus_minus_nat N_3) tptp.one_one_nat)) Xs_7)))))))))) (let ((_let_8 (forall ((Xs_11 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ tptp.butlas274947851le_alt Xs_11)) (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_11)) tptp.one_one_nat))))) (let ((_let_9 (forall ((X_9 tptp.arrow_475358991le_alt) (Xs_12 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_9))) (= (@ (@ tptp.take_A614047655le_alt tptp.one_one_nat) (@ _let_1 Xs_12)) (@ _let_1 tptp.nil_Ar1286194111le_alt)))))) (let ((_let_10 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_11 (@ _let_10 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))) (let ((_let_12 (not (= tptp.one_one_nat tptp.zero_zero_nat)))) (let ((_let_13 (@ _let_10 tptp.one_one_nat))) (let ((_let_14 (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))) (let ((_let_15 (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_16 (forall ((X_11 tptp.arrow_475358991le_alt) (Xs_13 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt tptp.one_one_nat) (@ (@ tptp.cons_A228743023le_alt X_11) Xs_13)) Xs_13)))) (let ((_let_17 (forall ((N_5 tptp.nat)) (= (@ tptp.suc N_5) (@ (@ tptp.plus_plus_nat N_5) tptp.one_one_nat))))) (let ((_let_18 (forall ((N_5 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N_5)) tptp.one_one_nat) N_5)))) (let ((_let_19 (forall ((I_2 tptp.nat) (Xs_16 tptp.list_A2115238852le_alt)) (= (@ tptp.rev_Ar1106406943le_alt (@ (@ tptp.drop_A1346709759le_alt I_2) Xs_16)) (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_16)) I_2)) (@ tptp.rev_Ar1106406943le_alt Xs_16)))))) (let ((_let_20 (forall ((N_11 tptp.nat) (Xs_20 tptp.list_A2115238852le_alt) (Ys_3 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.take_A614047655le_alt N_11))) (= (@ _let_1 (@ (@ tptp.append179082452le_alt Xs_20) Ys_3)) (@ (@ tptp.append179082452le_alt (@ _let_1 Xs_20)) (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat N_11) (@ tptp.size_s1858781230le_alt Xs_20))) Ys_3))))))) (let ((_let_21 (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N_5)) (= (@ (@ tptp.plus_plus_nat N_5) (@ (@ tptp.minus_minus_nat M) N_5)) M))))) (let ((_let_22 (forall ((N_5 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N_5) M)) N_5) M)))) (let ((_let_23 (forall ((A_31 tptp.arrow_475358991le_alt) (I_5 tptp.nat) (Xs_23 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_5) (@ tptp.size_s1858781230le_alt Xs_23)) (= (@ (@ (@ tptp.list_u62477863le_alt Xs_23) I_5) A_31) (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt I_5) Xs_23)) (@ (@ tptp.cons_A228743023le_alt A_31) (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc I_5)) Xs_23)))))))) (let ((_let_24 (forall ((I_8 tptp.nat) (J_1 tptp.nat) (Xs_28 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.plus_plus_nat I_8) J_1)) Xs_28) (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt I_8) Xs_28)) (@ (@ tptp.take_A614047655le_alt J_1) (@ (@ tptp.drop_A1346709759le_alt I_8) Xs_28))))))) (let ((_let_25 (forall ((Xs_29 tptp.list_A2115238852le_alt) (Ys_4 tptp.list_A2115238852le_alt) (Zs tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt Xs_29))) (= (= (@ (@ tptp.append179082452le_alt Xs_29) Ys_4) Zs) (and (= Xs_29 (@ (@ tptp.take_A614047655le_alt _let_1) Zs)) (= Ys_4 (@ (@ tptp.drop_A1346709759le_alt _let_1) Zs)))))))) (let ((_let_26 (forall ((N_17 tptp.nat) (X_16 tptp.arrow_475358991le_alt) (Xs_32 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_16))) (= (@ (@ tptp.take_A614047655le_alt (@ tptp.suc N_17)) (@ _let_1 Xs_32)) (@ _let_1 (@ (@ tptp.take_A614047655le_alt N_17) Xs_32))))))) (let ((_let_27 (forall ((N_18 tptp.nat) (Xs_33 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt N_18) Xs_33)) (@ (@ tptp.drop_A1346709759le_alt N_18) Xs_33)) Xs_33)))) (let ((_let_28 (forall ((N_19 tptp.nat)) (= (@ (@ tptp.take_A614047655le_alt N_19) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)))) (let ((_let_29 (forall ((I tptp.nat) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K_3) (=> (not (= K_3 (@ tptp.suc I))) (not (forall ((J_2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_2) (not (= K_3 (@ tptp.suc J_2))))))))))) (let ((_let_30 (forall ((X_21 tptp.arrow_475358991le_alt) (Xs_46 tptp.list_A2115238852le_alt) (N_32 tptp.nat)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_21) Xs_46)) (@ tptp.suc N_32)) (@ (@ tptp.nth_Ar125878976le_alt Xs_46) N_32))))) (let ((_let_31 (forall ((N_5 tptp.nat)) (= (@ (@ tptp.ord_less_nat N_5) (@ tptp.suc tptp.zero_zero_nat)) (= N_5 tptp.zero_zero_nat))))) (let ((_let_32 (forall ((A_41 tptp.arrow_475358991le_alt) (List_1 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ tptp.cons_A228743023le_alt A_41) List_1)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1858781230le_alt List_1)) (@ tptp.suc tptp.zero_zero_nat)))))) (let ((_let_33 (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N_5)) (or (@ _let_1 N_5) (= M N_5))))))) (let ((_let_34 (forall ((C_21 tptp.nat) (D_6 tptp.nat) (A_47 tptp.nat) (B_27 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_47) B_27) (=> (@ (@ tptp.ord_less_nat C_21) D_6) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_47) C_21)) (@ (@ tptp.plus_plus_nat B_27) D_6))))))) (let ((_let_35 (forall ((A_51 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_51) A_51)))) (let ((_let_36 (forall ((A_54 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_54) tptp.zero_zero_nat) A_54)))) (let ((_let_37 (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N_5) _let_1) (or (and (= M _let_1) (= N_5 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N_5 _let_1)))))))) (let ((_let_38 (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))) (let ((_let_39 (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N_5)) (@ tptp.suc (@ _let_1 N_5))))))) (let ((_let_40 (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N_5) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N_5)))))) (let ((_let_41 (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N_5) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N_5)))))) (let ((_let_42 (forall ((N_5 tptp.nat)) (@ (@ tptp.ord_less_nat N_5) (@ tptp.suc N_5))))) (let ((_let_43 (= tptp.bot_bot_nat tptp.zero_zero_nat))) (let ((_let_44 (forall ((J_4 tptp.nat) (I_12 tptp.nat) (Xs_56 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.nth_Ar125878976le_alt Xs_56))) (let ((_let_2 (@ tptp.size_s1858781230le_alt Xs_56))) (=> (@ tptp.distin236324274le_alt Xs_56) (=> (@ (@ tptp.ord_less_nat I_12) _let_2) (=> (@ (@ tptp.ord_less_nat J_4) _let_2) (= (= (@ _let_1 I_12) (@ _let_1 J_4)) (= I_12 J_4)))))))))) (let ((_let_45 (forall ((Xs_57 tptp.list_A2115238852le_alt)) (= (@ tptp.distin236324274le_alt Xs_57) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_s1858781230le_alt Xs_57)) (forall ((J_2 tptp.nat)) (let ((_let_1 (@ tptp.nth_Ar125878976le_alt Xs_57))) (=> (@ (@ tptp.ord_less_nat J_2) (@ tptp.size_s1858781230le_alt Xs_57)) (=> (not (= I_4 J_2)) (not (= (@ _let_1 I_4) (@ _let_1 J_2))))))))))))) (let ((_let_46 (forall ((N_35 tptp.nat) (Xs_61 tptp.list_A2115238852le_alt) (Y_7 tptp.arrow_475358991le_alt) (Ys_12 tptp.list_A2115238852le_alt)) (=> (= (@ (@ tptp.drop_A1346709759le_alt N_35) Xs_61) (@ (@ tptp.cons_A228743023le_alt Y_7) Ys_12)) (= (@ (@ tptp.nth_Ar125878976le_alt Xs_61) N_35) Y_7))))) (let ((_let_47 (forall ((N_36 tptp.nat) (Xs_62 tptp.list_A2115238852le_alt)) (=> (not (= Xs_62 tptp.nil_Ar1286194111le_alt)) (=> (@ (@ tptp.ord_less_nat N_36) (@ tptp.size_s1858781230le_alt Xs_62)) (= (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.drop_A1346709759le_alt N_36) Xs_62)) (@ (@ tptp.nth_Ar125878976le_alt Xs_62) N_36))))))) (let ((_let_48 (forall ((Xs_68 tptp.list_A2115238852le_alt) (I_15 tptp.nat)) (= (@ (@ (@ tptp.list_u62477863le_alt Xs_68) I_15) (@ (@ tptp.nth_Ar125878976le_alt Xs_68) I_15)) Xs_68)))) (let ((_let_49 (forall ((Z_6 tptp.nat) (X_40 tptp.nat) (Y_14 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_40))) (=> (@ _let_1 Y_14) (=> (@ (@ tptp.ord_less_nat Y_14) Z_6) (@ _let_1 Z_6))))))) (let ((_let_50 (@ tptp.linord810813188et_nat tptp.bot_bot_nat_o))) (let ((_let_51 (= _let_50 tptp.nil_nat))) (let ((_let_52 (= tptp.bot_bot_nat_o (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) false))))) (let ((_let_53 (@ tptp.size_s1858781230le_alt tptp.nil_Ar1286194111le_alt))) (let ((_let_54 (= _let_53 tptp.zero_zero_nat))) (let ((_let_55 (= (@ tptp.size_size_list_nat tptp.nil_nat) tptp.zero_zero_nat))) (let ((_let_56 (forall ((Xs_89 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ tptp.rotate335349260le_alt Xs_89)) (@ tptp.size_s1858781230le_alt Xs_89))))) (let ((_let_57 (forall ((X_69 tptp.arrow_475358991le_alt) (Xs_100 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_69) Xs_100)) tptp.zero_zero_nat) 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((_let_164 (ho_14 k_31 _let_101))) (let ((_let_165 (= _let_164 (ho_14 (ho_143 k_168 _let_163) _let_101)))) (let ((_let_166 (= _let_101 (ho_14 (ho_26 k_35 _let_164) (ho_14 (ho_13 k_12 _let_151) tptp.nil_Ar1286194111le_alt))))) (let ((_let_167 (ho_14 _let_147 _let_133))) (let ((_let_168 (ho_26 k_35 _let_143))) (let ((_let_169 (= (ho_14 _let_168 _let_167) (ho_45 _let_161 tptp.b)))) (let ((_let_170 (ho_14 k_64 _let_138))) (let ((_let_171 (= _let_138 _let_170))) (let ((_let_172 (ho_26 k_35 tptp.nil_Ar1286194111le_alt))) (let ((_let_173 (= _let_148 (ho_14 _let_172 _let_148)))) (let ((_let_174 (= (ho_14 _let_149 (ho_14 (ho_143 k_168 _let_126) _let_103)) (ho_14 _let_137 (ho_14 _let_149 _let_103))))) (let ((_let_175 (ho_14 _let_149 tptp.nil_Ar1286194111le_alt))) (let ((_let_176 (= (ho_14 _let_149 (ho_14 _let_172 _let_167)) (ho_14 (ho_26 k_35 _let_175) _let_167)))) (let ((_let_177 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 _let_157))) (let ((_let_178 (= _let_106 _let_175))) (let ((_let_179 (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2)))) (let ((_let_180 (@ tptp.size_size_list_nat _let_179))) (let ((_let_181 (= _let_53 _let_180))) (let ((_let_182 (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false))))) (let ((_let_183 (@ tptp.size_size_list_nat _let_182))) (let ((_let_184 (ASSUME :args (_let_63)))) (let ((_let_185 (SYMM (ASSUME :args (_let_55))))) (let ((_let_186 (EQ_RESOLVE (ASSUME :args (_let_52)) (MACRO_SR_EQ_INTRO :args (_let_52 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_187 (EQ_RESOLVE (SYMM (ASSUME :args (_let_51))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_186 _let_185 _let_184) :args ((= tptp.nil_nat _let_50) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_188 (EQ_RESOLVE (SYMM (ASSUME :args (_let_43))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_187 _let_186 _let_185 _let_184) :args ((= tptp.zero_zero_nat tptp.bot_bot_nat) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_189 (AND_INTRO _let_188 _let_187 _let_186 _let_185 _let_184))) (let ((_let_190 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO _let_189 :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) _let_188 _let_187 _let_186 _let_185 _let_184))) (let ((_let_191 (EQ_RESOLVE (ASSUME :args (_let_54)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_54 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_190 :args ((= tptp.zero_zero_nat _let_53) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= _let_53 _let_183) _let_181))) (PREPROCESS :args ((= _let_181 _let_97))))))) (let ((_let_192 (forall ((A_90 tptp.arrow_475358991le_alt) (B_48 tptp.arrow_475358991le_alt) (C tptp.arrow_475358991le_alt)) (not (ho_16 k_15 (ho_14 (ho_13 k_12 A_90) (ho_14 (ho_13 k_12 B_48) (ho_14 (ho_13 k_12 C) tptp.nil_Ar1286194111le_alt)))))))) (let ((_let_193 (0))) (let ((_let_194 (forall ((x |u_(-> tptp.list_int tptp.list_int)|) (y |u_(-> tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_195 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_196 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.list_int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.list_int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_117 x z) (ho_117 y z)))) (= x y))))) (let ((_let_197 (forall ((x |u_(-> tptp.list_int tptp.int tptp.int)|) (y |u_(-> tptp.list_int tptp.int tptp.int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_118 x z) (ho_118 y z)))) (= x y))))) (let ((_let_198 (forall ((x |u_(-> tptp.int tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_114 x z) (ho_114 y z)))) (= x y))))) (let ((_let_199 (forall ((x |u_(-> tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_112 x z) (ho_112 y z)))) (= x y))))) (let ((_let_200 (forall ((x |u_(-> tptp.list_A2115238852le_alt tptp.nat tptp.arrow_475358991le_alt)|) (y |u_(-> tptp.list_A2115238852le_alt tptp.nat tptp.arrow_475358991le_alt)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_201 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_202 (forall ((x |u_(-> _u_(-> tptp.arrow_475358991le_alt tptp.nat)_ tptp.list_A2115238852le_alt tptp.nat)|) (y |u_(-> _u_(-> tptp.arrow_475358991le_alt tptp.nat)_ tptp.list_A2115238852le_alt tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.arrow_475358991le_alt tptp.nat)|)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_203 (forall ((x |u_(-> tptp.arrow_475358991le_alt tptp.nat)|) (y |u_(-> tptp.arrow_475358991le_alt tptp.nat)|)) (or (not (forall ((z tptp.arrow_475358991le_alt)) (= (ho_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_204 (forall ((x |u_(-> tptp.list_A2115238852le_alt _u_(-> tptp.nat Bool)_ tptp.list_A2115238852le_alt)|) (y |u_(-> tptp.list_A2115238852le_alt _u_(-> tptp.nat Bool)_ tptp.list_A2115238852le_alt)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_91 x z) (ho_91 y z)))) (= x y))))) (let ((_let_205 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_A2115238852le_alt)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_A2115238852le_alt)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_206 (forall ((x |u_(-> tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_115 x z) (ho_115 y z)))) (= x y))))) (let ((_let_207 (forall ((x |u_(-> tptp.nat tptp.arrow_475358991le_alt)|) (y |u_(-> tptp.nat tptp.arrow_475358991le_alt)|)) (or (not (forall ((z tptp.nat)) (= (ho_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_208 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_209 (forall ((x |u_(-> tptp.list_nat tptp.nat Bool)|) (y |u_(-> tptp.list_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_210 (forall ((x |u_(-> tptp.list_A2115238852le_alt tptp.arrow_475358991le_alt Bool)|) (y |u_(-> tptp.list_A2115238852le_alt tptp.arrow_475358991le_alt Bool)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_211 (forall ((x |u_(-> tptp.arrow_475358991le_alt Bool)|) (y |u_(-> tptp.arrow_475358991le_alt Bool)|)) (or (not (forall ((z tptp.arrow_475358991le_alt)) (= (ho_74 x z) (ho_74 y z)))) (= x y))))) (let ((_let_212 (forall ((x |u_(-> tptp.int _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> tptp.int _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_68 x z) (ho_68 y z)))) (= x y))))) (let ((_let_213 (forall ((x |u_(-> tptp.list_A2115238852le_alt Bool)|) (y |u_(-> tptp.list_A2115238852le_alt Bool)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_16 x z) (ho_16 y z)))) (= x y))))) (let ((_let_214 (forall ((x |u_(-> tptp.list_int tptp.nat tptp.int)|) (y |u_(-> tptp.list_int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_111 x z) (ho_111 y z)))) (= x y))))) (let ((_let_215 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_216 (forall ((x |u_(-> tptp.list_A2115238852le_alt tptp.nat)|) (y |u_(-> tptp.list_A2115238852le_alt tptp.nat)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_217 (forall ((x |u_(-> tptp.list_nat tptp.list_A2115238852le_alt Bool)|) (y |u_(-> tptp.list_nat tptp.list_A2115238852le_alt Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_218 (forall ((x |u_(-> tptp.int Bool)|) (y |u_(-> tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_219 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_150 x z) (ho_150 y z)))) (= x y))))) (let ((_let_220 (forall ((x |u_(-> tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|) (y |u_(-> tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_26 x z) (ho_26 y z)))) (= x y))))) (let ((_let_221 (forall ((x |u_(-> tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_148 x z) (ho_148 y z)))) (= x y))))) (let ((_let_222 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_10 x z) (ho_10 y z)))) (= x y))))) (let ((_let_223 (forall ((x |u_(-> tptp.list_A2115238852le_alt tptp.list_nat)|) (y |u_(-> tptp.list_A2115238852le_alt tptp.list_nat)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_44 x z) (ho_44 y z)))) (= x y))))) (let ((_let_224 (forall ((x |u_(-> tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_21 x z) (ho_21 y z)))) (= x y))))) (let ((_let_225 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_226 (forall ((x |u_(-> tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_24 x z) (ho_24 y z)))) (= x y))))) (let ((_let_227 (forall ((x |u_(-> tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|) (y |u_(-> tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_14 x z) (ho_14 y z)))) (= x y))))) (let ((_let_228 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_19 x z) (ho_19 y z)))) (= x y))))) (let ((_let_229 (forall ((x |u_(-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|) (y |u_(-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|)) (or (not (forall ((z tptp.arrow_475358991le_alt)) (= (ho_13 x z) (ho_13 y z)))) (= x y))))) (let ((_let_230 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_231 (forall ((x |u_(-> tptp.nat tptp.nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_62 x z) (ho_62 y z)))) (= x y))))) (let ((_let_232 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_233 (forall ((x |u_(-> tptp.list_int Bool)|) (y |u_(-> tptp.list_int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_234 (forall ((x |u_(-> tptp.nat tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)|) (y |u_(-> tptp.nat tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)|)) (or (not (forall ((z tptp.nat)) (= (ho_60 x z) (ho_60 y z)))) (= x y))))) (let ((_let_235 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_nat tptp.list_nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_78 x z) (ho_78 y z)))) (= x y))))) (let ((_let_236 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_237 (forall ((x |u_(-> tptp.arrow_475358991le_alt tptp.list_nat)|) (y |u_(-> tptp.arrow_475358991le_alt tptp.list_nat)|)) (or (not (forall ((z tptp.arrow_475358991le_alt)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_238 (forall ((x |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_28 x z) (ho_28 y z)))) (= x y))))) (let ((_let_239 (forall ((x |u_(-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt Bool)|) (y |u_(-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt Bool)|)) (or (not (forall ((z tptp.arrow_475358991le_alt)) (= (ho_88 x z) (ho_88 y z)))) (= x y))))) (let ((_let_240 (forall ((x |u_(-> Bool Bool Bool)|) (y |u_(-> Bool Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_241 (forall ((x |u_(-> tptp.list_nat tptp.list_A2115238852le_alt)|) (y |u_(-> tptp.list_nat tptp.list_A2115238852le_alt)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_242 (forall ((x |u_(-> tptp.nat tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_23 x z) (ho_23 y z)))) (= x y))))) (let ((_let_243 (forall ((x |u_(-> tptp.nat tptp.list_A2115238852le_alt)|) (y |u_(-> tptp.nat tptp.list_A2115238852le_alt)|)) (or (not (forall ((z tptp.nat)) (= (ho_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_244 (forall ((x |u_(-> _u_(-> tptp.arrow_475358991le_alt Bool)_ tptp.list_A2115238852le_alt Bool)|) (y |u_(-> _u_(-> tptp.arrow_475358991le_alt Bool)_ tptp.list_A2115238852le_alt Bool)|)) (or (not (forall ((z |u_(-> tptp.arrow_475358991le_alt Bool)|)) (= (ho_84 x z) (ho_84 y z)))) (= x y))))) (let ((_let_245 (forall ((x |u_(-> tptp.list_nat tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_246 (forall ((x |u_(-> _u_(-> tptp.nat tptp.list_A2115238852le_alt)_ tptp.list_nat tptp.list_A2115238852le_alt)|) (y |u_(-> _u_(-> tptp.nat tptp.list_A2115238852le_alt)_ tptp.list_nat tptp.list_A2115238852le_alt)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.list_A2115238852le_alt)|)) (= (ho_39 x z) (ho_39 y z)))) (= x y))))) (let ((_let_247 (forall ((x |u_(-> _u_(-> tptp.arrow_475358991le_alt tptp.list_nat)_ tptp.list_A2115238852le_alt tptp.list_nat)|) (y |u_(-> _u_(-> tptp.arrow_475358991le_alt tptp.list_nat)_ tptp.list_A2115238852le_alt tptp.list_nat)|)) (or (not (forall ((z |u_(-> tptp.arrow_475358991le_alt tptp.list_nat)|)) (= (ho_43 x z) (ho_43 y z)))) (= x y))))) (let ((_let_248 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.list_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.list_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_249 (forall ((x |u_(-> tptp.list_nat _u_(-> tptp.nat Bool)_ tptp.list_nat)|) (y |u_(-> tptp.list_nat _u_(-> tptp.nat Bool)_ tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_250 (forall ((x |u_(-> tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt Bool)|) (y |u_(-> tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt Bool)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_50 x z) (ho_50 y z)))) (= x y))))) (let ((_let_251 (forall ((x |u_(-> _u_(-> tptp.arrow_475358991le_alt Bool)_ tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|) (y |u_(-> _u_(-> tptp.arrow_475358991le_alt Bool)_ tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|)) (or (not (forall ((z |u_(-> tptp.arrow_475358991le_alt Bool)|)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_252 (forall ((x |u_(-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)|) (y |u_(-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)|)) (or (not (forall ((z tptp.arrow_475358991le_alt)) (= (ho_45 x z) (ho_45 y z)))) (= x y))))) (let ((_let_253 (forall ((x |u_(-> _u_(-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)_ tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|) (y |u_(-> _u_(-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)_ tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|)) (or (not (forall ((z |u_(-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)|)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_254 (forall ((x |u_(-> tptp.list_A2115238852le_alt tptp.arrow_475358991le_alt)|) (y |u_(-> tptp.list_A2115238852le_alt tptp.arrow_475358991le_alt)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_54 x z) (ho_54 y z)))) (= x y))))) (let ((_let_255 (forall ((x |u_(-> tptp.list_nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_256 (forall ((x |u_(-> tptp.nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_63 x z) (ho_63 y z)))) (= x y))))) (let ((_let_257 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_124 x z) (ho_124 y z)))) (= x y))))) (let ((_let_258 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.list_nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.list_nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_259 (forall ((x |u_(-> tptp.list_A2115238852le_alt tptp.list_nat Bool)|) (y |u_(-> tptp.list_A2115238852le_alt tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_127 x z) (ho_127 y z)))) (= x y))))) (let ((_let_260 (forall ((x |u_(-> tptp.arrow_475358991le_alt tptp.option_nat)|) (y |u_(-> tptp.arrow_475358991le_alt tptp.option_nat)|)) (or (not (forall ((z tptp.arrow_475358991le_alt)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_261 (forall ((x |u_(-> _u_(-> tptp.arrow_475358991le_alt tptp.option_nat)_ tptp.list_A2115238852le_alt tptp.list_nat)|) (y |u_(-> _u_(-> tptp.arrow_475358991le_alt tptp.option_nat)_ tptp.list_A2115238852le_alt tptp.list_nat)|)) (or (not (forall ((z |u_(-> tptp.arrow_475358991le_alt tptp.option_nat)|)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_262 (forall ((x |u_(-> tptp.nat tptp.option514678660le_alt)|) (y |u_(-> tptp.nat tptp.option514678660le_alt)|)) (or (not (forall ((z tptp.nat)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_263 (forall ((x |u_(-> _u_(-> tptp.nat tptp.option514678660le_alt)_ tptp.list_nat tptp.list_A2115238852le_alt)|) (y |u_(-> _u_(-> tptp.nat tptp.option514678660le_alt)_ tptp.list_nat tptp.list_A2115238852le_alt)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.option514678660le_alt)|)) (= (ho_134 x z) (ho_134 y z)))) (= x y))))) (let ((_let_264 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_135 x z) (ho_135 y z)))) (= x y))))) (let ((_let_265 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.list_nat tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.list_nat tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_266 (forall ((x |u_(-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool)|) (y |u_(-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool)|)) (or (not (forall ((z tptp.arrow_475358991le_alt)) (= (ho_138 x z) (ho_138 y z)))) (= x y))))) (let ((_let_267 (forall ((x |u_(-> _u_(-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool)_ tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt Bool)|) (y |u_(-> _u_(-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool)_ tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt Bool)|)) (or (not (forall ((z |u_(-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool)|)) (= (ho_140 x z) (ho_140 y z)))) (= x y))))) (let ((_let_268 (forall ((x |u_(-> tptp.nat tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|) (y |u_(-> tptp.nat tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt)|)) (or (not (forall ((z tptp.nat)) (= (ho_143 x z) (ho_143 y z)))) (= x y))))) (let ((_let_269 (forall ((x |u_(-> tptp.list_A2115238852le_alt tptp.nat tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)|) (y |u_(-> tptp.list_A2115238852le_alt tptp.nat tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)|)) (or (not (forall ((z tptp.list_A2115238852le_alt)) (= (ho_146 x z) (ho_146 y z)))) (= x y))))) (let ((_let_270 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.nat tptp.nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_271 (forall ((x |u_(-> Bool Bool)|) (y |u_(-> Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_155 x z) (ho_155 y z)))) (= x y))))) (let ((_let_272 (forall ((x |u_(-> tptp.nat tptp.arrow_475358991le_alt Bool)|) (y |u_(-> tptp.nat tptp.arrow_475358991le_alt Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_157 x z) (ho_157 y z)))) (= x y))))) (let ((_let_273 (forall ((x |u_(-> _u_(-> tptp.arrow_475358991le_alt Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.arrow_475358991le_alt Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.arrow_475358991le_alt Bool)|)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_274 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_167 x z) (ho_167 y z)))) (= x y))))) (let ((_let_275 (forall ((x |u_(-> tptp.int tptp.nat)|) (y |u_(-> tptp.int tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_173 x z) (ho_173 y z)))) (= x y))))) (let ((_let_276 (forall ((BOUND_VARIABLE_16138 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_16135 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_16113 tptp.nat)) (let ((_let_1 (ho_9 k_8 BOUND_VARIABLE_16113))) (= (ho_4 (ho_7 (ho_6 k_5 BOUND_VARIABLE_16138) BOUND_VARIABLE_16135) BOUND_VARIABLE_16113) (and (ho_10 _let_1 BOUND_VARIABLE_16138) (not (ho_10 _let_1 BOUND_VARIABLE_16135)))))))) (let ((_let_277 (forall ((BOUND_VARIABLE_16106 tptp.nat)) (not (ho_4 k_11 BOUND_VARIABLE_16106))))) (let ((_let_278 (not _let_192))) (let ((_let_279 (forall ((BOUND_VARIABLE_16111 (-> tptp.nat Bool)) (BOUND_VARIABLE_16112 (-> tptp.nat Bool)) (BOUND_VARIABLE_16113 tptp.nat)) (let ((_let_1 (@ tptp.member_nat BOUND_VARIABLE_16113))) (= (and (@ _let_1 BOUND_VARIABLE_16111) (not (@ _let_1 BOUND_VARIABLE_16112))) (ll_3 BOUND_VARIABLE_16111 BOUND_VARIABLE_16112 BOUND_VARIABLE_16113)))))) (let ((_let_280 (forall ((BOUND_VARIABLE_16106 tptp.nat)) (not (ll_2 BOUND_VARIABLE_16106))))) (let ((_let_281 (and (not (forall ((A_90 tptp.arrow_475358991le_alt) (B_48 tptp.arrow_475358991le_alt) (C tptp.arrow_475358991le_alt)) (not (@ tptp.distin236324274le_alt (@ (@ tptp.cons_A228743023le_alt A_90) (@ (@ tptp.cons_A228743023le_alt B_48) (@ (@ tptp.cons_A228743023le_alt C) tptp.nil_Ar1286194111le_alt))))))) _let_280 _let_279))) (let ((_let_282 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_93)) (MACRO_SR_EQ_INTRO :args (_let_93 SB_DEFAULT SBA_FIXPOINT))) (PREPROCESS :args ((and _let_280 _let_279)))) :args (_let_281)) (PREPROCESS :args ((= _let_281 (and _let_278 _let_277 _let_276))))) (PREPROCESS :args ((and _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194)))) :args ((and _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194))) :args _let_193))) (let ((_let_283 (or))) (let ((_let_284 (_let_104))) (let ((_let_285 (not _let_104))) (let ((_let_286 (_let_278))) (let ((_let_287 (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_286)) :args _let_286) (REWRITE :args ((=> _let_278 (not _let_285)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_278) _let_192))) (REFL :args _let_284) :args _let_283)))) (let ((_let_288 (MACRO_RESOLUTION_TRUST _let_287 _let_282 :args (_let_104 true _let_192)))) (let ((_let_289 (forall ((BOUND_VARIABLE_9613 tptp.arrow_475358991le_alt) (BOUND_VARIABLE_9615 tptp.list_A2115238852le_alt)) (let ((_let_1 (ho_13 k_12 BOUND_VARIABLE_9613))) (= (ho_14 (ho_26 k_35 BOUND_VARIABLE_9615) (ho_14 _let_1 tptp.nil_Ar1286194111le_alt)) (ho_14 k_57 (ho_14 _let_1 BOUND_VARIABLE_9615))))))) (let ((_let_290 (1))) (let ((_let_291 (forall ((BOUND_VARIABLE_9613 tptp.arrow_475358991le_alt) (BOUND_VARIABLE_9615 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt BOUND_VARIABLE_9613))) (= (@ tptp.rotate335349260le_alt (@ _let_1 BOUND_VARIABLE_9615)) (@ (@ tptp.append179082452le_alt BOUND_VARIABLE_9615) (@ _let_1 tptp.nil_Ar1286194111le_alt))))))) (let ((_let_292 (and (= _let_179 (@ tptp.rotate1_nat _let_179)) _let_291))) (let ((_let_293 (_let_289))) (let ((_let_294 (forall ((X_88 tptp.arrow_475358991le_alt)) (= X_88 (ho_54 k_53 (ho_14 (ho_13 k_12 X_88) tptp.nil_Ar1286194111le_alt)))))) (let ((_let_295 (EQ_RESOLVE (ASSUME :args (_let_67)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_67 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X_88 tptp.arrow_475358991le_alt)) (= X_88 (@ tptp.last_A1217315288le_alt (@ (@ tptp.cons_A228743023le_alt X_88) tptp.nil_Ar1286194111le_alt)))) _let_294))))))) (let ((_let_296 (_let_294))) (let ((_let_297 ((ho_13 k_12 X_88)))) (let ((_let_298 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_295 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_178 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_297)) :args _let_296)) _let_295 :args (_let_110 false _let_294)))) (let ((_let_299 (forall ((X_82 tptp.arrow_475358991le_alt) (Xs_116 tptp.list_A2115238852le_alt)) (= X_82 (ho_54 k_70 (ho_14 (ho_13 k_12 X_82) Xs_116)))))) (let ((_let_300 (EQ_RESOLVE (ASSUME :args (_let_60)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_60 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X_82 tptp.arrow_475358991le_alt) (Xs_116 tptp.list_A2115238852le_alt)) (= X_82 (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.cons_A228743023le_alt X_82) Xs_116)))) _let_299))))))) (let ((_let_301 (_let_299))) (let ((_let_302 ((ho_14 (ho_13 k_12 X_82) Xs_116)))) (let ((_let_303 (forall ((X_69 tptp.arrow_475358991le_alt) (Xs_100 tptp.list_A2115238852le_alt)) (= X_69 (ho_107 (ho_106 k_105 (ho_14 (ho_13 k_12 X_69) Xs_100)) (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11)))))))) (let ((_let_304 (forall ((X_69 tptp.arrow_475358991le_alt) (Xs_100 tptp.list_A2115238852le_alt)) (= X_69 (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_69) Xs_100)) (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2)))))))) (let ((_let_305 (EQ_RESOLVE (ASSUME :args (_let_57)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_57 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_190 :args ((forall ((X_69 tptp.arrow_475358991le_alt) (Xs_100 tptp.list_A2115238852le_alt)) (= X_69 (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_69) Xs_100)) tptp.zero_zero_nat))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X_69 tptp.arrow_475358991le_alt) (Xs_100 tptp.list_A2115238852le_alt)) (= X_69 (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_69) Xs_100)) (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false))))))) _let_304))) (PREPROCESS :args ((= _let_304 _let_303))))))) (let ((_let_306 (_let_303))) (let ((_let_307 ((ho_14 (ho_13 k_12 X_69) Xs_100)))) (let ((_let_308 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_305 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_178 tptp.nil_Ar1286194111le_alt QUANTIFIERS_INST_E_MATCHING _let_307)) :args _let_306)) _let_305 :args (_let_112 false _let_303)))) (let ((_let_309 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_305 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 _let_99 QUANTIFIERS_INST_E_MATCHING _let_307)) :args _let_306)))) (let ((_let_310 (MACRO_RESOLUTION_TRUST _let_309 _let_305 :args (_let_114 false _let_303)))) (let ((_let_311 (forall ((A_41 tptp.arrow_475358991le_alt) (List_1 tptp.list_A2115238852le_alt)) (= (ho_100 (ho_124 k_161 (ho_99 k_109 List_1)) (ho_100 k_162 (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11))))) (ho_99 k_109 (ho_14 (ho_13 k_12 A_41) List_1)))))) (let ((_let_312 (forall ((A_41 tptp.arrow_475358991le_alt) (List_1 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ tptp.cons_A228743023le_alt A_41) List_1)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1858781230le_alt List_1)) (@ tptp.suc (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2))))))))) (let ((_let_313 (EQ_RESOLVE (ASSUME :args (_let_32)) (TRANS (MACRO_SR_EQ_INTRO _let_189 :args (_let_32 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A_41 tptp.arrow_475358991le_alt) (List_1 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ tptp.cons_A228743023le_alt A_41) List_1)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1858781230le_alt List_1)) (@ tptp.suc (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false)))))))) _let_312))) (PREPROCESS :args ((= _let_312 _let_311))))))) (let ((_let_314 (_let_311))) (let ((_let_315 ((ho_14 (ho_13 k_12 A_41) List_1)))) (let ((_let_316 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_313 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_178 tptp.nil_Ar1286194111le_alt QUANTIFIERS_INST_E_MATCHING _let_315)) :args _let_314)) _let_313 :args (_let_118 false _let_311)))) (let ((_let_317 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_313 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 _let_99 QUANTIFIERS_INST_E_MATCHING _let_315)) :args _let_314)) _let_313 :args (_let_120 false _let_311)))) (let ((_let_318 (forall ((N_5 tptp.nat) (M tptp.nat)) (= M (ho_100 (ho_124 k_169 (ho_100 (ho_124 k_161 N_5) M)) N_5))))) (let ((_let_319 (EQ_RESOLVE (ASSUME :args (_let_22)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N_5 tptp.nat) (M tptp.nat)) (= M (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N_5) M)) N_5))) _let_318))))))) (let ((_let_320 (_let_318))) (let ((_let_321 ((ho_100 (ho_124 k_161 N_5) M)))) (let ((_let_322 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_319 :args (_let_116 _let_116 QUANTIFIERS_INST_E_MATCHING _let_321)) :args _let_320)) _let_319 :args (_let_124 false _let_318)))) (let ((_let_323 (forall ((N_5 tptp.nat)) (= N_5 (ho_100 (ho_124 k_169 (ho_100 k_162 N_5)) (ho_100 k_162 (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11))))))))) (let ((_let_324 (forall ((N_5 tptp.nat)) (= N_5 (@ (@ tptp.minus_minus_nat (@ tptp.suc N_5)) (@ tptp.suc (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2))))))))) (let ((_let_325 (EQ_RESOLVE (ASSUME :args (_let_18)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_190 :args ((forall ((N_5 tptp.nat)) (= N_5 (@ (@ tptp.minus_minus_nat (@ tptp.suc N_5)) tptp.one_one_nat))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N_5 tptp.nat)) (= N_5 (@ (@ tptp.minus_minus_nat (@ tptp.suc N_5)) (@ tptp.suc (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false)))))))) _let_324))) (PREPROCESS :args ((= _let_324 _let_323))))))) (let ((_let_326 (_let_323))) (let ((_let_327 ((ho_100 k_162 N_5)))) (let ((_let_328 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_325 :args (_let_96 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_327)) :args _let_326)) _let_325 :args (_let_127 false _let_323)))) (let ((_let_329 (forall ((N_5 tptp.nat)) (= (ho_100 (ho_124 k_161 N_5) (ho_100 k_162 (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11))))) (ho_100 k_162 N_5))))) (let ((_let_330 (forall ((N_5 tptp.nat)) (= (@ tptp.suc N_5) (@ (@ tptp.plus_plus_nat N_5) (@ tptp.suc (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2))))))))) (let ((_let_331 (EQ_RESOLVE (ASSUME :args (_let_17)) (TRANS (MACRO_SR_EQ_INTRO _let_190 :args (_let_17 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N_5 tptp.nat)) (= (@ tptp.suc N_5) (@ (@ tptp.plus_plus_nat N_5) (@ tptp.suc (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false)))))))) _let_330))) (PREPROCESS :args ((= _let_330 _let_329))))))) (let ((_let_332 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_331 :args (_let_96 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_100 k_162 N_5)))) :args (_let_329)))) _let_331 :args (_let_130 false _let_329)))) (let ((_let_333 (forall ((X_11 tptp.arrow_475358991le_alt) (Xs_13 tptp.list_A2115238852le_alt)) (= Xs_13 (ho_14 (ho_143 k_142 (ho_100 k_162 (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11))))) (ho_14 (ho_13 k_12 X_11) Xs_13)))))) (let ((_let_334 (forall ((X_11 tptp.arrow_475358991le_alt) (Xs_13 tptp.list_A2115238852le_alt)) (= Xs_13 (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2))))) (@ (@ tptp.cons_A228743023le_alt X_11) Xs_13)))))) (let ((_let_335 (EQ_RESOLVE (ASSUME :args (_let_16)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_190 :args ((forall ((X_11 tptp.arrow_475358991le_alt) (Xs_13 tptp.list_A2115238852le_alt)) (= Xs_13 (@ (@ tptp.drop_A1346709759le_alt tptp.one_one_nat) (@ (@ tptp.cons_A228743023le_alt X_11) Xs_13)))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X_11 tptp.arrow_475358991le_alt) (Xs_13 tptp.list_A2115238852le_alt)) (= Xs_13 (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false)))))) (@ (@ tptp.cons_A228743023le_alt X_11) Xs_13)))) _let_334))) (PREPROCESS :args ((= _let_334 _let_333))))))) (let ((_let_336 (_let_333))) (let ((_let_337 ((ho_14 (ho_13 k_12 X_11) Xs_13)))) (let ((_let_338 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_335 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_178 tptp.nil_Ar1286194111le_alt QUANTIFIERS_INST_E_MATCHING _let_337)) :args _let_336)) _let_335 :args (_let_132 false _let_333)))) (let ((_let_339 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_335 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 _let_99 QUANTIFIERS_INST_E_MATCHING _let_337)) :args _let_336)) _let_335 :args (_let_134 false _let_333)))) (let ((_let_340 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_335 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_101 QUANTIFIERS_INST_E_MATCHING _let_337)) :args _let_336)) _let_335 :args (_let_136 false _let_333)))) (let ((_let_341 (forall ((X_9 tptp.arrow_475358991le_alt) (Xs_12 tptp.list_A2115238852le_alt)) (let ((_let_1 (ho_13 k_12 X_9))) (= (ho_14 (ho_143 k_168 (ho_100 k_162 (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11))))) (ho_14 _let_1 Xs_12)) (ho_14 _let_1 tptp.nil_Ar1286194111le_alt)))))) (let ((_let_342 (forall ((X_9 tptp.arrow_475358991le_alt) (Xs_12 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_9))) (= (@ _let_1 tptp.nil_Ar1286194111le_alt) (@ (@ tptp.take_A614047655le_alt (@ tptp.suc (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2))))) (@ _let_1 Xs_12))))))) (let ((_let_343 (EQ_RESOLVE (ASSUME :args (_let_9)) (TRANS (MACRO_SR_EQ_INTRO _let_190 :args (_let_9 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X_9 tptp.arrow_475358991le_alt) (Xs_12 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_9))) (= (@ _let_1 tptp.nil_Ar1286194111le_alt) (@ (@ tptp.take_A614047655le_alt (@ tptp.suc (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false)))))) (@ _let_1 Xs_12))))) _let_342))) (PREPROCESS :args ((= _let_342 _let_341))))))) (let ((_let_344 (_let_341))) (let ((_let_345 ((ho_14 (ho_13 k_12 X_9) Xs_12)))) (let ((_let_346 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_343 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 _let_99 QUANTIFIERS_INST_E_MATCHING _let_345)) :args _let_344))) _let_343 :args (_let_139 false _let_341)))) (let ((_let_347 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_343 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_101 QUANTIFIERS_INST_E_MATCHING _let_345)) :args _let_344))) _let_343 :args (_let_141 false _let_341)))) (let ((_let_348 (forall ((BOUND_VARIABLE_13052 tptp.arrow_475358991le_alt) (BOUND_VARIABLE_13054 tptp.list_A2115238852le_alt)) (= tptp.nil_Ar1286194111le_alt (ho_14 (ho_143 k_168 (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11)))) (ho_14 (ho_13 k_12 BOUND_VARIABLE_13052) BOUND_VARIABLE_13054)))))) (let ((_let_349 (forall ((BOUND_VARIABLE_13068 tptp.arrow_475358991le_alt) (BOUND_VARIABLE_13070 tptp.list_A2115238852le_alt) (BOUND_VARIABLE_13072 tptp.nat)) (let ((_let_1 (ho_13 k_12 BOUND_VARIABLE_13068))) (let ((_let_2 (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11))))) (or (= BOUND_VARIABLE_13072 _let_2) (= (ho_14 _let_1 (ho_14 (ho_143 k_168 (ho_100 (ho_124 k_169 BOUND_VARIABLE_13072) (ho_100 k_162 _let_2))) BOUND_VARIABLE_13070)) (ho_14 (ho_143 k_168 BOUND_VARIABLE_13072) (ho_14 _let_1 BOUND_VARIABLE_13070))))))))) (let ((_let_350 (and (forall ((BOUND_VARIABLE_13052 tptp.arrow_475358991le_alt) (BOUND_VARIABLE_13054 tptp.list_A2115238852le_alt)) (= tptp.nil_Ar1286194111le_alt (@ (@ tptp.take_A614047655le_alt (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2)))) (@ (@ tptp.cons_A228743023le_alt BOUND_VARIABLE_13052) BOUND_VARIABLE_13054)))) (forall ((BOUND_VARIABLE_13068 tptp.arrow_475358991le_alt) (BOUND_VARIABLE_13070 tptp.list_A2115238852le_alt) (BOUND_VARIABLE_13072 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2))))) (let ((_let_2 (@ tptp.cons_A228743023le_alt BOUND_VARIABLE_13068))) (or (= BOUND_VARIABLE_13072 _let_1) (= (@ (@ tptp.take_A614047655le_alt BOUND_VARIABLE_13072) (@ _let_2 BOUND_VARIABLE_13070)) (@ _let_2 (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat BOUND_VARIABLE_13072) (@ tptp.suc _let_1))) BOUND_VARIABLE_13070)))))))))) (let ((_let_351 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_190 :args ((and (forall ((BOUND_VARIABLE_13052 tptp.arrow_475358991le_alt) (BOUND_VARIABLE_13054 tptp.list_A2115238852le_alt)) (= tptp.nil_Ar1286194111le_alt (@ (@ tptp.take_A614047655le_alt tptp.zero_zero_nat) (@ (@ tptp.cons_A228743023le_alt BOUND_VARIABLE_13052) BOUND_VARIABLE_13054)))) (forall ((BOUND_VARIABLE_13068 tptp.arrow_475358991le_alt) (BOUND_VARIABLE_13070 tptp.list_A2115238852le_alt) (BOUND_VARIABLE_13072 tptp.nat)) (let ((_let_1 (@ tptp.cons_A228743023le_alt BOUND_VARIABLE_13068))) (or (= tptp.zero_zero_nat BOUND_VARIABLE_13072) (= (@ (@ tptp.take_A614047655le_alt BOUND_VARIABLE_13072) (@ _let_1 BOUND_VARIABLE_13070)) (@ _let_1 (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat BOUND_VARIABLE_13072) tptp.one_one_nat)) BOUND_VARIABLE_13070))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (forall ((BOUND_VARIABLE_13052 tptp.arrow_475358991le_alt) (BOUND_VARIABLE_13054 tptp.list_A2115238852le_alt)) (= tptp.nil_Ar1286194111le_alt (@ (@ tptp.take_A614047655le_alt (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false))))) (@ (@ tptp.cons_A228743023le_alt BOUND_VARIABLE_13052) BOUND_VARIABLE_13054)))) (forall ((BOUND_VARIABLE_13068 tptp.arrow_475358991le_alt) (BOUND_VARIABLE_13070 tptp.list_A2115238852le_alt) (BOUND_VARIABLE_13072 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false)))))) (let ((_let_2 (@ tptp.cons_A228743023le_alt BOUND_VARIABLE_13068))) (or (= BOUND_VARIABLE_13072 _let_1) (= (@ (@ tptp.take_A614047655le_alt BOUND_VARIABLE_13072) (@ _let_2 BOUND_VARIABLE_13070)) (@ _let_2 (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat BOUND_VARIABLE_13072) (@ tptp.suc _let_1))) BOUND_VARIABLE_13070)))))))) _let_350))) (PREPROCESS :args ((= _let_350 (and _let_348 _let_349)))))))) (let ((_let_352 (AND_ELIM _let_351 :args _let_193))) (let ((_let_353 (_let_348))) (let ((_let_354 ((ho_14 (ho_13 k_12 BOUND_VARIABLE_13052) BOUND_VARIABLE_13054)))) (let ((_let_355 (ASSUME :args _let_353))) (let ((_let_356 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_355 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 _let_99 QUANTIFIERS_INST_E_MATCHING _let_354)) :args _let_353)) _let_352 :args (_let_144 false _let_348)))) (let ((_let_357 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_355 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_101 QUANTIFIERS_INST_E_MATCHING _let_354)) :args _let_353)) _let_352 :args (_let_146 false _let_348)))) (let ((_let_358 (forall ((C tptp.arrow_475358991le_alt)) (not (ho_16 k_15 (ho_14 (ho_13 k_12 tptp.a) (ho_14 (ho_13 k_12 tptp.b) (ho_14 (ho_13 k_12 C) tptp.nil_Ar1286194111le_alt)))))))) (let ((_let_359 (not _let_150))) (let ((_let_360 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((C tptp.arrow_475358991le_alt)) (not (@ tptp.distin236324274le_alt (@ (@ tptp.cons_A228743023le_alt tptp.a) (@ (@ tptp.cons_A228743023le_alt tptp.b) (@ (@ tptp.cons_A228743023le_alt C) tptp.nil_Ar1286194111le_alt)))))) _let_358))))))) (let ((_let_361 (_let_358))) (let ((_let_362 ((ho_13 k_12 C)))) (let ((_let_363 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_360 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_178 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_362)) :args _let_361)) _let_360 :args (_let_359 false _let_358)))) (let ((_let_364 (= tptp.nil_Ar1286194111le_alt _let_99))) (let ((_let_365 (or _let_364 _let_152))) (let ((_let_366 (forall ((X_87 tptp.arrow_475358991le_alt) (Xs_128 tptp.list_A2115238852le_alt)) (or (= tptp.nil_Ar1286194111le_alt Xs_128) (= (ho_54 k_53 Xs_128) (ho_54 k_53 (ho_14 (ho_13 k_12 X_87) Xs_128))))))) (let ((_let_367 (EQ_RESOLVE (ASSUME :args (_let_66)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_66 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X_87 tptp.arrow_475358991le_alt) (Xs_128 tptp.list_A2115238852le_alt)) (or (= tptp.nil_Ar1286194111le_alt Xs_128) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.cons_A228743023le_alt X_87) Xs_128)) (@ tptp.last_A1217315288le_alt Xs_128)))) _let_366))))))) (let ((_let_368 (_let_366))) (let ((_let_369 ((ho_14 (ho_13 k_12 X_87) Xs_128)))) (let ((_let_370 (forall ((A_92 tptp.arrow_475358991le_alt) (List_6 tptp.list_A2115238852le_alt)) (not (= tptp.nil_Ar1286194111le_alt (ho_14 (ho_13 k_12 A_92) List_6)))))) (let ((_let_371 (not _let_364))) (let ((_let_372 (EQ_RESOLVE (ASSUME :args (_let_92)) (PREPROCESS :args ((= _let_92 _let_370)))))) (let ((_let_373 (_let_370))) (let ((_let_374 ((ho_14 (ho_13 k_12 A_92) List_6)))) (let ((_let_375 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_372 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_178 tptp.nil_Ar1286194111le_alt QUANTIFIERS_INST_E_MATCHING _let_374)) :args _let_373)) _let_372 :args (_let_371 false _let_370)))) (let ((_let_376 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_365)) :args ((or _let_364 _let_152 (not _let_365)))) _let_375 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_367 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 _let_99 QUANTIFIERS_INST_E_MATCHING _let_369)) :args _let_368)) _let_367 :args (_let_365 false _let_366)) :args (_let_152 true _let_364 false _let_365)))) (let ((_let_377 (not _let_154))) (let ((_let_378 (ho_135 k_144 _let_96))) (let ((_let_379 (not (ho_4 _let_378 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_211)))) (let ((_let_380 (or _let_379 _let_377))) (let ((_let_381 (forall ((J_2 tptp.nat)) (let ((_let_1 (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11))))) (let ((_let_2 (ho_100 k_162 _let_1))) (or (not (ho_4 (ho_135 k_144 _let_1) J_2)) (not (= (ho_100 k_162 J_2) (ho_100 (ho_124 k_161 _let_2) _let_2))))))))) (let ((_let_382 (not _let_380))) (let ((_let_383 (not _let_381))) (let ((_let_384 (= _let_116 _let_122))) (let ((_let_385 (ho_4 _let_378 _let_122))) (let ((_let_386 (not _let_385))) (let ((_let_387 (or _let_386 _let_384 _let_383))) (let ((_let_388 (forall ((I tptp.nat) (K_3 tptp.nat)) (or (not (ho_4 (ho_135 k_144 I) K_3)) (= K_3 (ho_100 k_162 I)) (not (forall ((J_2 tptp.nat)) (or (not (ho_4 (ho_135 k_144 I) J_2)) (not (= K_3 (ho_100 k_162 J_2)))))))))) (let ((_let_389 (EQ_RESOLVE (ASSUME :args (_let_29)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((I tptp.nat) (K_3 tptp.nat)) (or (not (@ (@ tptp.ord_less_nat I) K_3)) (= K_3 (@ tptp.suc I)) (not (forall ((J_2 tptp.nat)) (or (not (@ (@ tptp.ord_less_nat I) J_2)) (not (= K_3 (@ tptp.suc J_2)))))))) _let_388))))))) (let ((_let_390 (= _let_96 _let_116))) (let ((_let_391 (= _let_390 _let_384))) (let ((_let_392 (not _let_384))) (let ((_let_393 (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11))))) (let ((_let_2 (ho_100 k_162 _let_1))) (= (or (and (= M _let_2) (= N_5 _let_1)) (and (= M _let_1) (= N_5 _let_2))) (= _let_2 (ho_100 (ho_124 k_161 M) N_5)))))))) (let ((_let_394 (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2))))) (let ((_let_2 (@ tptp.suc _let_1))) (= (= (@ (@ tptp.plus_plus_nat M) N_5) _let_2) (or (and (= M _let_2) (= N_5 _let_1)) (and (= M _let_1) (= N_5 _let_2))))))))) (let ((_let_395 (EQ_RESOLVE (ASSUME :args (_let_37)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_189 :args ((forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N_5)) (or (and (= M _let_1) (= tptp.zero_zero_nat N_5)) (and (= tptp.zero_zero_nat M) (= N_5 _let_1)))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false)))))) (let ((_let_2 (@ tptp.suc _let_1))) (= (or (and (= M _let_2) (= N_5 _let_1)) (and (= M _let_1) (= N_5 _let_2))) (= (@ (@ tptp.plus_plus_nat M) N_5) _let_2))))) _let_394))) (PREPROCESS :args ((= _let_394 _let_393))))))) (let ((_let_396 (@ tptp.suc _let_180))) (let ((_let_397 (not (= _let_180 _let_396)))) (let ((_let_398 (@ tptp.suc _let_183))) (let ((_let_399 (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO _let_190 :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (= _let_183 _let_398)) _let_397))) (PREPROCESS :args ((= _let_397 (not _let_390)))))))) (let ((_let_400 (@ tptp.ord_less_nat _let_180))) (let ((_let_401 (@ _let_400 (@ (@ tptp.plus_plus_nat _let_396) _let_396)))) (let ((_let_402 (@ tptp.ord_less_nat _let_183))) (let ((_let_403 (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO _let_190 :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ _let_402 (@ (@ tptp.plus_plus_nat _let_398) _let_398)) _let_401))) (PREPROCESS :args ((= _let_401 _let_385))))))) (let ((_let_404 (_let_383))) (let ((_let_405 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_380 1)) (CONG (REFL :args (_let_380)) (MACRO_SR_PRED_INTRO :args ((= (not _let_377) _let_154))) :args _let_283)) :args ((or _let_154 _let_380))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_404)) :args _let_404) (REWRITE :args ((=> _let_383 (not (or _let_379 (not (= _let_153 _let_122))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_383) _let_381))) (REFL :args (_let_382)) :args _let_283)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_387)) :args ((or _let_386 _let_384 _let_383 (not _let_387)))) _let_403 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((_let_407 (forall ((Xs_171 tptp.list_A2115238852le_alt) (X_108 tptp.arrow_475358991le_alt)) (= Xs_171 (ho_14 k_31 (ho_14 (ho_26 k_35 Xs_171) (ho_14 (ho_13 k_12 X_108) tptp.nil_Ar1286194111le_alt))))))) (let ((_let_408 (EQ_RESOLVE (ASSUME :args (_let_86)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_86 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xs_171 tptp.list_A2115238852le_alt) (X_108 tptp.arrow_475358991le_alt)) (= Xs_171 (@ tptp.butlas274947851le_alt (@ (@ tptp.append179082452le_alt Xs_171) (@ (@ tptp.cons_A228743023le_alt X_108) tptp.nil_Ar1286194111le_alt))))) _let_407))))))) (let ((_let_409 (forall ((N_18 tptp.nat) (Xs_33 tptp.list_A2115238852le_alt)) (= Xs_33 (ho_14 (ho_26 k_35 (ho_14 (ho_143 k_168 N_18) Xs_33)) (ho_14 (ho_143 k_142 N_18) Xs_33)))))) (let ((_let_410 (EQ_RESOLVE (ASSUME :args (_let_27)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N_18 tptp.nat) (Xs_33 tptp.list_A2115238852le_alt)) (= Xs_33 (@ (@ 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(_let_165 false _let_415)))) (let ((_let_419 (= tptp.nil_Ar1286194111le_alt _let_101))) (let ((_let_420 (or _let_419 _let_166))) (let ((_let_421 (forall ((Xs_145 tptp.list_A2115238852le_alt)) (or (= tptp.nil_Ar1286194111le_alt Xs_145) (= Xs_145 (ho_14 (ho_26 k_35 (ho_14 k_31 Xs_145)) (ho_14 (ho_13 k_12 (ho_54 k_53 Xs_145)) tptp.nil_Ar1286194111le_alt))))))) (let ((_let_422 (EQ_RESOLVE (ASSUME :args (_let_77)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_77 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xs_145 tptp.list_A2115238852le_alt)) (or (= tptp.nil_Ar1286194111le_alt Xs_145) (= Xs_145 (@ (@ tptp.append179082452le_alt (@ tptp.butlas274947851le_alt Xs_145)) (@ (@ tptp.cons_A228743023le_alt (@ tptp.last_A1217315288le_alt Xs_145)) tptp.nil_Ar1286194111le_alt))))) _let_421))))))) (let ((_let_423 (not _let_419))) (let ((_let_424 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_372 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 _let_99 QUANTIFIERS_INST_E_MATCHING _let_374)) :args _let_373)) _let_372 :args (_let_423 false _let_370)))) (let ((_let_425 (ho_4 _let_378 _let_119))) (let ((_let_426 (not _let_425))) (let ((_let_427 (or _let_426 _let_169))) (let ((_let_428 (forall ((A_31 tptp.arrow_475358991le_alt) (I_5 tptp.nat) (Xs_23 tptp.list_A2115238852le_alt)) (or (not (ho_4 (ho_135 k_144 I_5) (ho_99 k_109 Xs_23))) (= (ho_14 (ho_26 k_35 (ho_14 (ho_143 k_168 I_5) Xs_23)) (ho_14 (ho_13 k_12 A_31) (ho_14 (ho_143 k_142 (ho_100 k_162 I_5)) Xs_23))) (ho_45 (ho_60 (ho_146 k_145 Xs_23) I_5) A_31)))))) (let ((_let_429 (EQ_RESOLVE (ASSUME :args (_let_23)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A_31 tptp.arrow_475358991le_alt) (I_5 tptp.nat) (Xs_23 tptp.list_A2115238852le_alt)) (or (not (@ (@ tptp.ord_less_nat I_5) (@ tptp.size_s1858781230le_alt Xs_23))) (= (@ (@ (@ tptp.list_u62477863le_alt Xs_23) I_5) A_31) (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt I_5) Xs_23)) (@ (@ tptp.cons_A228743023le_alt A_31) (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc I_5)) Xs_23)))))) _let_428))))))) (let ((_let_430 (and _let_97 _let_385 _let_118 _let_120 _let_130))) (let ((_let_431 (TRUE_INTRO _let_403))) (let ((_let_432 (APPLY_UF ho_4))) (let ((_let_433 (APPLY_UF ho_100))) (let ((_let_434 (REFL :args (_let_116)))) (let ((_let_435 (APPLY_UF ho_124))) (let ((_let_436 (ASSUME :args (_let_130)))) (let ((_let_437 (SYMM _let_436))) (let ((_let_438 (SYMM _let_437))) (let ((_let_439 (SYMM _let_438))) (let ((_let_440 (SYMM _let_191))) (let ((_let_441 (SYMM _let_440))) (let ((_let_442 (REFL :args (k_161)))) (let ((_let_443 (CONG (CONG _let_442 (SYMM _let_441) :args _let_435) _let_434 :args _let_433))) (let ((_let_444 (ASSUME :args (_let_118)))) (let ((_let_445 (SYMM _let_444))) (let ((_let_446 (SYMM _let_445))) (let ((_let_447 (SYMM _let_446))) (let ((_let_448 (CONG (CONG _let_442 (TRANS _let_447 _let_443 _let_439) :args _let_435) _let_434 :args _let_433))) (let ((_let_449 (ASSUME :args (_let_120)))) (let ((_let_450 (SYMM _let_449))) (let ((_let_451 (SYMM _let_450))) (let ((_let_452 (SYMM _let_451))) (let ((_let_453 (TRANS _let_452 _let_448))) (let ((_let_454 (REFL :args (_let_378)))) (let ((_let_455 (forall ((X_91 tptp.arrow_475358991le_alt) (Xs_132 tptp.list_A2115238852le_alt)) (let ((_let_1 (ho_14 (ho_13 k_12 X_91) tptp.nil_Ar1286194111le_alt))) (= (= Xs_132 _let_1) (= _let_1 (ho_14 k_64 Xs_132))))))) (let ((_let_456 (EQ_RESOLVE (ASSUME :args (_let_68)) (PREPROCESS :args ((= _let_68 _let_455)))))) (let ((_let_457 (_let_455))) (let ((_let_458 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_456 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 _let_138 QUANTIFIERS_INST_CBQI_PROP)) :args _let_457))) _let_456 :args (_let_171 false _let_455)))) (let ((_let_459 (forall ((Ys_42 tptp.list_A2115238852le_alt) (Xs_159 tptp.list_A2115238852le_alt)) (= (= tptp.nil_Ar1286194111le_alt Xs_159) (= Ys_42 (ho_14 (ho_26 k_35 Xs_159) Ys_42)))))) (let ((_let_460 (EQ_RESOLVE (ASSUME :args (_let_81)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_81 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Ys_42 tptp.list_A2115238852le_alt) (Xs_159 tptp.list_A2115238852le_alt)) (= (= Ys_42 (@ (@ tptp.append179082452le_alt Xs_159) Ys_42)) (= tptp.nil_Ar1286194111le_alt Xs_159))) _let_459))))))) (let ((_let_461 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_460 :args (_let_148 tptp.nil_Ar1286194111le_alt QUANTIFIERS_INST_CBQI_PROP)) :args (_let_459)))) _let_460 :args (_let_173 false _let_459)))) (let ((_let_462 (or _let_390 _let_174))) (let ((_let_463 (_let_349))) (let ((_let_464 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_462)) :args ((or _let_390 _let_174 (not _let_462)))) _let_399 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_463) :args (tptp.a _let_103 _let_116 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_463))) (AND_ELIM 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SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_231))) (let ((_let_473 (ho_4 _let_472 _let_116))) (let ((_let_474 (= _let_471 _let_473))) (let ((_let_475 (ho_14 _let_137 _let_99))) (let ((_let_476 (= _let_99 _let_475))) (let ((_let_477 (ho_99 k_109 _let_475))) (let ((_let_478 (ho_4 _let_472 _let_477))) (let ((_let_479 (ho_14 _let_147 _let_103))) (let ((_let_480 (ho_14 (ho_143 k_168 _let_122) _let_479))) (let ((_let_481 (ho_106 k_105 _let_480))) (let ((_let_482 (= (ho_107 _let_481 _let_96) (ho_107 _let_481 _let_116)))) (let ((_let_483 (ho_14 k_64 tptp.nil_Ar1286194111le_alt))) (let ((_let_484 (= tptp.nil_Ar1286194111le_alt _let_483))) (let ((_let_485 (= _let_99 (ho_14 (ho_26 k_25 _let_99) tptp.nil_Ar1286194111le_alt)))) (let ((_let_486 (= _let_138 (ho_14 (ho_13 k_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177) tptp.nil_Ar1286194111le_alt)))) (let ((_let_487 (ho_14 k_64 _let_99))) (let ((_let_488 (ho_26 k_35 _let_483))) (let ((_let_489 (ho_14 _let_488 _let_99))) (let ((_let_490 (= _let_489 _let_487))) (let 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k_17 k_11)))))))) (let ((_let_672 (forall ((A_54 tptp.nat)) (= A_54 (@ (@ tptp.plus_plus_nat A_54) (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2)))))))) (let ((_let_673 (EQ_RESOLVE (ASSUME :args (_let_36)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_189 :args ((forall ((A_54 tptp.nat)) (= A_54 (@ (@ tptp.plus_plus_nat A_54) tptp.zero_zero_nat))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A_54 tptp.nat)) (= A_54 (@ (@ tptp.plus_plus_nat A_54) (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false))))))) _let_672))) (PREPROCESS :args ((= _let_672 _let_671))))))) (let ((_let_674 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_673 :args (_let_116 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_124 k_161 A_54)))) :args (_let_671))) _let_673 :args (_let_500 false _let_671)))) (let ((_let_675 (forall 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(SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 _let_99 QUANTIFIERS_INST_E_MATCHING _let_679)) :args _let_678)) _let_677 :args (_let_505 false _let_675)))) (let ((_let_682 (not _let_588))) (let ((_let_683 (not _let_505))) (let ((_let_684 (not _let_120))) (let ((_let_685 (not _let_500))) (let ((_let_686 (not _let_499))) (let ((_let_687 (REFL :args (_let_683)))) (let ((_let_688 (REFL :args (_let_684)))) (let ((_let_689 (REFL :args (_let_685)))) (let ((_let_690 (REFL :args (_let_686)))) (let ((_let_691 (and _let_97 _let_499 _let_500 _let_118 _let_120 _let_130 _let_476 _let_505 _let_666))) (let ((_let_692 (ASSUME :args (_let_666)))) (let ((_let_693 (TRANS _let_438 _let_656 _let_446 _let_655))) (let ((_let_694 (REFL :args (k_162)))) (let ((_let_695 (CONG _let_694 _let_693 :args _let_433))) (let ((_let_696 (ASSUME :args (_let_500)))) (let ((_let_697 (SYMM _let_696))) (let ((_let_698 (SYMM _let_697))) (let ((_let_699 (CONG _let_694 (SYMM _let_698) :args _let_433))) (let ((_let_700 (ASSUME :args 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_let_296)) _let_295 :args (_let_565 false _let_294)))) (let ((_let_768 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_313 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_101 QUANTIFIERS_INST_E_MATCHING _let_315)) :args _let_314))) _let_313 :args (_let_502 false _let_311)))) (let ((_let_769 (forall ((Xs_89 tptp.list_A2115238852le_alt)) (= (ho_99 k_109 Xs_89) (ho_99 k_109 (ho_14 k_57 Xs_89)))))) (let ((_let_770 (EQ_RESOLVE (ASSUME :args (_let_56)) (PREPROCESS :args ((= _let_56 _let_769)))))) (let ((_let_771 (_let_103 QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_772 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_770 :args _let_771) :args (_let_769))) _let_770 :args (_let_521 false _let_769)))) (let ((_let_773 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_335 :args (tptp.a _let_566 QUANTIFIERS_INST_E_MATCHING _let_337)) :args _let_336)) _let_335 :args (_let_599 false _let_333)))) (let ((_let_774 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_300 :args (tptp.b _let_138 QUANTIFIERS_INST_E_MATCHING _let_302)) :args _let_301)) _let_300 :args (_let_600 false _let_299)))) (let ((_let_775 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_325 :args (_let_122 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_327)) :args _let_326)) _let_325 :args (_let_524 false _let_323)))) (let ((_let_776 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_319 :args (_let_515 _let_116 QUANTIFIERS_INST_E_MATCHING _let_321)) :args _let_320)) _let_319 :args (_let_601 false _let_318)))) (let ((_let_777 (= tptp.nil_Ar1286194111le_alt _let_566))) (let ((_let_778 (or _let_777 _let_577))) (let ((_let_779 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_778)) :args ((or _let_777 _let_577 (not _let_778)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_372 :args (tptp.b _let_138 QUANTIFIERS_INST_E_MATCHING _let_374)) :args _let_373)) _let_372 :args ((not _let_777) false 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(EQ_RESOLVE (ASSUME :args (_let_47)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_47 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N_36 tptp.nat) (Xs_62 tptp.list_A2115238852le_alt)) (or (= tptp.nil_Ar1286194111le_alt Xs_62) (not (@ (@ tptp.ord_less_nat N_36) (@ tptp.size_s1858781230le_alt Xs_62))) (= (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.drop_A1346709759le_alt N_36) Xs_62)) (@ (@ tptp.nth_Ar125878976le_alt Xs_62) N_36)))) _let_885))))))) (let ((_let_887 (_let_885))) (let ((_let_888 ((ho_14 (ho_143 k_142 N_36) Xs_62)))) (let ((_let_889 (ho_4 _let_881 _let_518))) (let ((_let_890 (forall ((I tptp.nat) (M tptp.nat)) (ho_4 (ho_135 k_144 I) (ho_100 k_162 (ho_100 (ho_124 k_161 M) I)))))) (let ((_let_891 (EQ_RESOLVE (ASSUME :args (_let_38)) (PREPROCESS :args ((= _let_38 _let_890)))))) (let ((_let_892 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_891 :args (_let_116 _let_116 QUANTIFIERS_INST_E_MATCHING ((ho_100 (ho_124 k_161 M) I)))) :args (_let_890))) _let_891 :args (_let_889 false _let_890)))) (let ((_let_893 (and _let_97 _let_499 _let_889 _let_500 _let_118 _let_120 _let_124 _let_130 _let_139 _let_154 _let_519 _let_571 _let_573 _let_574 _let_165))) (let ((_let_894 (ASSUME :args (_let_889)))) (let ((_let_895 (TRUE_INTRO _let_894))) (let ((_let_896 (CONG _let_442 (TRANS _let_452 _let_448 _let_702 _let_699) :args _let_435))) (let ((_let_897 (SYMM _let_728))) (let ((_let_898 (REFL :args (_let_881)))) (let ((_let_899 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_884)) :args ((or _let_872 _let_883 _let_602 (not _let_884)))) _let_879 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_893)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_894 _let_761 _let_696 _let_700 _let_436 _let_191 _let_444 _let_449 _let_739 _let_743 _let_753 _let_750 _let_732 _let_729 _let_727) (SCOPE (TRUE_ELIM (TRANS (CONG _let_898 (TRANS _let_897 (CONG (TRANS (CONG _let_442 (TRANS (SYMM _let_731) (CONG (CONG _let_442 (TRANS (CONG _let_654 (TRANS 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QUANTIFIERS_INST_E_MATCHING _let_307)) :args _let_306)))) (let ((_let_1027 (MACRO_RESOLUTION_TRUST _let_1026 _let_305 :args (_let_569 false _let_303)))) (let ((_let_1028 (not _let_586))) (let ((_let_1029 (not _let_569))) (let ((_let_1030 (and _let_97 _let_565 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_139 _let_154 _let_519 _let_521 _let_569 _let_524 _let_581 _let_577 _let_571 _let_573 _let_574 _let_165 _let_580 _let_582 _let_586 _let_603 _let_583))) (let ((_let_1031 (CONG _let_442 (TRANS _let_450 _let_939 _let_700 _let_759) :args _let_435))) (let ((_let_1032 (CONG (TRANS _let_973 (CONG _let_744 (TRANS _let_946 _let_944 (CONG (TRANS _let_1031 (CONG _let_442 (TRANS _let_758 _let_701 (CONG (CONG _let_442 (TRANS _let_739 _let_757 _let_950 _let_755 (CONG _let_654 (TRANS _let_752 (CONG (CONG _let_749 (TRANS _let_949 _let_746 _let_740) :args _let_738) _let_737 :args _let_736) _let_733) :args _let_650)) :args _let_435) _let_434 :args _let_433) _let_731) :args _let_435)) _let_434 :args _let_433) _let_728) :args _let_435)) _let_434 :args _let_433))) (let ((_let_1033 (CONG (TRANS (CONG _let_744 (TRANS _let_763 (CONG (SYMM _let_1031) _let_434 :args _let_433) _let_943 _let_945) :args _let_435) _let_975) _let_434 :args _let_433))) (let ((_let_1034 (SYMM _let_972))) (let ((_let_1035 (ASSUME :args (_let_586)))) (let ((_let_1036 (CONG _let_963 (SYMM (SYMM _let_1035)) :args _let_933))) (let ((_let_1037 (ASSUME :args (_let_569)))) (let ((_let_1038 (SYMM _let_1037))) (let ((_let_1039 (SYMM _let_1038))) (let ((_let_1040 (ASSUME :args (_let_3)))) (let ((_let_1041 (and _let_97 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_476 _let_139 _let_154 _let_521 _let_599 _let_569 _let_600 _let_601 _let_571 _let_573 _let_574 _let_165 _let_580 _let_582 _let_586 _let_602 _let_607))) (let ((_let_1042 (not _let_561))) (let ((_let_1043 (and _let_97 _let_118 _let_130 _let_476 _let_1042))) (let ((_let_1044 (ASSUME :args (_let_1042)))) (let ((_let_1045 (not _let_562))) (let ((_let_1046 (and _let_97 _let_565 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_139 _let_154 _let_519 _let_521 _let_569 _let_524 _let_581 _let_577 _let_571 _let_573 _let_574 _let_165 _let_580 _let_582 _let_562 _let_584 _let_583))) (let ((_let_1047 (ASSUME :args (_let_562)))) (let ((_let_1048 (SYMM (SYMM _let_1047)))) (let ((_let_1049 (CONG _let_963 _let_1048 :args _let_933))) (let ((_let_1050 (and _let_619 _let_562))) (let ((_let_1051 (_let_619 _let_562))) (let ((_let_1052 (and _let_97 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_476 _let_139 _let_154 _let_521 _let_599 _let_569 _let_600 _let_601 _let_571 _let_573 _let_574 _let_165 _let_580 _let_582 _let_562 _let_602 _let_595))) (let ((_let_1053 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1052)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_925 _let_928 _let_931 _let_934 _let_696 _let_700 _let_436 _let_191 _let_444 _let_449 _let_942 _let_945 _let_739 _let_743 _let_753 _let_750 _let_732 _let_729 _let_727 _let_958 _let_651 _let_659 _let_965 _let_1047 _let_1037) (SCOPE (TRANS _let_1039 _let_1049 _let_1013 _let_966 _let_1012 _let_1011 _let_953 _let_932 _let_930 _let_926) :args (_let_600 _let_599 _let_602 _let_601 _let_500 _let_499 _let_130 _let_97 _let_118 _let_120 _let_502 _let_521 _let_124 _let_154 _let_574 _let_165 _let_139 _let_571 _let_573 _let_580 _let_476 _let_595 _let_582 _let_562 _let_569))) :args (_let_97 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_476 _let_139 _let_154 _let_521 _let_599 _let_569 _let_600 _let_601 _let_571 _let_573 _let_574 _let_165 _let_580 _let_582 _let_562 _let_602 _let_595))) :args (true _let_1052)) :args ((or _let_2 _let_637 _let_686 _let_685 _let_636 _let_684 _let_919 _let_918 _let_635 _let_634 _let_917 _let_377 _let_915 _let_914 _let_1029 _let_912 _let_910 _let_907 _let_906 _let_905 _let_904 _let_903 _let_613 _let_1045 _let_901 _let_657))) _let_899 _let_871 _let_789 _let_418 _let_719 _let_720 _let_721 _let_776 _let_774 _let_1027 _let_773 _let_772 _let_405 _let_346 _let_612 _let_332 _let_322 _let_768 _let_317 _let_316 _let_674 _let_670 _let_1040 _let_191 _let_661 _let_667 _let_665 _let_1018 _let_612 _let_332 _let_316 _let_191 _let_711 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_1025 _let_1024 _let_766 _let_765 (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_1050)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_644 _let_1047) (SCOPE (FALSE_ELIM (TRANS (CONG _let_1048 _let_647 :args _let_646) _let_645)) :args _let_1051)) :args _let_1051)) :args (true _let_1050)) (CONG _let_638 (REFL :args (_let_1045)) (REFL :args (_let_1028)) :args _let_283)) _let_632 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1046)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_986 _let_983 _let_980 _let_977 _let_958 _let_727 _let_729 _let_732 _let_739 _let_743 _let_436 _let_191 _let_444 _let_449 _let_750 _let_753 _let_700 _let_696 _let_942 _let_945 _let_761 _let_971 _let_969 _let_965 _let_1047 _let_1037) (SCOPE (TRANS _let_1039 _let_1049 _let_1013 _let_966 _let_1012 (CONG _let_960 (TRANS _let_970 _let_1034 _let_1033 _let_1032) :args _let_933) _let_978 _let_981 _let_984 _let_987) :args (_let_565 _let_581 _let_577 _let_583 _let_580 _let_573 _let_571 _let_139 _let_124 _let_154 _let_130 _let_97 _let_118 _let_120 _let_165 _let_574 _let_499 _let_500 _let_502 _let_521 _let_519 _let_524 _let_584 _let_582 _let_562 _let_569))) :args (_let_97 _let_565 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_139 _let_154 _let_519 _let_521 _let_569 _let_524 _let_581 _let_577 _let_571 _let_573 _let_574 _let_165 _let_580 _let_582 _let_562 _let_584 _let_583))) :args (true _let_1046)) :args ((or _let_637 _let_920 _let_686 _let_685 _let_636 _let_684 _let_919 _let_918 _let_635 _let_917 _let_377 _let_916 _let_915 _let_1029 _let_911 _let_909 _let_908 _let_907 _let_906 _let_905 _let_904 _let_903 _let_613 _let_470 _let_1045 _let_902 _let_900))) _let_880 _let_871 _let_870 _let_789 _let_779 _let_418 _let_719 _let_720 _let_721 _let_775 _let_1027 _let_772 _let_724 _let_405 _let_346 _let_332 _let_322 _let_768 _let_317 _let_316 _let_674 _let_670 _let_767 _let_191 (REORDERING (CNF_EQUIV_POS1 :args (_let_563)) :args ((or _let_562 _let_1042 (not _let_563)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_1021 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_233 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_1023)) :args _let_1022))) _let_1021 :args (_let_563 false _let_1019)) (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_1043)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1044 _let_436 _let_191 _let_444 _let_651) (SCOPE (FALSE_ELIM (TRANS (CONG _let_996 (TRANS _let_956 _let_445 _let_937 _let_437) :args _let_432) (FALSE_INTRO _let_1044))) :args (_let_1042 _let_130 _let_97 _let_118 _let_476))) :args (_let_97 _let_118 _let_130 _let_476 _let_1042))) :args (true _let_1043)) (CONG _let_642 _let_641 _let_640 _let_639 (MACRO_SR_PRED_INTRO :args ((= (not _let_1042) _let_561))) (REFL :args ((not _let_560))) :args _let_283)) _let_612 _let_332 _let_316 _let_191 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1041)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_925 _let_928 _let_931 _let_934 _let_696 _let_700 _let_436 _let_191 _let_444 _let_449 _let_942 _let_945 _let_739 _let_743 _let_753 _let_750 _let_732 _let_729 _let_727 _let_958 _let_651 _let_648 _let_965 _let_1035 _let_1037) (SCOPE (TRANS _let_1039 _let_1036 _let_968 _let_967 _let_964 _let_961 _let_953 _let_932 _let_930 _let_926) :args (_let_600 _let_599 _let_602 _let_601 _let_500 _let_499 _let_130 _let_97 _let_118 _let_120 _let_502 _let_521 _let_124 _let_154 _let_574 _let_165 _let_139 _let_571 _let_573 _let_580 _let_476 _let_607 _let_582 _let_586 _let_569))) :args (_let_97 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_476 _let_139 _let_154 _let_521 _let_599 _let_569 _let_600 _let_601 _let_571 _let_573 _let_574 _let_165 _let_580 _let_582 _let_586 _let_602 _let_607))) :args (true _let_1041)) :args ((or _let_2 _let_637 _let_686 _let_685 _let_636 _let_684 _let_919 _let_918 _let_635 _let_634 _let_917 _let_377 _let_915 _let_914 _let_1029 _let_912 _let_910 _let_907 _let_906 _let_905 _let_904 _let_903 _let_613 _let_1028 _let_901 _let_611))) _let_899 _let_871 _let_789 _let_418 _let_719 _let_720 _let_721 _let_776 _let_774 _let_1027 _let_773 _let_772 _let_405 _let_346 _let_612 _let_332 _let_322 _let_768 _let_317 _let_316 _let_674 _let_670 _let_1040 _let_191 _let_989 _let_992 _let_990 _let_997 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_1003 _let_1002 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1030)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_986 _let_983 _let_980 _let_977 _let_958 _let_727 _let_729 _let_732 _let_739 _let_743 _let_436 _let_191 _let_444 _let_449 _let_750 _let_753 _let_700 _let_696 _let_942 _let_945 _let_761 _let_971 _let_1007 _let_965 _let_1035 _let_1037) (SCOPE (TRANS _let_1039 _let_1036 _let_968 _let_967 _let_964 (CONG _let_960 (TRANS _let_1008 _let_1034 _let_1033 _let_1032) :args _let_933) _let_978 _let_981 _let_984 _let_987) :args (_let_565 _let_581 _let_577 _let_583 _let_580 _let_573 _let_571 _let_139 _let_124 _let_154 _let_130 _let_97 _let_118 _let_120 _let_165 _let_574 _let_499 _let_500 _let_502 _let_521 _let_519 _let_524 _let_603 _let_582 _let_586 _let_569))) :args (_let_97 _let_565 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_139 _let_154 _let_519 _let_521 _let_569 _let_524 _let_581 _let_577 _let_571 _let_573 _let_574 _let_165 _let_580 _let_582 _let_586 _let_603 _let_583))) :args (true _let_1030)) :args ((or _let_637 _let_920 _let_686 _let_685 _let_636 _let_684 _let_919 _let_918 _let_635 _let_917 _let_377 _let_916 _let_915 _let_1029 _let_911 _let_909 _let_908 _let_907 _let_906 _let_905 _let_904 _let_903 _let_613 _let_470 _let_1028 _let_1004 _let_900))) _let_880 _let_871 _let_870 _let_789 _let_779 _let_418 _let_719 _let_720 _let_721 _let_775 _let_1027 _let_772 _let_724 _let_405 _let_346 _let_332 _let_322 _let_768 _let_317 _let_316 _let_674 _let_670 _let_767 _let_191 _let_1025 _let_1024 _let_1018 _let_612 _let_332 _let_316 _let_191 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1010)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_922 _let_925 _let_928 _let_931 _let_934 _let_696 _let_700 _let_436 _let_191 _let_444 _let_449 _let_942 _let_945 _let_739 _let_743 _let_753 _let_750 _let_732 _let_729 _let_727 _let_958 _let_651 _let_659 _let_965 _let_1007 _let_971 _let_761 _let_977 _let_980 _let_983 _let_986) (SCOPE (TRANS _let_988 _let_985 _let_982 _let_979 (CONG _let_963 (TRANS _let_976 _let_974 _let_972 _let_1009) :args _let_933) _let_1013 _let_966 _let_1012 _let_1011 _let_953 _let_932 _let_930 _let_926 _let_924) :args (_let_158 _let_600 _let_599 _let_602 _let_601 _let_500 _let_499 _let_130 _let_97 _let_118 _let_120 _let_502 _let_521 _let_124 _let_154 _let_574 _let_165 _let_139 _let_571 _let_573 _let_580 _let_476 _let_595 _let_582 _let_603 _let_524 _let_519 _let_583 _let_577 _let_581 _let_565))) :args (_let_97 _let_565 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_476 _let_139 _let_154 _let_519 _let_521 _let_599 _let_158 _let_600 _let_524 _let_601 _let_581 _let_577 _let_571 _let_573 _let_574 _let_165 _let_580 _let_582 _let_603 _let_602 _let_583 _let_595))) :args (true _let_1010)) :args ((or _let_637 _let_920 _let_686 _let_685 _let_636 _let_684 _let_919 _let_918 _let_635 _let_634 _let_917 _let_377 _let_916 _let_915 _let_914 _let_913 _let_912 _let_911 _let_910 _let_909 _let_908 _let_907 _let_906 _let_905 _let_904 _let_903 _let_613 _let_177 _let_1004 _let_901 _let_900 _let_657))) _let_899 _let_880 _let_871 _let_870 _let_789 _let_779 _let_418 _let_719 _let_720 _let_721 _let_776 _let_775 _let_774 _let_406 _let_773 _let_772 _let_724 _let_405 _let_346 _let_612 _let_332 _let_322 _let_768 _let_317 _let_316 _let_674 _let_670 _let_767 _let_191 _let_661 _let_667 _let_665 _let_711 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_766 _let_765 (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_1005)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_644 _let_1007) (SCOPE (FALSE_ELIM (TRANS (CONG _let_1009 _let_647 :args _let_646) _let_645)) :args _let_1006)) :args _let_1006)) :args (true _let_1005)) (CONG _let_638 (REFL :args (_let_1004)) (REFL :args (_let_902)) :args _let_283)) _let_632 _let_1003 _let_1002 _let_997 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_992 _let_990 _let_989 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_921)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_922 _let_925 _let_928 _let_931 _let_934 _let_696 _let_700 _let_436 _let_191 _let_444 _let_449 _let_942 _let_945 _let_739 _let_743 _let_753 _let_750 _let_732 _let_729 _let_727 _let_958 _let_651 _let_648 _let_965 _let_969 _let_971 _let_761 _let_977 _let_980 _let_983 _let_986) (SCOPE (TRANS _let_988 _let_985 _let_982 _let_979 (CONG _let_963 (TRANS _let_976 _let_974 _let_972 (SYMM _let_970)) :args _let_933) _let_968 _let_967 _let_964 _let_961 _let_953 _let_932 _let_930 _let_926 _let_924) :args (_let_158 _let_600 _let_599 _let_602 _let_601 _let_500 _let_499 _let_130 _let_97 _let_118 _let_120 _let_502 _let_521 _let_124 _let_154 _let_574 _let_165 _let_139 _let_571 _let_573 _let_580 _let_476 _let_607 _let_582 _let_584 _let_524 _let_519 _let_583 _let_577 _let_581 _let_565))) :args (_let_97 _let_565 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_476 _let_139 _let_154 _let_519 _let_521 _let_599 _let_158 _let_600 _let_524 _let_601 _let_581 _let_577 _let_571 _let_573 _let_574 _let_165 _let_580 _let_582 _let_584 _let_602 _let_583 _let_607))) :args (true _let_921)) :args ((or _let_637 _let_920 _let_686 _let_685 _let_636 _let_684 _let_919 _let_918 _let_635 _let_634 _let_917 _let_377 _let_916 _let_915 _let_914 _let_913 _let_912 _let_911 _let_910 _let_909 _let_908 _let_907 _let_906 _let_905 _let_904 _let_903 _let_613 _let_177 _let_902 _let_901 _let_900 _let_611))) _let_899 _let_880 _let_871 _let_870 _let_789 _let_779 _let_418 _let_719 _let_720 _let_721 _let_776 _let_775 _let_774 _let_406 _let_773 _let_772 _let_724 _let_405 _let_346 _let_612 _let_332 _let_322 _let_768 _let_317 _let_316 _let_674 _let_670 _let_767 _let_191 _let_766 _let_765 _let_711 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_667 _let_665 _let_661 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_658)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_659 _let_651 _let_444 _let_191 _let_436) (SCOPE (TRANS _let_438 _let_656 _let_446 _let_655 _let_660) :args (_let_595 _let_476 _let_118 _let_97 _let_130))) :args (_let_97 _let_118 _let_130 _let_476 _let_595))) :args (true _let_658)) :args ((or _let_637 _let_636 _let_635 _let_634 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_let_599 false _let_521 false _let_519 false _let_154 false _let_139 false _let_476 false _let_130 false _let_124 false _let_502 false _let_120 false _let_118 false _let_500 false _let_499 false _let_565 false _let_97 false _let_584 false _let_589 true _let_588 false _let_505 false _let_476 false _let_130 false _let_120 false _let_118 false _let_500 false _let_499 false _let_97 true _let_593 false _let_597 true _let_596 true _let_595 false _let_476 false _let_130 false _let_118 false _let_97 true _let_610 true _let_585 false _let_476 false _let_130 false _let_118 false _let_97)) :args ((or _let_177 _let_560 _let_594) false _let_602 false _let_583 false _let_582 false _let_581 false _let_580 false _let_577 false _let_165 false _let_574 false _let_573 false _let_571 false _let_601 false _let_524 false _let_600 false _let_158 false _let_599 false _let_521 false _let_519 false _let_154 false _let_139 false _let_476 false _let_130 false _let_124 false _let_502 false _let_120 false _let_118 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(_let_1058))))) (let ((_let_1112 (EQ_RESOLVE (ASSUME :args (_let_49)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_49 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Z_6 tptp.nat) (X_40 tptp.nat) (Y_14 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_40))) (or (not (@ _let_1 Y_14)) (not (@ (@ tptp.ord_less_nat Y_14) Z_6)) (@ _let_1 Z_6)))) _let_1062))))))) (let ((_let_1113 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1112 :args (_let_501 _let_96 _let_116 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_1062))))) (let ((_let_1114 (ho_4 (ho_135 k_144 _let_498) _let_517))) (let ((_let_1115 (ho_4 _let_881 _let_515))) (let ((_let_1116 (not _let_1115))) (let ((_let_1117 (or _let_1116 _let_1067 _let_1114))) (let ((_let_1118 (forall ((C_21 tptp.nat) (D_6 tptp.nat) (A_47 tptp.nat) (B_27 tptp.nat)) (or (not (ho_4 (ho_135 k_144 A_47) B_27)) (not (ho_4 (ho_135 k_144 C_21) D_6)) (ho_4 (ho_135 k_144 (ho_100 (ho_124 k_161 A_47) C_21)) (ho_100 (ho_124 k_161 B_27) D_6)))))) (let ((_let_1119 (EQ_RESOLVE (ASSUME 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(SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_362)) :args _let_361)) _let_360 :args ((not _let_1222) false _let_358)))) (let ((_let_1225 (_let_1088))) (let ((_let_1226 (_let_1221))) (let ((_let_1227 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_1226)) :args _let_1226) (REWRITE :args ((=> _let_1221 (not (not (= _let_1087 _let_1054)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_1221) _let_1220))) (REFL :args _let_1225) :args _let_283)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_1223)) :args ((or _let_1222 _let_1221 (not _let_1223)))) _let_1224 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_784 :args (_let_1054 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_786)) :args _let_785))) _let_784 :args (_let_1223 false _let_783)) :args (_let_1221 true _let_1222 false _let_1223)) :args (_let_1088 true _let_1220)))) (let ((_let_1228 (not _let_1089))) (let ((_let_1229 (ho_4 _let_1092 _let_1080))) (let ((_let_1230 (not _let_1229))) (let ((_let_1231 (ho_4 _let_472 _let_1080))) (let ((_let_1232 (not _let_1231))) (let ((_let_1233 (or _let_1232 _let_1230 _let_1100 _let_1228))) (let ((_let_1234 (forall ((I_4 tptp.nat) (BOUND_VARIABLE_11822 tptp.nat)) (let ((_let_1 (ho_14 (ho_13 k_12 tptp.a) (ho_14 (ho_13 k_12 tptp.b) (ho_14 (ho_13 k_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176) tptp.nil_Ar1286194111le_alt))))) (let ((_let_2 (ho_106 k_105 _let_1))) (let ((_let_3 (ho_99 k_109 _let_1))) (or (not (ho_4 (ho_135 k_144 I_4) _let_3)) (not (ho_4 (ho_135 k_144 BOUND_VARIABLE_11822) _let_3)) (= I_4 BOUND_VARIABLE_11822) (not (= (ho_107 _let_2 BOUND_VARIABLE_11822) (ho_107 _let_2 I_4)))))))))) (let ((_let_1235 (not _let_1233))) (let ((_let_1236 (= _let_1222 _let_1234))) (let ((_let_1237 (not _let_1234))) (let ((_let_1238 (_let_1237))) (let ((_let_1239 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_1238)) :args 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_let_1107))) (let ((_let_1333 (not _let_1106))) (let ((_let_1334 (not _let_1105))) (let ((_let_1335 (and _let_97 _let_118 _let_130 _let_476 _let_1105 _let_158 _let_1057 _let_1106 _let_1088 _let_1089 _let_470 _let_471 _let_1107 _let_1096))) (let ((_let_1336 (ASSUME :args (_let_1106)))) (let ((_let_1337 (SYMM _let_1336))) (let ((_let_1338 (ASSUME :args (_let_1105)))) (let ((_let_1339 (SYMM _let_1338))) (let ((_let_1340 (CONG _let_929 _let_1339 :args _let_927))) (let ((_let_1341 (ASSUME :args (_let_1107)))) (let ((_let_1342 (SYMM _let_1341))) (let ((_let_1343 (SYMM _let_1342))) (let ((_let_1344 (ASSUME :args (_let_1096)))) (let ((_let_1345 (SYMM _let_1344))) (let ((_let_1346 (CONG _let_1279 (TRANS (SYMM _let_1345) _let_956 _let_445 _let_937 _let_437) :args _let_933))) (let ((_let_1347 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_1021 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_231 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_1023)) :args _let_1022))) _let_1021 :args (_let_474 false _let_1019)))) (let ((_let_1348 (not _let_473))) (let ((_let_1349 (REORDERING (CNF_EQUIV_POS2 :args (_let_474)) :args ((or _let_471 _let_1348 (not _let_474)))))) (let ((_let_1350 (and _let_97 _let_118 _let_130 _let_476 _let_1348))) (let ((_let_1351 (ASSUME :args (_let_1348)))) (let ((_let_1352 (TRANS _let_1017 _let_447 _let_443 _let_439))) (let ((_let_1353 (REFL :args (_let_472)))) (let ((_let_1354 (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_1350)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1351 _let_436 _let_191 _let_444 _let_651) (SCOPE (FALSE_ELIM (TRANS (CONG _let_1353 _let_1352 :args _let_432) (FALSE_INTRO _let_1351))) :args (_let_1348 _let_130 _let_97 _let_118 _let_476))) :args (_let_97 _let_118 _let_130 _let_476 _let_1348))) :args (true _let_1350)) (CONG _let_642 _let_641 _let_640 _let_639 (MACRO_SR_PRED_INTRO :args ((= (not _let_1348) _let_473))) (REFL :args ((not _let_478))) :args _let_283)))) (let ((_let_1355 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_231 _let_477))) (let ((_let_1356 (or _let_478 _let_1355))) (let ((_let_1357 (ho_4 _let_472 _let_592))) (let ((_let_1358 (= _let_1356 _let_1357))) (let ((_let_1359 (ho_4 _let_472 _let_122))) (let ((_let_1360 (= _let_122 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_231))) (let ((_let_1361 (or _let_1359 _let_1360))) (let ((_let_1362 (= _let_122 (ho_100 _let_516 _let_96)))) (let ((_let_1363 (= _let_116 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_231))) (let ((_let_1364 (forall ((M tptp.nat) (N_5 tptp.nat)) (= (ho_100 (ho_124 k_161 M) (ho_100 k_162 N_5)) (ho_100 (ho_124 k_161 (ho_100 k_162 M)) N_5))))) (let ((_let_1365 (EQ_RESOLVE (ASSUME :args (_let_41)) (PREPROCESS :args ((= _let_41 _let_1364)))))) (let ((_let_1366 (not _let_1360))) (let ((_let_1367 (ASSUME :args (_let_1362)))) (let ((_let_1368 (SYMM (SYMM _let_1367)))) (let ((_let_1369 (ASSUME :args (_let_1360)))) (let ((_let_1370 (SYMM _let_1369))) (let ((_let_1371 (forall ((N_17 tptp.nat) (X_16 tptp.arrow_475358991le_alt) (Xs_32 tptp.list_A2115238852le_alt)) (let ((_let_1 (ho_13 k_12 X_16))) (= (ho_14 _let_1 (ho_14 (ho_143 k_168 N_17) Xs_32)) (ho_14 (ho_143 k_168 (ho_100 k_162 N_17)) (ho_14 _let_1 Xs_32))))))) (let ((_let_1372 (EQ_RESOLVE (ASSUME :args (_let_26)) (PREPROCESS :args ((= _let_26 _let_1371)))))) (let ((_let_1373 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1372 :args (_let_116 tptp.b _let_103 QUANTIFIERS_INST_E_MATCHING ((ho_14 (ho_13 k_12 X_16) (ho_14 (ho_143 k_168 N_17) Xs_32))))) :args (_let_1371))) _let_1372 :args (_let_541 false _let_1371)))) (let ((_let_1374 (ho_14 _let_131 _let_155))) (let ((_let_1375 (= _let_106 _let_1374))) (let ((_let_1376 (not _let_1375))) (let ((_let_1377 (or _let_1376 _let_556))) (let ((_let_1378 (forall ((N_35 tptp.nat) (Xs_61 tptp.list_A2115238852le_alt) (Y_7 tptp.arrow_475358991le_alt) (Ys_12 tptp.list_A2115238852le_alt)) (or (not (= (ho_14 (ho_13 k_12 Y_7) Ys_12) (ho_14 (ho_143 k_142 N_35) Xs_61))) (= Y_7 (ho_107 (ho_106 k_105 Xs_61) N_35)))))) (let ((_let_1379 (EQ_RESOLVE (ASSUME :args (_let_46)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_46 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N_35 tptp.nat) (Xs_61 tptp.list_A2115238852le_alt) (Y_7 tptp.arrow_475358991le_alt) (Ys_12 tptp.list_A2115238852le_alt)) (or (not (= (@ (@ tptp.drop_A1346709759le_alt N_35) Xs_61) (@ (@ tptp.cons_A228743023le_alt Y_7) Ys_12))) (= Y_7 (@ (@ tptp.nth_Ar125878976le_alt Xs_61) N_35)))) _let_1378))))))) (let ((_let_1380 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_335 :args (tptp.b _let_106 QUANTIFIERS_INST_E_MATCHING _let_337)) :args _let_336)) _let_335 :args (_let_1375 false _let_333)))) (let ((_let_1381 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_1377)) :args ((or _let_1376 _let_556 (not _let_1377)))) _let_1380 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1379 :args (_let_116 _let_155 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 tptp.nil_Ar1286194111le_alt QUANTIFIERS_INST_E_MATCHING ((ho_14 (ho_13 k_12 Y_7) Ys_12) (ho_14 (ho_143 k_142 N_35) Xs_61)))) :args (_let_1378))) _let_1379 :args (_let_1377 false _let_1378)) :args (_let_556 false _let_1375 false _let_1377)))) (let ((_let_1382 (and _let_97 _let_1079 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_141 _let_154 _let_519 _let_521 _let_1105 _let_158 _let_1106 _let_524 _let_1085 _let_1084 _let_536 _let_538 _let_1081 _let_541 _let_1088 _let_1089 _let_556 _let_1091 _let_1107 _let_1090 _let_1363))) (let ((_let_1383 (TRANS (CONG (TRANS (CONG _let_744 (TRANS _let_1267 _let_1327) :args _let_435) _let_747) _let_434 :args _let_433) _let_746 _let_740))) (let ((_let_1384 (REFL :args (_let_479)))) (let ((_let_1385 (CONG _let_749 (TRANS _let_758 _let_701) :args _let_738))) (let ((_let_1386 (ASSUME :args (_let_541)))) (let ((_let_1387 (SYMM _let_1386))) (let ((_let_1388 (ASSUME :args (_let_141)))) (let ((_let_1389 (SYMM _let_1388))) (let ((_let_1390 (SYMM _let_1389))) (let ((_let_1391 (REFL :args (_let_147)))) (let ((_let_1392 (CONG _let_959 (TRANS (CONG _let_1391 _let_1390 :args _let_736) (SYMM _let_1387) (CONG _let_1385 _let_1384 :args _let_736)) :args _let_957))) (let ((_let_1393 (CONG _let_1392 _let_1383 :args _let_933))) (let ((_let_1394 (CONG (REFL :args (_let_156)) (SYMM _let_1383) :args _let_933))) (let ((_let_1395 (ASSUME :args (_let_556)))) (let ((_let_1396 (SYMM (SYMM _let_1395)))) (let ((_let_1397 (CONG (TRANS _let_973 (CONG _let_744 (TRANS _let_946 _let_944 (CONG (TRANS _let_1031 (CONG _let_442 (TRANS _let_758 _let_701 (SYMM _let_1327) _let_1266) :args _let_435)) _let_434 :args _let_433) _let_1265) :args _let_435)) _let_434 :args _let_433))) (let ((_let_1398 (ASSUME :args (_let_1363)))) (let ((_let_1399 (CONG _let_929 (SYMM _let_1339) :args _let_927))) (let ((_let_1400 (SYMM _let_1337))) (let ((_let_1401 (REFL :args (_let_96)))) (let ((_let_1402 (CONG (SYMM _let_1392) _let_1401 :args _let_933))) (let ((_let_1403 (ho_4 _let_472 _let_518))) (let ((_let_1404 (= _let_1403 _let_1361))) (let ((_let_1405 (and _let_97 _let_499 _let_500 _let_118 _let_120 _let_130 _let_519 _let_536 _let_538 _let_1081 _let_1231))) (let ((_let_1406 (ASSUME :args (_let_1231)))) (let ((_let_1407 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_1404)) :args ((or _let_1361 (not _let_1403) (not _let_1404)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_1405)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1406 _let_1264 _let_1266 _let_1269 _let_191 _let_436 _let_444 _let_700 _let_696 _let_449 _let_761) (SCOPE (TRUE_ELIM (TRANS (CONG _let_1353 _let_1296 :args _let_432) (TRUE_INTRO _let_1406))) :args (_let_1231 _let_1081 _let_538 _let_536 _let_97 _let_130 _let_118 _let_499 _let_500 _let_120 _let_519))) :args (_let_97 _let_499 _let_500 _let_118 _let_120 _let_130 _let_519 _let_536 _let_538 _let_1081 _let_1231))) :args (true _let_1405)) _let_191 _let_670 _let_674 _let_316 _let_317 _let_332 _let_724 _let_1163 _let_1164 _let_1165 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_1233 0)) (CONG _let_1240 (MACRO_SR_PRED_INTRO :args ((= (not _let_1232) _let_1231))) :args _let_283)) :args ((or _let_1231 _let_1233))) _let_1239 :args (_let_1231 true _let_1233)) :args (_let_1403 false _let_97 false _let_499 false _let_500 false _let_118 false _let_120 false _let_130 false _let_519 false _let_536 false _let_538 false _let_1081 false _let_1231)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_663 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_231 _let_122 QUANTIFIERS_INST_E_MATCHING _let_714)) :args _let_664))) _let_663 :args (_let_1404 false _let_662)) :args (_let_1361 false _let_1403 false _let_1404)))) (let ((_let_1408 (REORDERING (CNF_OR_POS :args (_let_1361)) :args ((or _let_1359 _let_1360 (not _let_1361)))))) (let ((_let_1409 (and _let_97 _let_499 _let_500 _let_118 _let_120 _let_130 _let_476 _let_505 _let_1359))) (let ((_let_1410 (ASSUME :args (_let_1359)))) (let ((_let_1411 (RESOLUTION (CNF_AND_NEG :args (_let_1409)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1410 _let_436 _let_191 _let_444 _let_449 _let_705 _let_700 _let_696 _let_651) (SCOPE (TRUE_ELIM (TRANS (CONG _let_1353 (TRANS (CONG _let_694 _let_1352 :args _let_433) _let_758 _let_701 (SYMM _let_448) _let_449 _let_709) :args _let_432) (CONG _let_1353 (TRANS _let_707 _let_450 _let_448) :args _let_432) (TRUE_INTRO _let_1410))) :args (_let_1359 _let_130 _let_97 _let_118 _let_120 _let_505 _let_499 _let_500 _let_476))) :args (_let_97 _let_499 _let_500 _let_118 _let_120 _let_130 _let_476 _let_505 _let_1359))) :args (true _let_1409)))) (let ((_let_1412 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_663 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_231 _let_477 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_664)) _let_663 :args (_let_1358 false _let_662)))) (let ((_let_1413 (REORDERING (CNF_EQUIV_POS2 :args (_let_1358)) :args ((or _let_1356 (not _let_1357) (not _let_1358)))))) (let ((_let_1414 (REORDERING (CNF_OR_POS :args (_let_1356)) :args ((or _let_478 _let_1355 (not _let_1356)))))) (let ((_let_1415 (not _let_1355))) (let ((_let_1416 (and _let_97 _let_118 _let_130 _let_476 _let_1355))) (let ((_let_1417 (ASSUME :args (_let_1355)))) (let ((_let_1418 (SYMM _let_1417))) (let ((_let_1419 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1416)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1417 _let_651 _let_444 _let_191 _let_436) (SCOPE (TRANS _let_438 _let_656 _let_446 _let_655 _let_1418) :args (_let_1355 _let_476 _let_118 _let_97 _let_130))) :args (_let_97 _let_118 _let_130 _let_476 _let_1355))) :args (true _let_1416)) :args ((or _let_637 _let_636 _let_635 _let_634 _let_1363 _let_1415))) _let_612 _let_332 _let_316 _let_191 _let_1414 _let_1413 _let_1412 _let_1411 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_1408 _let_1407 (RESOLUTION (CNF_AND_NEG :args (_let_1382)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_761 _let_1388 _let_739 _let_942 _let_696 _let_436 _let_945 _let_700 _let_922 _let_1256 _let_1395 _let_191 _let_1336 _let_971 _let_743 _let_1269 _let_1283 _let_444 _let_1258 _let_1260 _let_1262 _let_1338 _let_1266 _let_1398 _let_1264 _let_1386 _let_449 _let_1276 _let_1278 _let_1341) (SCOPE (TRANS _let_1402 _let_923 _let_1400 _let_1399 _let_1342 (CONG _let_1281 (SYMM (SYMM _let_1398)) :args _let_933) _let_1286 _let_1284 _let_1282 (CONG _let_1279 (TRANS _let_1277 _let_1034 _let_1033 _let_1397) :args _let_933) _let_1263 _let_1261 _let_1259 _let_1257 _let_1396 _let_1394 _let_1393) :args (_let_519 _let_141 _let_124 _let_502 _let_500 _let_130 _let_521 _let_499 _let_158 _let_1079 _let_556 _let_97 _let_1106 _let_524 _let_154 _let_536 _let_1089 _let_118 _let_1085 _let_1084 _let_1090 _let_1105 _let_538 _let_1363 _let_1081 _let_541 _let_120 _let_1091 _let_1088 _let_1107))) :args (_let_97 _let_1079 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_141 _let_154 _let_519 _let_521 _let_1105 _let_158 _let_1106 _let_524 _let_1085 _let_1084 _let_536 _let_538 _let_1081 _let_541 _let_1088 _let_1089 _let_556 _let_1091 _let_1107 _let_1090 _let_1363))) :args (true _let_1382)) _let_1330 _let_1245 _let_1381 _let_1241 _let_1227 _let_1219 _let_1168 _let_1373 _let_1165 _let_1164 _let_1163 _let_775 _let_1322 _let_406 _let_1321 _let_772 _let_724 _let_405 _let_347 _let_332 _let_322 _let_768 _let_317 _let_316 _let_674 _let_670 _let_1161 _let_191 (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_1367 _let_1369 _let_1276 _let_1312) :args (_let_1362 _let_1306 _let_1091 _let_1360)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_1313) (TRUE_INTRO (TRANS _let_1370 _let_1368 (SYMM (TRANS _let_1277 _let_1368)))))) :args (_let_1362 _let_1360 _let_1091 _let_1306)) :args ((not (and _let_1362 _let_1306 _let_1091 _let_1360)) SB_LITERAL))) (CONG (REFL :args ((not _let_1362))) _let_1309 (REFL :args (_let_1247)) (REFL :args (_let_1366)) :args _let_283)) _let_1307 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1365 :args (_let_116 _let_96 QUANTIFIERS_INST_E_MATCHING ((ho_100 (ho_124 k_161 M) (ho_100 k_162 N_5))))) :args (_let_1364))) _let_1365 :args (_let_1362 false _let_1364)) :args ((or _let_478 _let_1247 _let_482) false _let_476 false _let_130 false _let_118 false _let_97 false _let_1355 false _let_1356 false _let_1358 false _let_1357 false _let_505 false _let_476 false _let_130 false _let_120 false _let_118 false _let_500 false _let_499 false _let_97 false _let_1359 false _let_1361 true _let_1363 false _let_1107 false _let_1090 false _let_556 false _let_1089 false _let_1088 false _let_1085 false _let_1084 false _let_541 false _let_1081 false _let_538 false _let_536 false _let_524 false _let_1106 false _let_158 false _let_1105 false _let_521 false _let_519 false _let_154 false _let_141 false _let_130 false _let_124 false _let_502 false _let_120 false _let_118 false _let_500 false _let_499 false _let_1079 false _let_97 true _let_1360 true _let_1100 false _let_1362)))) (let ((_let_1420 (and _let_1306 _let_1096))) (let ((_let_1421 (_let_1306 _let_1096))) (let ((_let_1422 (not _let_556))) (let ((_let_1423 (not _let_541))) (let ((_let_1424 (not _let_141))) (let ((_let_1425 (and _let_97 _let_1079 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_476 _let_141 _let_154 _let_519 _let_521 _let_1105 _let_158 _let_1106 _let_524 _let_1085 _let_1084 _let_536 _let_538 _let_1081 _let_541 _let_1088 _let_1089 _let_556 _let_1360 _let_1107 _let_1090 _let_1096))) (let ((_let_1426 (CONG _let_1281 _let_1285 :args _let_933))) (let ((_let_1427 (SYMM _let_1284))) (let ((_let_1428 (CONG _let_1279 _let_1280 :args _let_933))) (let ((_let_1429 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1425)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_761 _let_1388 _let_739 _let_942 _let_651 _let_449 _let_696 _let_436 _let_945 _let_700 _let_922 _let_1256 _let_1395 _let_191 _let_1336 _let_1369 _let_971 _let_743 _let_1269 _let_1283 _let_1344 _let_444 _let_1258 _let_1260 _let_1262 _let_1338 _let_1266 _let_1264 _let_1386 _let_1278 _let_1341) (SCOPE (TRANS _let_1402 _let_923 _let_1400 _let_1399 _let_1342 (CONG _let_1281 (TRANS _let_436 (SYMM _let_937) _let_444 _let_655 _let_1345) :args _let_933) _let_1428 _let_1427 _let_1426 (CONG _let_1279 (TRANS _let_1370 _let_1034 _let_1033 _let_1397) :args _let_933) _let_1263 _let_1261 _let_1259 _let_1257 _let_1396 _let_1394 _let_1393) :args (_let_519 _let_141 _let_124 _let_502 _let_476 _let_120 _let_500 _let_130 _let_521 _let_499 _let_158 _let_1079 _let_556 _let_97 _let_1106 _let_1360 _let_524 _let_154 _let_536 _let_1089 _let_1096 _let_118 _let_1085 _let_1084 _let_1090 _let_1105 _let_538 _let_1081 _let_541 _let_1088 _let_1107))) :args (_let_97 _let_1079 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_130 _let_476 _let_141 _let_154 _let_519 _let_521 _let_1105 _let_158 _let_1106 _let_524 _let_1085 _let_1084 _let_536 _let_538 _let_1081 _let_541 _let_1088 _let_1089 _let_556 _let_1360 _let_1107 _let_1090 _let_1096))) :args (true _let_1425)) :args ((or _let_637 _let_1254 _let_686 _let_685 _let_636 _let_684 _let_919 _let_918 _let_635 _let_634 _let_1424 _let_377 _let_916 _let_915 _let_1334 _let_913 _let_1333 _let_911 _let_1253 _let_1252 _let_1251 _let_1250 _let_1249 _let_1423 _let_1248 _let_1228 _let_1422 _let_1366 _let_1332 _let_1246 _let_482 _let_1331))) _let_1330 _let_1245 _let_1381 _let_1241 _let_1227 _let_1219 _let_1168 _let_1373 _let_1165 _let_1164 _let_1163 _let_775 _let_1322 _let_406 _let_1321 _let_772 _let_724 _let_405 _let_347 _let_612 _let_332 _let_322 _let_768 _let_317 _let_316 _let_674 _let_670 _let_1161 _let_191 _let_1408 _let_1407 _let_1411 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_1413 _let_1412 _let_1414 (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_1420)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1312 _let_1344) (SCOPE (FALSE_ELIM (TRANS (CONG _let_1285 _let_1345 :args _let_646) _let_1313)) :args _let_1421)) :args _let_1421)) :args (true _let_1420)) (CONG _let_1309 (REFL :args (_let_1331)) (REFL :args (_let_1415)) :args _let_283)) :args ((or _let_1100 _let_1415 _let_1331))) _let_1307 :args ((or _let_478 _let_482 _let_1331) false _let_1107 false _let_1090 false _let_556 false _let_1089 false _let_1088 false _let_1085 false _let_1084 false _let_541 false _let_1081 false _let_538 false _let_536 false _let_524 false _let_1106 false _let_158 false _let_1105 false _let_521 false _let_519 false _let_154 false _let_141 false _let_476 false _let_130 false _let_124 false _let_502 false _let_120 false _let_118 false _let_500 false _let_499 false _let_1079 false _let_97 false _let_1360 false _let_1361 true _let_1359 false _let_505 false _let_476 false _let_130 false _let_120 false _let_118 false _let_500 false _let_499 false _let_97 true _let_1357 false _let_1358 true _let_1356 true _let_1355 true _let_1100)))) (let ((_let_1430 (and _let_97 _let_118 _let_130 _let_476 _let_1105 _let_158 _let_1057 _let_1106 _let_1088 _let_1089 _let_470 _let_1101 _let_1107 _let_1355))) (let ((_let_1431 (CONG _let_1279 (TRANS (SYMM _let_1418) _let_956 _let_445 _let_937 _let_437) :args _let_933))) (let ((_let_1432 (ASSUME :args (_let_1101)))) (let ((_let_1433 (SYMM _let_1432))) (let ((_let_1434 (CONG _let_1281 (SYMM _let_1433) :args _let_933))) (let ((_let_1435 (and _let_97 _let_1079 _let_499 _let_500 _let_118 _let_120 _let_502 _let_130 _let_519 _let_521 _let_1057 _let_524 _let_1085 _let_1084 _let_536 _let_538 _let_1081 _let_1088 _let_1089 _let_1101 _let_1360 _let_1090))) (let ((_let_1436 (forall ((X_113 tptp.arrow_475358991le_alt)) (= (ho_14 (ho_13 k_12 X_113) tptp.nil_Ar1286194111le_alt) (ho_14 (ho_13 k_29 X_113) tptp.nil_Ar1286194111le_alt))))) (let ((_let_1437 (EQ_RESOLVE (ASSUME :args (_let_88)) (PREPROCESS :args ((= _let_88 _let_1436)))))) (let ((_let_1438 (_let_1436))) (let ((_let_1439 ((ho_13 k_12 X_113)))) (let ((_let_1440 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1437 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_177 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_1439)) :args _let_1438)) _let_1437 :args (_let_486 false _let_1436)))) (let ((_let_1441 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_826 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_101 QUANTIFIERS_INST_E_MATCHING _let_829)) :args _let_827)) _let_826 :args (_let_497 false _let_825)))) (let ((_let_1442 (or _let_419 _let_510))) (let ((_let_1443 (ho_4 _let_881 _let_96))) (let ((_let_1444 (or _let_1443 _let_513))) (let ((_let_1445 (forall ((M tptp.nat) (N_5 tptp.nat)) (or (ho_4 (ho_135 k_144 M) N_5) (= M (ho_100 (ho_124 k_161 N_5) (ho_100 (ho_124 k_169 M) N_5))))))) (let ((_let_1446 (EQ_RESOLVE (ASSUME :args (_let_21)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((M tptp.nat) (N_5 tptp.nat)) (or (@ (@ tptp.ord_less_nat M) N_5) (= M (@ (@ tptp.plus_plus_nat N_5) (@ (@ tptp.minus_minus_nat M) N_5))))) _let_1445))))))) (let ((_let_1447 (not (@ (@ tptp.ord_less_nat _let_396) _let_180)))) (let ((_let_1448 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_1444)) :args ((or _let_1443 _let_513 (not _let_1444)))) (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO _let_190 :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (@ (@ tptp.ord_less_nat _let_398) _let_183)) _let_1447))) (PREPROCESS :args ((= _let_1447 (not _let_1443)))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1446 :args (_let_116 _let_96 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_4 (ho_135 k_144 M) N_5) true))))) :args (_let_1445))) _let_1446 :args (_let_1444 false _let_1445)) :args (_let_513 true _let_1443 false _let_1444)))) (let ((_let_1449 (forall ((A_51 tptp.nat)) (= A_51 (ho_100 (ho_124 k_161 (ho_56 k_89 (ho_19 k_18 (ho_7 k_17 k_11)))) A_51))))) (let ((_let_1450 (forall ((A_51 tptp.nat)) (= A_51 (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat ll_2)))) A_51))))) (let ((_let_1451 (EQ_RESOLVE (ASSUME :args (_let_35)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_189 :args ((forall ((A_51 tptp.nat)) (= A_51 (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_51))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A_51 tptp.nat)) (= A_51 (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat (@ tptp.linord810813188et_nat (@ tptp.collect_nat (lambda ((BOUND_VARIABLE_14858 tptp.nat)) false))))) A_51))) _let_1450))) (PREPROCESS :args ((= _let_1450 _let_1449))))))) (let ((_let_1452 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1451 :args (_let_511 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_1449))) _let_1451 :args (_let_520 false _let_1449)))) (let ((_let_1453 (= tptp.nil_Ar1286194111le_alt _let_103))) (let ((_let_1454 (or _let_1453 _let_523))) (let ((_let_1455 (forall ((Xs_121 tptp.list_A2115238852le_alt)) (or (= tptp.nil_Ar1286194111le_alt Xs_121) (= (ho_54 k_53 Xs_121) (ho_54 k_70 (ho_14 k_64 Xs_121))))))) (let ((_let_1456 (EQ_RESOLVE (ASSUME :args (_let_64)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_64 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xs_121 tptp.list_A2115238852le_alt)) (or (= tptp.nil_Ar1286194111le_alt Xs_121) (= (@ tptp.hd_Arr1965683346le_alt (@ tptp.rev_Ar1106406943le_alt Xs_121)) (@ tptp.last_A1217315288le_alt Xs_121)))) _let_1455))))))) (let ((_let_1457 (not _let_1453))) (let ((_let_1458 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_372 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_101 QUANTIFIERS_INST_E_MATCHING _let_374)) :args _let_373)) _let_372 :args (_let_1457 false _let_370)))) (let ((_let_1459 (forall ((I_8 tptp.nat) (J_1 tptp.nat) (Xs_28 tptp.list_A2115238852le_alt)) (= (ho_14 (ho_26 k_35 (ho_14 (ho_143 k_168 I_8) Xs_28)) (ho_14 (ho_143 k_168 J_1) (ho_14 (ho_143 k_142 I_8) Xs_28))) (ho_14 (ho_143 k_168 (ho_100 (ho_124 k_161 I_8) J_1)) Xs_28))))) (let ((_let_1460 (EQ_RESOLVE (ASSUME :args (_let_24)) (PREPROCESS :args ((= _let_24 _let_1459)))))) (let ((_let_1461 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_410 :args (_let_96 _let_101 QUANTIFIERS_INST_E_MATCHING _let_412)) :args _let_411)) _let_410 :args (_let_526 false _let_409)))) (let ((_let_1462 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1437 :args (tptp.a QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_1439)) :args _let_1438)) _let_1437 :args (_let_527 false _let_1436)))) (let ((_let_1463 (forall ((N_19 tptp.nat)) (= tptp.nil_Ar1286194111le_alt (ho_14 (ho_143 k_168 N_19) tptp.nil_Ar1286194111le_alt))))) (let ((_let_1464 (EQ_RESOLVE (ASSUME :args (_let_28)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N_19 tptp.nat)) (= tptp.nil_Ar1286194111le_alt (@ (@ tptp.take_A614047655le_alt N_19) tptp.nil_Ar1286194111le_alt))) _let_1463))))))) (let ((_let_1465 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1464 :args (_let_116 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_143 k_168 N_19)))) :args (_let_1463))) _let_1464 :args (_let_540 false _let_1463)))) (let ((_let_1466 (forall ((N_11 tptp.nat) (Xs_20 tptp.list_A2115238852le_alt) (Ys_3 tptp.list_A2115238852le_alt)) (let ((_let_1 (ho_143 k_168 N_11))) (= (ho_14 (ho_26 k_35 (ho_14 _let_1 Xs_20)) (ho_14 (ho_143 k_168 (ho_100 (ho_124 k_169 N_11) (ho_99 k_109 Xs_20))) Ys_3)) (ho_14 _let_1 (ho_14 (ho_26 k_35 Xs_20) Ys_3))))))) (let ((_let_1467 (EQ_RESOLVE (ASSUME :args (_let_20)) (PREPROCESS :args ((= _let_20 _let_1466)))))) (let ((_let_1468 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1467 :args (_let_116 tptp.nil_Ar1286194111le_alt _let_101 QUANTIFIERS_INST_E_MATCHING ((ho_14 (ho_143 k_168 (ho_100 (ho_124 k_169 N_11) (ho_99 k_109 Xs_20))) Ys_3)))) :args (_let_1466))) _let_1467 :args (_let_543 false _let_1466)))) (let ((_let_1469 (forall ((I_2 tptp.nat) (Xs_16 tptp.list_A2115238852le_alt)) (= (ho_14 (ho_143 k_168 (ho_100 (ho_124 k_169 (ho_99 k_109 Xs_16)) I_2)) (ho_14 k_64 Xs_16)) (ho_14 k_64 (ho_14 (ho_143 k_142 I_2) Xs_16)))))) (let ((_let_1470 (EQ_RESOLVE (ASSUME :args (_let_19)) (PREPROCESS :args ((= _let_19 _let_1469)))))) (let ((_let_1471 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1470 :args (_let_116 _let_103 QUANTIFIERS_INST_E_MATCHING ((ho_14 (ho_143 k_142 I_2) Xs_16)))) :args (_let_1469))) _let_1470 :args (_let_544 false _let_1469)))) (let ((_let_1472 (= tptp.nil_Ar1286194111le_alt _let_495))) (let ((_let_1473 (or _let_1472 _let_547))) (let ((_let_1474 (forall ((Xs_118 tptp.list_A2115238852le_alt)) (or (= tptp.nil_Ar1286194111le_alt Xs_118) (= (ho_14 (ho_26 k_35 (ho_14 k_72 Xs_118)) (ho_14 (ho_13 k_12 (ho_54 k_70 Xs_118)) tptp.nil_Ar1286194111le_alt)) (ho_14 k_57 Xs_118)))))) (let ((_let_1475 (EQ_RESOLVE (ASSUME :args (_let_62)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_62 SB_DEFAULT SBA_FIXPOINT)) 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_let_1500)))))) (let ((_let_1502 (ho_16 k_15 _let_495))) (let ((_let_1503 (= _let_1502 _let_557))) (let ((_let_1504 (forall ((Xs_133 tptp.list_A2115238852le_alt)) (= (ho_16 k_15 Xs_133) (ho_16 k_15 (ho_14 k_57 Xs_133)))))) (let ((_let_1505 (EQ_RESOLVE (ASSUME :args (_let_69)) (PREPROCESS :args ((= _let_69 _let_1504)))))) (let ((_let_1506 (= _let_104 _let_1502))) (let ((_let_1507 (forall ((Xs_135 tptp.list_A2115238852le_alt)) (= (ho_16 k_15 Xs_135) (ho_16 k_15 (ho_14 k_64 Xs_135)))))) (let ((_let_1508 (EQ_RESOLVE (ASSUME :args (_let_70)) (PREPROCESS :args ((= _let_70 _let_1507)))))) (let ((_let_1509 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_1506)) :args ((or _let_285 _let_1502 (not _let_1506)))) _let_288 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1508 :args (_let_103 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_14 k_64 Xs_135)))) :args (_let_1507))) _let_1508 :args (_let_1506 false _let_1507)) :args (_let_1502 false _let_104 false _let_1506)))) (let 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(MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_814 :args (tptp.nil_Ar1286194111le_alt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_101 QUANTIFIERS_INST_CBQI_PROP)) :args _let_815))) _let_814 :args (_let_1479 false _let_813)) :args (_let_1480 true _let_1478 false _let_1479)) :args (_let_1477 false _let_497 true _let_1476)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1475 :args (_let_495 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_54 k_70 Xs_118)))) :args (_let_1474))) _let_1475 :args (_let_1473 false _let_1474)) :args (_let_547 true _let_1472 false _let_1473)) _let_1471 _let_1468 _let_1373 _let_1465 _let_1164 _let_1163 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_826 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 tptp.nil_Ar1286194111le_alt QUANTIFIERS_INST_E_MATCHING _let_829)) :args _let_827))) _let_826 :args (_let_534 false _let_825)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_826 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_99 QUANTIFIERS_INST_E_MATCHING ((ho_14 (ho_26 k_35 (ho_14 k_64 Xs_142)) (ho_14 _let_828 tptp.nil_Ar1286194111le_alt))))) :args _let_827)) _let_826 :args (_let_532 false _let_825)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_466 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_178 tptp.nil_Ar1286194111le_alt _let_106 QUANTIFIERS_INST_E_MATCHING ((ho_14 (ho_26 k_35 (ho_14 _let_468 Xs_164)) Ys_47)))) :args _let_467))) _let_466 :args (_let_529 false _let_465)) _let_1462 _let_1461 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1460 :args (_let_96 _let_116 _let_103 QUANTIFIERS_INST_E_MATCHING ((ho_14 (ho_143 k_168 J_1) (ho_14 (ho_143 k_142 I_8) Xs_28))))) :args (_let_1459))) _let_1460 :args (_let_525 false _let_1459)) _let_775 _let_406 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_1454)) :args ((or _let_1453 _let_523 (not _let_1454)))) _let_1458 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1456 :args _let_771) :args (_let_1455))) _let_1456 :args (_let_1454 false _let_1455)) :args (_let_523 true _let_1453 false _let_1454)) _let_772 _let_1452 _let_724 _let_809 _let_405 _let_1448 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_1442)) :args ((or _let_419 _let_510 (not _let_1442)))) _let_424 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_367 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_101 QUANTIFIERS_INST_E_MATCHING _let_369)) :args _let_368)) _let_367 :args (_let_1442 false _let_366)) :args (_let_510 true _let_419 false _let_1442)) _let_376 _let_363 _let_357 _let_356 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_355 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_178 tptp.nil_Ar1286194111le_alt QUANTIFIERS_INST_E_MATCHING _let_354)) :args _let_353)) _let_352 :args (_let_508 false _let_348)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_680 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_101 QUANTIFIERS_INST_E_MATCHING _let_679)) :args _let_678)) _let_677 :args (_let_507 false _let_675)) _let_681 _let_347 _let_346 _let_340 _let_339 _let_338 _let_332 _let_328 _let_322 _let_768 _let_317 _let_316 _let_674 _let_670 _let_308 _let_298 _let_1441 _let_843 _let_830 _let_1440 _let_824 _let_191 _let_844 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1435)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1256 _let_1258 _let_1260 _let_1262 _let_1278 _let_1264 _let_1266 _let_1269 _let_191 _let_436 _let_444 _let_700 _let_696 _let_449 _let_942 _let_945 _let_761 _let_971 _let_1369 _let_1283 _let_1432 _let_1146) (SCOPE (TRANS _let_1158 _let_1434 _let_1428 _let_1427 _let_1426 (CONG _let_1279 (TRANS _let_1370 _let_1034 _let_1275 _let_1274) :args _let_933) _let_1263 _let_1261 _let_1259 _let_1257) :args (_let_1079 _let_1085 _let_1084 _let_1090 _let_1088 _let_1081 _let_538 _let_536 _let_97 _let_130 _let_118 _let_499 _let_500 _let_120 _let_502 _let_521 _let_519 _let_524 _let_1360 _let_1089 _let_1101 _let_1057))) :args (_let_97 _let_1079 _let_499 _let_500 _let_118 _let_120 _let_502 _let_130 _let_519 _let_521 _let_1057 _let_524 _let_1085 _let_1084 _let_536 _let_538 _let_1081 _let_1088 _let_1089 _let_1101 _let_1360 _let_1090))) :args (true _let_1435)) :args ((or _let_637 _let_1254 _let_686 _let_685 _let_636 _let_684 _let_919 _let_635 _let_916 _let_915 _let_1138 _let_911 _let_1253 _let_1252 _let_1251 _let_1250 _let_1249 _let_1248 _let_1228 _let_1077 _let_1308 _let_1366 _let_1246))) _let_1245 _let_1241 _let_1227 _let_1219 _let_1168 _let_1165 _let_1164 _let_1163 _let_775 _let_1162 _let_772 _let_724 _let_332 _let_768 _let_317 _let_316 _let_674 _let_670 _let_1161 _let_191 _let_1408 _let_1407 _let_1411 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_1413 _let_1412 _let_1414 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1430)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_922 _let_1336 _let_1338 _let_1341 _let_1278 _let_436 _let_191 _let_444 _let_651 _let_1417 _let_1283 _let_1432 _let_1146 _let_1151) (SCOPE (TRANS _let_1152 _let_1158 _let_1434 _let_1428 _let_1427 _let_1426 _let_1431 _let_1343 _let_1340 _let_1337 _let_924) :args (_let_158 _let_1106 _let_1105 _let_1107 _let_1088 _let_130 _let_97 _let_118 _let_476 _let_1355 _let_1089 _let_1101 _let_1057 _let_470))) :args (_let_97 _let_118 _let_130 _let_476 _let_1105 _let_158 _let_1057 _let_1106 _let_1088 _let_1089 _let_470 _let_1101 _let_1107 _let_1355))) :args (true _let_1430)) :args ((or _let_637 _let_636 _let_635 _let_634 _let_1334 _let_913 _let_1138 _let_1333 _let_1248 _let_1228 _let_177 _let_1136 _let_1308 _let_1332 _let_1415))) _let_1330 _let_1241 _let_1227 _let_1322 _let_1162 _let_406 _let_1321 _let_612 _let_332 _let_316 _let_191 _let_1316 _let_1315 _let_1319 _let_612 _let_332 _let_316 _let_191 _let_1320 _let_1429 _let_1305 _let_1304 _let_1303 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_1299 _let_1298 _let_1419 _let_1160 _let_1155 _let_309 _let_1135 _let_1134 _let_399 _let_1132 _let_287 _let_282 _let_1131 _let_1129 _let_1128 _let_1124 _let_1127 _let_1113 _let_1112 _let_1111 _let_1110 _let_1109 _let_1026 _let_305 _let_1053 :args ((or _let_177 _let_478 _let_482) false _let_1090 false _let_1089 false _let_1088 false _let_1085 false _let_1084 false _let_1081 false _let_538 false _let_536 false _let_524 false _let_1057 false _let_521 false _let_519 false _let_130 false _let_502 false _let_120 false _let_118 false _let_500 false _let_499 false _let_1079 false _let_97 false _let_1360 false _let_1361 true _let_1359 false _let_505 false _let_476 false _let_130 false _let_120 false _let_118 false _let_500 false _let_499 false _let_97 true _let_1357 false _let_1358 true _let_1356 true _let_1355 false _let_1107 false _let_1089 false _let_1088 false _let_1106 false _let_1057 false _let_158 false _let_1105 false _let_476 false _let_130 false _let_118 false _let_97 false _let_1101 false _let_1103 false _let_1102 false _let_476 false _let_130 false _let_118 false _let_97 false _let_1097 true _let_1096 false _let_1098 false _let_1099 false _let_1095 false _let_505 false _let_476 false _let_130 false _let_120 false _let_118 false _let_500 false _let_499 false _let_97 false _let_1093 false _let_1094 true _let_1091 true _let_1077 true _let_1076 false _let_114 false _let_1075 true _let_1071 true _let_390 false _let_1072 false _let_104 true _let_192 false _let_1074 false _let_1069 false _let_1063 false _let_1066 false _let_1064 false _let_1068 false _let_1062 false _let_1061 false _let_1058 false _let_1057 false _let_569 false _let_303 false _let_470)) _let_1354 _let_612 _let_332 _let_316 _let_191 _let_1349 _let_1347 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1335)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_922 _let_1336 _let_1338 _let_1341 _let_1278 _let_436 _let_191 _let_444 _let_651 _let_1344 _let_1283 _let_1287 _let_1146 _let_1151) (SCOPE (TRANS _let_1152 _let_1158 _let_1290 _let_1286 _let_1284 _let_1282 _let_1346 _let_1343 _let_1340 _let_1337 _let_924) :args (_let_158 _let_1106 _let_1105 _let_1107 _let_1088 _let_130 _let_97 _let_118 _let_476 _let_1096 _let_1089 _let_471 _let_1057 _let_470))) :args (_let_97 _let_118 _let_130 _let_476 _let_1105 _let_158 _let_1057 _let_1106 _let_1088 _let_1089 _let_470 _let_471 _let_1107 _let_1096))) :args (true _let_1335)) :args ((or _let_637 _let_636 _let_635 _let_634 _let_1334 _let_913 _let_1138 _let_1333 _let_1248 _let_1228 _let_177 _let_1136 _let_1108 _let_1332 _let_1331))) _let_1330 _let_1241 _let_1227 _let_1322 _let_1162 _let_406 _let_1321 _let_612 _let_332 _let_316 _let_191 _let_1320 _let_1319 _let_612 _let_332 _let_316 _let_191 _let_1316 _let_1315 _let_1314 _let_1307 _let_1305 _let_1304 _let_1303 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_1299 _let_1298 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1255)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1256 _let_1258 _let_1260 _let_1262 _let_1278 _let_1264 _let_1266 _let_1269 _let_191 _let_436 _let_444 _let_700 _let_696 _let_449 _let_942 _let_945 _let_761 _let_971 _let_1276 _let_1283 _let_1287 _let_1146) (SCOPE (TRANS _let_1158 _let_1290 _let_1286 _let_1284 _let_1282 (CONG _let_1279 (TRANS _let_1277 _let_1034 _let_1275 _let_1274) :args _let_933) _let_1263 _let_1261 _let_1259 _let_1257) :args (_let_1079 _let_1085 _let_1084 _let_1090 _let_1088 _let_1081 _let_538 _let_536 _let_97 _let_130 _let_118 _let_499 _let_500 _let_120 _let_502 _let_521 _let_519 _let_524 _let_1091 _let_1089 _let_471 _let_1057))) :args (_let_97 _let_1079 _let_499 _let_500 _let_118 _let_120 _let_502 _let_130 _let_519 _let_521 _let_1057 _let_524 _let_1085 _let_1084 _let_536 _let_538 _let_1081 _let_1088 _let_1089 _let_471 _let_1091 _let_1090))) :args (true _let_1255)) :args ((or _let_637 _let_1254 _let_686 _let_685 _let_636 _let_684 _let_919 _let_635 _let_916 _let_915 _let_1138 _let_911 _let_1253 _let_1252 _let_1251 _let_1250 _let_1249 _let_1248 _let_1228 _let_1077 _let_1108 _let_1247 _let_1246))) _let_1245 _let_1241 _let_1227 _let_1219 _let_1168 _let_1165 _let_1164 _let_1163 _let_775 _let_1162 _let_772 _let_724 _let_332 _let_768 _let_317 _let_316 _let_674 _let_670 _let_1161 _let_191 _let_1160 _let_1155 _let_309 _let_1135 _let_1134 _let_399 _let_1132 _let_287 _let_282 _let_1131 _let_1129 _let_1128 _let_1124 _let_1127 _let_1113 _let_1112 _let_1111 _let_1110 _let_1109 _let_1026 _let_305 _let_1053 :args ((or _let_177 _let_1108) false _let_1107 false _let_1089 false _let_1088 false _let_1106 false _let_1057 false _let_158 false _let_1105 false _let_476 false _let_130 false _let_118 false _let_97 false _let_1096 true _let_1097 false _let_476 false _let_130 false _let_118 false _let_97 true _let_1102 false _let_1103 true _let_1101 true _let_1100 false _let_1098 false _let_1099 false _let_1095 false _let_505 false _let_476 false _let_130 false _let_120 false _let_118 false _let_500 false _let_499 false _let_97 false _let_1093 false _let_1094 true _let_1091 false _let_1090 false _let_1089 false _let_1088 false _let_1085 false _let_1084 false _let_1081 false _let_538 false _let_536 false _let_524 false _let_1057 false _let_521 false _let_519 false _let_130 false _let_502 false _let_120 false _let_118 false _let_500 false _let_499 false _let_1079 false _let_97 true _let_1077 true _let_1076 false _let_114 false _let_1075 true _let_1071 true _let_390 false _let_1072 false _let_104 true _let_192 false _let_1074 false _let_1069 false _let_1063 false _let_1066 false _let_1064 false _let_1068 false _let_1062 false _let_1061 false _let_1058 false _let_1057 false _let_569 false _let_303 false _let_470)) _let_1053 :args (_let_177 false _let_558 false _let_557 false _let_556 false _let_555 false _let_176 false _let_553 false _let_174 false _let_551 false _let_550 false _let_548 false _let_173 false _let_171 false _let_547 false _let_544 false _let_543 false _let_541 false _let_540 false _let_538 false _let_536 false _let_534 false _let_532 false _let_529 false _let_527 false _let_526 false _let_525 false _let_524 false _let_158 false _let_523 false _let_521 false _let_520 false _let_519 false _let_514 false _let_154 false _let_513 false _let_510 false _let_152 true _let_150 false _let_146 false _let_144 false _let_508 false _let_507 false _let_505 false _let_141 false _let_139 false _let_136 false _let_134 false _let_132 false _let_130 false _let_127 false _let_124 false _let_502 false _let_120 false _let_118 false _let_500 false _let_499 false _let_112 false _let_110 false _let_497 false _let_494 false _let_490 false _let_486 false _let_485 false _let_97 false _let_484 false _let_482 true _let_478 false _let_476 false _let_130 false _let_118 false _let_97 true _let_473 false _let_474 true _let_471 false _let_470)))) (let ((_let_1684 (= _let_106 (ho_14 (ho_13 k_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176) tptp.nil_Ar1286194111le_alt)))) (let ((_let_1685 (= _let_390 _let_482))) (let ((_let_1686 (ho_99 k_109 _let_480))) (let ((_let_1687 (ho_4 _let_378 _let_1686))) (let ((_let_1688 (not _let_1687))) (let ((_let_1689 (ho_4 _let_881 _let_1686))) (let ((_let_1690 (not _let_1689))) (let ((_let_1691 (ho_16 k_15 _let_480))) (let ((_let_1692 (not _let_1691))) (let ((_let_1693 (or _let_1692 _let_1690 _let_1688 _let_1685))) (let ((_let_1694 (and _let_97 _let_385 _let_499 _let_500 _let_130 _let_141 _let_536 _let_538 _let_541))) (let ((_let_1695 (CONG _let_1391 (SYMM _let_1390) :args _let_736))) (let ((_let_1696 (TRANS _let_702 _let_699))) (let ((_let_1697 (TRANS (CONG _let_654 (TRANS (CONG (CONG _let_749 _let_1696 :args _let_738) _let_1384 :args _let_736) _let_1387 _let_1695) :args _let_650) (SYMM _let_1268) (CONG (CONG _let_442 (TRANS (SYMM _let_1271) _let_443 _let_439) :args _let_435) _let_434 :args _let_433)))) (let ((_let_1698 (and _let_97 _let_1115 _let_499 _let_500 _let_130 _let_141 _let_536 _let_538 _let_541))) (let ((_let_1699 (ASSUME :args (_let_1115)))) (let ((_let_1700 (ho_16 k_15 _let_546))) (let ((_let_1701 (ho_14 _let_137 _let_155))) (let ((_let_1702 (= _let_155 (ho_14 (ho_26 k_35 _let_1701) _let_1374)))) (let ((_let_1703 (ho_14 _let_147 tptp.nil_Ar1286194111le_alt))) (let ((_let_1704 (= _let_1703 _let_1701))) (let ((_let_1705 (= _let_1703 (ho_14 (ho_13 k_29 tptp.b) tptp.nil_Ar1286194111le_alt)))) (let ((_let_1706 (or _let_1510 _let_1700))) (let ((_let_1707 (forall ((Xs_115 tptp.list_A2115238852le_alt)) (or (not (ho_16 k_15 Xs_115)) (ho_16 k_15 (ho_14 k_72 Xs_115)))))) (let ((_let_1708 (EQ_RESOLVE (ASSUME :args (_let_59)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_59 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Xs_115 tptp.list_A2115238852le_alt)) (or (not (@ tptp.distin236324274le_alt Xs_115)) (@ tptp.distin236324274le_alt (@ tptp.tl_Arr465451158le_alt Xs_115)))) _let_1707))))))) (let ((_let_1709 (not _let_177))) (let ((_let_1710 (and _let_484 _let_97 _let_486 _let_490 _let_494 _let_497 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_513 _let_130 _let_136 _let_139 _let_141 _let_505 _let_144 _let_514 _let_519 _let_520 _let_521 _let_1375 _let_158 _let_524 _let_526 _let_1705 _let_540 _let_541 _let_543 _let_544 _let_1704 _let_177 _let_1702 _let_548 _let_553 _let_1700 _let_558))) (let ((_let_1711 (ASSUME :args (_let_1700)))) (let ((_let_1712 (SYMM _let_1666))) (let ((_let_1713 (CONG _let_1609 (SYMM _let_1712) :args _let_736))) (let ((_let_1714 (CONG (CONG _let_442 _let_799 :args _let_435) _let_434 :args _let_433))) (let ((_let_1715 (CONG (TRANS (TRANS _let_1385 (CONG _let_749 (TRANS _let_1034 (CONG (TRANS (CONG _let_744 (TRANS _let_763 (CONG (CONG _let_442 (TRANS _let_758 _let_701 _let_1714 _let_451) :args _let_435) _let_434 :args _let_433) _let_943 _let_945) :args _let_435) _let_1672) _let_434 :args _let_433) _let_1675) :args _let_738)) _let_1674) _let_1671 :args _let_736))) (let ((_let_1716 (SYMM _let_1592))) (let ((_let_1717 (CONG (CONG _let_749 _let_742 :args _let_738) _let_737 :args _let_736))) (let ((_let_1718 (ASSUME :args (_let_1375)))) (let ((_let_1719 (ASSUME :args (_let_177)))) (let ((_let_1720 (SYMM _let_1719))) (let ((_let_1721 (ASSUME :args (_let_1705)))) (let ((_let_1722 (ASSUME :args (_let_1704)))) (let ((_let_1723 (ASSUME :args (_let_1702)))) (let ((_let_1724 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_1685)) :args ((or _let_390 _let_1528 (not _let_1685)))) _let_399 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_1693)) :args ((or _let_1692 _let_1690 _let_1688 _let_1685 (not _let_1693)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1710)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1711 _let_1491 _let_1678 _let_1665 _let_1668 _let_945 _let_942 _let_449 _let_444 _let_191 _let_436 _let_700 _let_696 _let_761 _let_971 _let_862 _let_839 _let_844 _let_858 _let_732 _let_1663 _let_1661 _let_1658 _let_1656 _let_1653 _let_1591 _let_705 _let_1651 _let_739 _let_1649 _let_1634 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_let_737 :args _let_736) _let_735) :args _let_736) _let_861 _let_1526 (SYMM _let_1713) _let_1669 (SYMM _let_1715)) :args _let_736) (CONG _let_1677 (TRANS _let_1715 _let_1670 _let_1713) :args _let_736)) :args _let_854) _let_1606 :args _let_736) (SYMM _let_1679) (CONG _let_1677 (SYMM _let_1492) :args _let_736)) :args _let_1585) (TRUE_INTRO _let_1711))) :args (_let_1700 _let_497 _let_558 _let_136 _let_544 _let_521 _let_502 _let_120 _let_118 _let_97 _let_130 _let_499 _let_500 _let_519 _let_524 _let_494 _let_490 _let_484 _let_514 _let_139 _let_513 _let_520 _let_548 _let_540 _let_543 _let_144 _let_505 _let_526 _let_124 _let_553 _let_486 _let_177 _let_158 _let_1705 _let_1704 _let_1375 _let_1702 _let_141 _let_541))) :args (_let_484 _let_97 _let_486 _let_490 _let_494 _let_497 _let_499 _let_500 _let_118 _let_120 _let_502 _let_124 _let_513 _let_130 _let_136 _let_139 _let_141 _let_505 _let_144 _let_514 _let_519 _let_520 _let_521 _let_1375 _let_158 _let_524 _let_526 _let_1705 _let_540 _let_541 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_let_1468 _let_1471 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_343 :args (tptp.b _let_106 QUANTIFIERS_INST_E_MATCHING _let_345)) :args _let_344))) _let_343 :args (_let_1704 false _let_341)) _let_1683 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_410 :args (_let_116 _let_155 QUANTIFIERS_INST_CBQI_PROP)) :args _let_411)) _let_410 :args (_let_1702 false _let_409)) _let_1494 _let_1499 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_1706)) :args ((or _let_1510 _let_1700 (not _let_1706)))) _let_1509 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_1708 :args (_let_495 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_14 k_72 Xs_115)))) :args (_let_1707))) _let_1708 :args (_let_1706 false _let_1707)) :args (_let_1700 false _let_1502 false _let_1706)) _let_1527 :args (_let_1691 false _let_484 false _let_97 false _let_486 false _let_490 false _let_494 false _let_497 false _let_499 false _let_500 false _let_118 false 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(INSTANTIATE _let_1129 :args (_let_96 _let_116 _let_480 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_1130)) _let_1129 :args (_let_1693 false _let_1069)) :args (_let_1685 false _let_1691 false _let_1689 false _let_1687 false _let_1693)) :args (_let_1528 true _let_390 false _let_1685)))) (let ((_let_1725 (REFL :args (_let_1709)))) (let ((_let_1726 (and _let_3 _let_114 _let_158 _let_177))) (let ((_let_1727 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_1726)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1040 _let_922 _let_1719 _let_1148) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.a)) (SYMM (TRANS (SYMM (TRANS _let_1149 (SYMM _let_1720) _let_923)) _let_1149)) :args _let_646) (FALSE_INTRO _let_1040))) :args (_let_3 _let_158 _let_177 _let_114))) :args (_let_3 _let_114 _let_158 _let_177))) :args (true _let_1726)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_3) _let_2))) _let_1143 _let_1569 _let_1725 _let_1142 :args _let_283)) _let_1040 _let_310 _let_406 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((_let_1735 (SYMM _let_1259))) (let ((_let_1736 (SYMM _let_1257))) (let ((_let_1737 (ASSUME :args (_let_1684)))) (let ((_let_1738 (SYMM (SYMM _let_1737)))) (let ((_let_1739 (and _let_97 _let_1684 _let_1079 _let_499 _let_500 _let_118 _let_120 _let_502 _let_130 _let_519 _let_521 _let_1057 _let_524 _let_527 _let_1085 _let_1084 _let_536 _let_538 _let_1081 _let_1088 _let_1089 _let_471 _let_1091 _let_1090))) (let ((_let_1740 (and _let_97 _let_118 _let_130 _let_476 _let_1105 _let_158 _let_1057 _let_1106 _let_1088 _let_1089 _let_177 _let_471 _let_1107 _let_1096))) (let ((_let_1741 (not _let_178))) (let ((_let_1742 (not _let_169))) (let ((_let_1743 (not _let_162))) (let ((_let_1744 (not _let_166))) (let ((_let_1745 (not _let_160))) (let ((_let_1746 (not _let_159))) (let ((_let_1747 (not _let_111))) (let ((_let_1748 (not _let_108))) (let ((_let_1749 (ASSUME :args _let_284))) (let ((_let_1750 (ASSUME :args (_let_160)))) (let ((_let_1751 (ASSUME :args (_let_162)))) (let ((_let_1752 (APPLY_UF ho_45))) (let ((_let_1753 (APPLY_UF ho_60))) (let ((_let_1754 (APPLY_UF ho_146))) (let ((_let_1755 (ASSUME :args (_let_159)))) (let ((_let_1756 (ASSUME :args (_let_108)))) (let ((_let_1757 (REFL :args (k_145)))) (let ((_let_1758 (CONG _let_1757 (TRANS (CONG (REFL :args (k_31)) (SYMM _let_1756) :args _let_736) (SYMM _let_1755)) :args _let_1754))) (let ((_let_1759 (ASSUME :args (_let_166)))) (let ((_let_1760 (ASSUME :args (_let_111)))) (let ((_let_1761 (TRANS (CONG (TRANS (CONG _let_1603 (TRANS (CONG _let_929 _let_1589 :args _let_927) (SYMM _let_1760)) :args _let_1599) _let_1641) _let_868 :args _let_736) (CONG (TRANS _let_1640 (CONG _let_1603 (TRANS (SYMM _let_1643) (SYMM _let_1645)) :args _let_1599)) _let_869 :args _let_736)))) (let ((_let_1762 (CONG _let_856 _let_733 :args _let_854))) (let ((_let_1763 (TRANS (CONG (TRANS (CONG _let_1757 (TRANS (CONG (TRANS _let_1637 (SYMM _let_1762)) (SYMM _let_1761) :args _let_736) (CONG (TRANS _let_1762 (CONG _let_856 (TRANS _let_734 (CONG (CONG _let_749 (TRANS _let_741 (CONG _let_747 _let_434 :args _let_433) (CONG (TRANS _let_745 (CONG _let_744 (TRANS _let_1714 _let_451) :args _let_435)) _let_434 :args _let_433)) :args _let_738) _let_737 :args _let_736) _let_751) :args _let_854)) _let_1761 :args _let_736) (SYMM _let_1759)) :args _let_1754) (SYMM _let_1758)) _let_1401 :args _let_1753) (CONG _let_1758 _let_1401 :args _let_1753)))) (let ((_let_1764 (ASSUME :args (_let_169)))) (let ((_let_1765 (CONG _let_1391 _let_1588 :args _let_736))) (let ((_let_1766 (CONG _let_856 _let_1716 :args _let_854))) (let ((_let_1767 (CONG _let_1766 _let_1765 :args _let_736))) (let ((_let_1768 (SYMM _let_1587))) (let ((_let_1769 (ASSUME :args (_let_178)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_1749 _let_1750 _let_1388 _let_1769 _let_1616 _let_1627 _let_1628 _let_1665 _let_1751 _let_1755 _let_1756 _let_1759 _let_750 _let_449 _let_444 _let_191 _let_436 _let_743 _let_739 _let_732 _let_1644 _let_1642 _let_1639 _let_868 _let_1760 _let_1588 _let_1636 _let_1148 _let_1719 _let_922 _let_1764 _let_1591 _let_1586 _let_1597 _let_1583) :args (_let_97 _let_104 _let_108 _let_110 _let_152 _let_111 _let_112 _let_114 _let_118 _let_120 _let_124 _let_127 _let_130 _let_132 _let_134 _let_136 _let_139 _let_141 _let_144 _let_146 _let_359 _let_154 _let_158 _let_159 _let_160 _let_166 _let_162 _let_169 _let_165 _let_177 _let_171 _let_173 _let_174 _let_178 _let_176)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_1584) (CONG _let_1681 (TRANS (CONG _let_1596 (TRANS _let_1768 _let_1767 (CONG (SYMM _let_1766) _let_1594 :args _let_736)) :args _let_736) (SYMM _let_1598) (CONG (TRANS _let_1630 (TRANS _let_1629 (CONG _let_856 (SYMM _let_1769) :args _let_854)) (CONG _let_856 _let_1390 :args _let_854)) (TRANS (SYMM _let_1765) _let_1768 _let_1767 (SYMM (SYMM _let_1764)) (CONG (SYMM _let_1763) (REFL :args (tptp.b)) :args _let_1752) (CONG _let_1763 (TRANS _let_924 _let_1720 _let_1150) :args _let_1752) (SYMM _let_1751) _let_1712) :args _let_736) (SYMM _let_1750)) :args _let_1585) (TRUE_INTRO _let_1749))) :args (_let_104 _let_160 _let_141 _let_178 _let_146 _let_127 _let_174 _let_136 _let_162 _let_159 _let_108 _let_166 _let_165 _let_120 _let_118 _let_97 _let_130 _let_154 _let_124 _let_139 _let_152 _let_110 _let_112 _let_132 _let_111 _let_134 _let_171 _let_114 _let_177 _let_158 _let_169 _let_144 _let_173 _let_176 _let_359)) :args ((not (and _let_97 _let_104 _let_108 _let_110 _let_152 _let_111 _let_112 _let_114 _let_118 _let_120 _let_124 _let_127 _let_130 _let_132 _let_134 _let_136 _let_139 _let_141 _let_144 _let_146 _let_359 _let_154 _let_158 _let_159 _let_160 _let_166 _let_162 _let_169 _let_165 _let_177 _let_171 _let_173 _let_174 _let_178 _let_176)) SB_LITERAL))) (CONG _let_642 (REFL :args (_let_285)) (REFL :args (_let_1748)) _let_1582 _let_1581 (REFL :args (_let_1747)) _let_1580 _let_1143 _let_641 _let_688 _let_1579 _let_1578 _let_640 _let_865 _let_1577 _let_1576 _let_1575 _let_1574 _let_1573 _let_1572 _let_1571 _let_1570 _let_1569 (REFL :args (_let_1746)) (REFL :args (_let_1745)) (REFL :args (_let_1744)) (REFL :args (_let_1743)) (REFL :args (_let_1742)) (REFL :args (_let_904)) _let_1725 _let_1568 _let_1567 _let_1566 (REFL :args (_let_1741)) _let_1565 :args _let_283)) :args ((or _let_637 _let_285 _let_150 _let_1748 _let_1563 _let_1562 _let_1747 _let_1560 _let_1141 _let_636 _let_684 _let_918 _let_1558 _let_635 _let_864 _let_1557 _let_1556 _let_917 _let_1424 _let_1553 _let_1552 _let_377 _let_913 _let_1746 _let_1745 _let_1744 _let_1743 _let_1742 _let_904 _let_1709 _let_1539 _let_1538 _let_1534 _let_1741 _let_1532))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1740)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1719 _let_922 _let_1336 _let_1338 _let_1341 _let_1278 _let_436 _let_191 _let_444 _let_651 _let_1344 _let_1283 _let_1287 _let_1146) (SCOPE (TRANS _let_1158 _let_1290 _let_1286 _let_1284 _let_1282 _let_1346 _let_1343 _let_1340 _let_1337 _let_924 _let_1720) :args (_let_177 _let_158 _let_1106 _let_1105 _let_1107 _let_1088 _let_130 _let_97 _let_118 _let_476 _let_1096 _let_1089 _let_471 _let_1057))) :args (_let_97 _let_118 _let_130 _let_476 _let_1105 _let_158 _let_1057 _let_1106 _let_1088 _let_1089 _let_177 _let_471 _let_1107 _let_1096))) :args (true _let_1740)) :args ((or _let_637 _let_636 _let_635 _let_634 _let_1334 _let_913 _let_1138 _let_1333 _let_1248 _let_1228 _let_1709 _let_470 _let_1108 _let_1332 _let_1331))) _let_1727 _let_1683 _let_1330 _let_1241 _let_1227 _let_1322 _let_1162 _let_406 _let_1321 _let_612 _let_332 _let_316 _let_191 _let_1320 _let_1305 _let_1304 _let_1303 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_1299 _let_1298 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1739)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1631 _let_1146 _let_1278 _let_1287 _let_1283 _let_1276 _let_971 _let_761 _let_696 _let_700 _let_436 _let_191 _let_444 _let_449 _let_942 _let_945 _let_1269 _let_1266 _let_1264 _let_1262 _let_1260 _let_1258 _let_1256 _let_1737) (SCOPE (TRANS _let_1738 (CONG (CONG _let_1633 (TRANS _let_1736 _let_1735 _let_1734 _let_1733 (CONG _let_1281 (TRANS _let_1732 _let_974 _let_972 (SYMM _let_1277)) :args _let_933) _let_1428 _let_1427 _let_1426 (CONG _let_1279 _let_1288 :args _let_933) _let_1147) :args _let_1599) _let_1493 :args _let_736) _let_1632) :args (_let_527 _let_1057 _let_1088 _let_471 _let_1089 _let_1091 _let_524 _let_519 _let_500 _let_499 _let_130 _let_97 _let_118 _let_120 _let_502 _let_521 _let_536 _let_538 _let_1081 _let_1090 _let_1084 _let_1085 _let_1079 _let_1684))) :args (_let_97 _let_1684 _let_1079 _let_499 _let_500 _let_118 _let_120 _let_502 _let_130 _let_519 _let_521 _let_1057 _let_524 _let_527 _let_1085 _let_1084 _let_536 _let_538 _let_1081 _let_1088 _let_1089 _let_471 _let_1091 _let_1090))) :args (true _let_1739)) :args ((or _let_637 _let_1730 _let_1254 _let_686 _let_685 _let_636 _let_684 _let_919 _let_635 _let_916 _let_915 _let_1138 _let_911 _let_1547 _let_1253 _let_1252 _let_1251 _let_1250 _let_1249 _let_1248 _let_1228 _let_178 _let_1108 _let_1247 _let_1246))) _let_1245 _let_1241 _let_1227 _let_1219 _let_1168 _let_1165 _let_1164 _let_1163 _let_1462 _let_775 _let_1162 _let_772 _let_724 _let_332 _let_768 _let_317 _let_316 _let_674 _let_670 _let_1161 _let_1729 _let_191 _let_1319 _let_612 _let_332 _let_316 _let_191 _let_1316 _let_1315 _let_1314 _let_1307 _let_1349 _let_1347 _let_1354 _let_612 _let_332 _let_316 _let_191 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1731)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1631 _let_1146 _let_1278 _let_1432 _let_1283 _let_1369 _let_971 _let_761 _let_696 _let_700 _let_436 _let_191 _let_444 _let_449 _let_942 _let_945 _let_1269 _let_1266 _let_1264 _let_1262 _let_1260 _let_1258 _let_1256 _let_1737) (SCOPE (TRANS _let_1738 (CONG (CONG _let_1633 (TRANS _let_1736 _let_1735 _let_1734 _let_1733 (CONG _let_1281 (TRANS _let_1732 _let_974 _let_972 (SYMM _let_1370)) :args _let_933) _let_1286 _let_1284 _let_1282 (CONG _let_1279 _let_1433 :args _let_933) _let_1147) :args _let_1599) _let_1493 :args _let_736) _let_1632) :args (_let_527 _let_1057 _let_1088 _let_1101 _let_1089 _let_1360 _let_524 _let_519 _let_500 _let_499 _let_130 _let_97 _let_118 _let_120 _let_502 _let_521 _let_536 _let_538 _let_1081 _let_1090 _let_1084 _let_1085 _let_1079 _let_1684))) :args (_let_97 _let_1684 _let_1079 _let_499 _let_500 _let_118 _let_120 _let_502 _let_130 _let_519 _let_521 _let_1057 _let_524 _let_527 _let_1085 _let_1084 _let_536 _let_538 _let_1081 _let_1088 _let_1089 _let_1101 _let_1360 _let_1090))) :args (true _let_1731)) :args ((or _let_637 _let_1730 _let_1254 _let_686 _let_685 _let_636 _let_684 _let_919 _let_635 _let_916 _let_915 _let_1138 _let_911 _let_1547 _let_1253 _let_1252 _let_1251 _let_1250 _let_1249 _let_1248 _let_1228 _let_178 _let_1308 _let_1366 _let_1246))) _let_1245 _let_1241 _let_1227 _let_1219 _let_1168 _let_1165 _let_1164 _let_1163 _let_1462 _let_775 _let_1162 _let_772 _let_724 _let_332 _let_768 _let_317 _let_316 _let_674 _let_670 _let_1161 _let_1729 _let_191 _let_1408 _let_1407 _let_1411 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_1413 _let_1412 _let_1414 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_1728)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_1719 _let_922 _let_1336 _let_1338 _let_1341 _let_1278 _let_436 _let_191 _let_444 _let_651 _let_1417 _let_1283 _let_1432 _let_1146) (SCOPE (TRANS _let_1158 _let_1434 _let_1428 _let_1427 _let_1426 _let_1431 _let_1343 _let_1340 _let_1337 _let_924 _let_1720) :args (_let_177 _let_158 _let_1106 _let_1105 _let_1107 _let_1088 _let_130 _let_97 _let_118 _let_476 _let_1355 _let_1089 _let_1101 _let_1057))) :args (_let_97 _let_118 _let_130 _let_476 _let_1105 _let_158 _let_1057 _let_1106 _let_1088 _let_1089 _let_177 _let_1101 _let_1107 _let_1355))) :args (true _let_1728)) :args ((or _let_637 _let_636 _let_635 _let_634 _let_1334 _let_913 _let_1138 _let_1333 _let_1248 _let_1228 _let_1709 _let_470 _let_1308 _let_1332 _let_1415))) _let_1727 _let_1683 _let_1330 _let_1241 _let_1227 _let_1322 _let_1162 _let_406 _let_1321 _let_612 _let_332 _let_316 _let_191 _let_1316 _let_1315 _let_1319 _let_612 _let_332 _let_316 _let_191 _let_1320 _let_1305 _let_1304 _let_1303 _let_681 _let_612 _let_332 _let_317 _let_316 _let_674 _let_670 _let_191 _let_1299 _let_1298 _let_1429 _let_1724 _let_1419 _let_1724 :args ((or _let_178 _let_478) false _let_1090 false _let_1089 false _let_1088 false _let_1085 false _let_1084 false _let_1081 false _let_538 false _let_536 false _let_527 false _let_524 false _let_1057 false _let_521 false _let_519 false _let_130 false _let_502 false _let_120 false _let_118 false _let_500 false _let_499 false _let_1079 false _let_1684 false _let_97 false _let_1360 false _let_1361 true _let_1359 false _let_505 false _let_476 false _let_130 false _let_120 false _let_118 false _let_500 false _let_499 false _let_97 true _let_1357 false _let_1358 true _let_1356 true _let_1355 true _let_470 false _let_177 false _let_1107 false _let_1089 false _let_1088 false _let_1106 false _let_1057 false _let_158 false _let_1105 false _let_476 false _let_130 false _let_118 false _let_97 false _let_1101 false _let_1103 false _let_1102 false _let_476 false _let_130 false _let_118 false _let_97 false _let_1097 false _let_1098 false _let_1099 false _let_1095 false _let_505 false _let_476 false _let_130 false _let_120 false _let_118 false _let_500 false _let_499 false _let_97 false _let_1093 false _let_1094 true _let_1096 true _let_482 true _let_1091 true _let_482)) :args (_let_178 true _let_470 false _let_177 false _let_1107 false _let_1089 false _let_1088 false _let_1106 false _let_1057 false _let_158 false _let_1105 false _let_476 false _let_130 false _let_118 false _let_97 false _let_1096 false _let_1098 false _let_1099 false _let_1095 false _let_505 false _let_476 false _let_130 false _let_120 false _let_118 false _let_500 false _let_499 false _let_97 false _let_1093 false _let_1094 true _let_1091 false _let_1090 false _let_1089 false _let_1088 false _let_1085 false _let_1084 false _let_1081 false _let_538 false _let_536 false _let_527 false _let_524 false _let_1057 false _let_521 false _let_519 false _let_130 false _let_502 false _let_120 false _let_118 false _let_500 false _let_499 false _let_1079 false _let_1684 false _let_97 true _let_1097 false _let_476 false _let_130 false _let_118 false _let_97 true _let_1102 false _let_1103 true _let_1101 true _let_1100 false _let_471 false _let_474 false _let_473 false _let_476 false _let_130 false _let_118 false _let_97 false _let_478)) _let_1683 _let_469 _let_464 _let_461 _let_458 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_427)) :args ((or _let_426 _let_169 (not _let_427)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_430)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_403 _let_436 _let_191 _let_444 _let_449) (SCOPE (TRUE_ELIM (TRANS (CONG _let_454 _let_453 :args _let_432) _let_431)) :args (_let_385 _let_130 _let_97 _let_118 _let_120))) :args (_let_97 _let_385 _let_118 _let_120 _let_130))) :args (true _let_430)) _let_191 _let_403 _let_316 _let_317 _let_332 :args (_let_425 false _let_97 false _let_385 false _let_118 false _let_120 false _let_130)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_429 :args (tptp.b _let_96 _let_101 QUANTIFIERS_INST_E_MATCHING ((ho_14 (ho_13 k_12 A_31) (ho_14 (ho_143 k_142 (ho_100 k_162 I_5)) Xs_23))))) :args (_let_428))) _let_429 :args (_let_427 false _let_428)) :args (_let_169 false _let_425 false _let_427)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_420)) :args ((or _let_419 _let_166 (not _let_420)))) _let_424 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_422 :args (_let_101 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_54 k_53 Xs_145)))) :args (_let_421))) _let_422 :args (_let_420 false _let_421)) :args (_let_166 true _let_419 false _let_420)) _let_418 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_414 :args (_let_101 _let_96 QUANTIFIERS_INST_E_MATCHING ((ho_107 (ho_106 k_105 Xs_68) I_15)))) :args (_let_413))) _let_414 :args (_let_162 false _let_413)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_410 :args (_let_116 _let_103 QUANTIFIERS_INST_E_MATCHING _let_412)) :args _let_411)) _let_410 :args (_let_160 false _let_409)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_408 :args (_let_101 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 QUANTIFIERS_INST_E_MATCHING ((ho_14 (ho_26 k_35 Xs_171) (ho_14 (ho_13 k_12 X_108) tptp.nil_Ar1286194111le_alt))))) :args (_let_407))) _let_408 :args (_let_159 false _let_407)) _let_406 _let_405 _let_376 _let_363 _let_357 _let_356 _let_347 _let_346 _let_340 _let_339 _let_338 _let_332 _let_328 _let_322 _let_317 _let_316 _let_310 _let_308 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_300 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_178 tptp.nil_Ar1286194111le_alt QUANTIFIERS_INST_E_MATCHING _let_302)) :args _let_301)) _let_300 :args (_let_111 false _let_299)) _let_298 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_293) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_176 _let_101 QUANTIFIERS_INST_E_MATCHING ((ho_14 (ho_13 k_12 BOUND_VARIABLE_9613) BOUND_VARIABLE_9615)))) :args _let_293)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_76)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_76 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_190 :args ((and (= tptp.nil_nat (@ tptp.rotate1_nat tptp.nil_nat)) _let_291) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (= _let_182 (@ tptp.rotate1_nat _let_182)) _let_291) _let_292))) (PREPROCESS :args ((= _let_292 (and (= _let_95 (ho_24 k_58 _let_95)) _let_289)))))) :args _let_290) :args (_let_108 false _let_289)) _let_288 _let_191 :args (false false _let_178 false _let_177 false _let_176 false _let_174 false _let_173 false _let_171 false _let_169 false _let_166 false _let_165 false _let_162 false _let_160 false _let_159 false _let_158 false _let_154 false _let_152 true _let_150 false _let_146 false _let_144 false _let_141 false _let_139 false _let_136 false _let_134 false _let_132 false _let_130 false _let_127 false _let_124 false _let_120 false _let_118 false _let_114 false _let_112 false _let_111 false _let_110 false _let_108 false _let_104 false _let_97)) :args (_let_93 (@ tptp.distin236324274le_alt tptp.nil_Ar1286194111le_alt) (@ tptp.distinct_nat tptp.nil_nat) _let_92 (forall ((A_92 tptp.nat) (List_6 tptp.list_nat)) (not (= tptp.nil_nat (@ (@ tptp.cons_nat A_92) List_6)))) (forall ((A_91 tptp.arrow_475358991le_alt) (List_5 tptp.list_A2115238852le_alt)) (not (= (@ (@ tptp.cons_A228743023le_alt A_91) List_5) tptp.nil_Ar1286194111le_alt))) (forall ((A_91 tptp.nat) (List_5 tptp.list_nat)) (not (= (@ (@ tptp.cons_nat A_91) List_5) tptp.nil_nat))) (forall ((Xs_183 tptp.list_A2115238852le_alt)) (= (not (= Xs_183 tptp.nil_Ar1286194111le_alt)) (exists ((Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (= Xs_183 (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5))))) (forall ((Xs_183 tptp.list_nat)) (= (not (= Xs_183 tptp.nil_nat)) (exists ((Y_3 tptp.nat) (Ys_5 tptp.list_nat)) (= Xs_183 (@ (@ tptp.cons_nat Y_3) Ys_5))))) (forall ((Y_44 tptp.list_A2115238852le_alt)) (=> (not (= Y_44 tptp.nil_Ar1286194111le_alt)) (not (forall ((A_90 tptp.arrow_475358991le_alt) (List_4 tptp.list_A2115238852le_alt)) (not (= Y_44 (@ (@ tptp.cons_A228743023le_alt A_90) List_4))))))) (forall ((Y_44 tptp.list_nat)) (=> (not (= Y_44 tptp.nil_nat)) (not (forall ((A_90 tptp.nat) (List_4 tptp.list_nat)) (not (= Y_44 (@ (@ tptp.cons_nat A_90) List_4))))))) _let_91 (forall ((X_114 tptp.arrow_475358991le_alt) (Xs_181 tptp.list_A2115238852le_alt)) (not (= (@ (@ tptp.cons_A228743023le_alt X_114) Xs_181) Xs_181))) _let_90 _let_89 (forall ((V_4 tptp.nat) (Va tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat V_4) Va))) (= (@ (@ tptp.splice_nat _let_1) tptp.nil_nat) _let_1))) _let_88 (forall ((X_113 tptp.nat)) (= (@ (@ tptp.insert_nat X_113) tptp.nil_nat) (@ (@ tptp.cons_nat X_113) tptp.nil_nat))) (forall ((P_33 (-> tptp.list_A2115238852le_alt Bool)) (Xs_180 tptp.list_A2115238852le_alt)) (=> (not (= Xs_180 tptp.nil_Ar1286194111le_alt)) (=> (forall ((X_1 tptp.arrow_475358991le_alt)) (@ P_33 (@ (@ tptp.cons_A228743023le_alt X_1) tptp.nil_Ar1286194111le_alt))) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt)) (=> (not (= Xs_54 tptp.nil_Ar1286194111le_alt)) (=> (@ P_33 Xs_54) (@ P_33 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54))))) (@ P_33 Xs_180))))) (forall ((P_33 (-> tptp.list_nat Bool)) (Xs_180 tptp.list_nat)) (=> (not (= Xs_180 tptp.nil_nat)) (=> (forall ((X_1 tptp.nat)) (@ P_33 (@ (@ tptp.cons_nat X_1) tptp.nil_nat))) (=> (forall ((X_1 tptp.nat) (Xs_54 tptp.list_nat)) (=> (not (= Xs_54 tptp.nil_nat)) (=> (@ P_33 Xs_54) (@ P_33 (@ (@ tptp.cons_nat X_1) Xs_54))))) (@ P_33 Xs_180))))) (forall ((Xs_179 tptp.list_A2115238852le_alt)) (=> (not (= Xs_179 tptp.nil_Ar1286194111le_alt)) (=> (@ tptp.distin236324274le_alt Xs_179) (@ tptp.distin236324274le_alt (@ tptp.butlas274947851le_alt Xs_179))))) (forall ((Xs_179 tptp.list_nat)) (=> (not (= Xs_179 tptp.nil_nat)) (=> (@ tptp.distinct_nat Xs_179) (@ tptp.distinct_nat (@ tptp.butlast_nat Xs_179))))) (= (@ tptp.butlas274947851le_alt tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt) (= (@ tptp.butlast_nat tptp.nil_nat) tptp.nil_nat) (forall ((X_112 tptp.arrow_475358991le_alt) (Xs_178 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_178) (@ tptp.distin236324274le_alt (@ (@ tptp.insert2120566741le_alt X_112) Xs_178)))) (forall ((X_111 tptp.arrow_475358991le_alt) (Xs_177 tptp.list_A2115238852le_alt) (Y_43 tptp.arrow_475358991le_alt) (Ys_54 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt Y_43))) (let ((_let_2 (@ tptp.cons_A228743023le_alt X_111))) (= (@ (@ tptp.splice1520898450le_alt (@ _let_2 Xs_177)) (@ _let_1 Ys_54)) (@ _let_2 (@ _let_1 (@ (@ tptp.splice1520898450le_alt Xs_177) Ys_54))))))) (forall ((Xs_176 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.splice1520898450le_alt Xs_176) tptp.nil_Ar1286194111le_alt) Xs_176)) (forall ((Xs_176 tptp.list_nat)) (= (@ (@ tptp.splice_nat Xs_176) tptp.nil_nat) Xs_176)) (forall ((Ys_53 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.splice1520898450le_alt tptp.nil_Ar1286194111le_alt) Ys_53) Ys_53)) (forall ((Ys_53 tptp.list_nat)) (= (@ (@ tptp.splice_nat tptp.nil_nat) Ys_53) Ys_53)) _let_87 (forall ((X_110 tptp.nat) (Xs_175 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X_110))) (let ((_let_2 (@ tptp.butlast_nat (@ _let_1 Xs_175)))) (let ((_let_3 (= Xs_175 tptp.nil_nat))) (and (=> _let_3 (= _let_2 tptp.nil_nat)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_nat Xs_175))))))))) (forall ((Xs_174 tptp.list_A2115238852le_alt)) (= (= Xs_174 tptp.nil_Ar1286194111le_alt) (@ tptp.null_A1520965063le_alt Xs_174))) (forall ((Xs_174 tptp.list_nat)) (= (= Xs_174 tptp.nil_nat) (@ tptp.null_nat Xs_174))) (forall ((Xs_173 tptp.list_A2115238852le_alt)) (= (@ tptp.null_A1520965063le_alt Xs_173) (= Xs_173 tptp.nil_Ar1286194111le_alt))) (forall ((Xs_173 tptp.list_nat)) (= (@ tptp.null_nat Xs_173) (= Xs_173 tptp.nil_nat))) (@ tptp.null_A1520965063le_alt tptp.nil_Ar1286194111le_alt) (@ tptp.null_nat tptp.nil_nat) (forall ((X_109 tptp.arrow_475358991le_alt) (Xs_172 tptp.list_A2115238852le_alt)) (not (@ tptp.null_A1520965063le_alt (@ (@ tptp.cons_A228743023le_alt X_109) Xs_172)))) _let_86 (forall ((Xs_171 tptp.list_nat) (X_108 tptp.nat)) (= (@ tptp.butlast_nat (@ (@ tptp.append_nat Xs_171) (@ (@ tptp.cons_nat X_108) tptp.nil_nat))) Xs_171)) (forall ((F_7 (-> tptp.nat tptp.list_A2115238852le_alt))) (= (@ (@ tptp.maps_n1127956422le_alt F_7) tptp.nil_nat) tptp.nil_Ar1286194111le_alt)) (forall ((F_7 (-> tptp.arrow_475358991le_alt tptp.list_nat))) (= (@ (@ tptp.maps_A2124894076lt_nat F_7) tptp.nil_Ar1286194111le_alt) tptp.nil_nat)) (forall ((F_7 (-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt))) (= (@ (@ tptp.maps_A409156225le_alt F_7) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)) (forall ((X_107 tptp.nat)) (@ tptp.linorder_sorted_nat (@ (@ tptp.cons_nat X_107) tptp.nil_nat))) (@ tptp.linorder_sorted_nat tptp.nil_nat) _let_85 (forall ((Xs_169 tptp.list_A2115238852le_alt) (Ys_51 tptp.list_A2115238852le_alt) (Zs_8 tptp.list_A2115238852le_alt) (Ts tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Xs_169) Ys_51) (@ (@ tptp.append179082452le_alt Zs_8) Ts)) (exists ((Us_1 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Us_1))) (or (and (= Xs_169 (@ (@ tptp.append179082452le_alt Zs_8) Us_1)) (= (@ _let_1 Ys_51) Ts)) (and (= (@ (@ tptp.append179082452le_alt Xs_169) Us_1) Zs_8) (= Ys_51 (@ _let_1 Ts)))))))) (forall ((Xs_168 tptp.list_A2115238852le_alt) (Ys_50 tptp.list_A2115238852le_alt) (Zs_7 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Xs_168))) (= (= (@ _let_1 Ys_50) (@ _let_1 Zs_7)) (= Ys_50 Zs_7)))) (forall ((Ys_49 tptp.list_A2115238852le_alt) (Xs_167 tptp.list_A2115238852le_alt) (Zs_6 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Ys_49) Xs_167) (@ (@ tptp.append179082452le_alt Zs_6) Xs_167)) (= Ys_49 Zs_6))) (forall ((Ys_48 tptp.list_A2115238852le_alt) (Us tptp.list_A2115238852le_alt) (Xs_166 tptp.list_A2115238852le_alt) (Xs1_1 tptp.list_A2115238852le_alt) (Zs_5 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Xs_166))) (=> (= (@ _let_1 Xs1_1) Zs_5) (=> (= Ys_48 (@ (@ tptp.append179082452le_alt Xs1_1) Us)) (= (@ _let_1 Ys_48) (@ (@ tptp.append179082452le_alt Zs_5) Us)))))) (forall ((F_6 (-> tptp.arrow_475358991le_alt tptp.list_A2115238852le_alt)) (X_106 tptp.arrow_475358991le_alt) (Xs_165 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.maps_A409156225le_alt F_6))) (= (@ _let_1 (@ (@ tptp.cons_A228743023le_alt X_106) Xs_165)) (@ (@ tptp.append179082452le_alt (@ F_6 X_106)) (@ _let_1 Xs_165))))) _let_84 (forall ((Xs_163 tptp.list_A2115238852le_alt) (Zs_4 tptp.list_A2115238852le_alt) (X_104 tptp.arrow_475358991le_alt) (Xs1 tptp.list_A2115238852le_alt) (Ys_46 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_104))) (=> (= (@ _let_1 Xs1) Ys_46) (=> (= Xs_163 (@ (@ tptp.append179082452le_alt Xs1) Zs_4)) (= (@ _let_1 Xs_163) (@ (@ tptp.append179082452le_alt Ys_46) Zs_4)))))) _let_83 (forall ((Ys_45 tptp.list_nat)) (= (@ (@ tptp.append_nat tptp.nil_nat) Ys_45) Ys_45)) (forall ((Xs_162 tptp.list_A2115238852le_alt) (Ys_44 tptp.list_A2115238852le_alt)) (= (= tptp.nil_Ar1286194111le_alt (@ (@ tptp.append179082452le_alt Xs_162) Ys_44)) (and (= Xs_162 tptp.nil_Ar1286194111le_alt) (= Ys_44 tptp.nil_Ar1286194111le_alt)))) (forall ((Xs_162 tptp.list_nat) (Ys_44 tptp.list_nat)) (= (= tptp.nil_nat (@ (@ tptp.append_nat Xs_162) Ys_44)) (and (= Xs_162 tptp.nil_nat) (= Ys_44 tptp.nil_nat)))) (forall ((Xs_161 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.append179082452le_alt Xs_161) tptp.nil_Ar1286194111le_alt) Xs_161)) (forall ((Xs_161 tptp.list_nat)) (= (@ (@ tptp.append_nat Xs_161) tptp.nil_nat) Xs_161)) _let_82 (forall ((Xs_160 tptp.list_nat) (Ys_43 tptp.list_nat)) (= (= Xs_160 (@ (@ tptp.append_nat Xs_160) Ys_43)) (= Ys_43 tptp.nil_nat))) _let_81 (forall ((Ys_42 tptp.list_nat) (Xs_159 tptp.list_nat)) (= (= Ys_42 (@ (@ tptp.append_nat Xs_159) Ys_42)) (= Xs_159 tptp.nil_nat))) (forall ((Xs_158 tptp.list_A2115238852le_alt) (Ys_41 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Xs_158) Ys_41) tptp.nil_Ar1286194111le_alt) (and (= Xs_158 tptp.nil_Ar1286194111le_alt) (= Ys_41 tptp.nil_Ar1286194111le_alt)))) (forall ((Xs_158 tptp.list_nat) (Ys_41 tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs_158) Ys_41) tptp.nil_nat) (and (= Xs_158 tptp.nil_nat) (= Ys_41 tptp.nil_nat)))) (forall ((Xs_157 tptp.list_A2115238852le_alt) (Ys_40 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Xs_157) Ys_40) Xs_157) (= Ys_40 tptp.nil_Ar1286194111le_alt))) (forall ((Xs_157 tptp.list_nat) (Ys_40 tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs_157) Ys_40) Xs_157) (= Ys_40 tptp.nil_nat))) (forall ((Xs_156 tptp.list_A2115238852le_alt) (Ys_39 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.append179082452le_alt Xs_156) Ys_39) Ys_39) (= Xs_156 tptp.nil_Ar1286194111le_alt))) (forall ((Xs_156 tptp.list_nat) (Ys_39 tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs_156) Ys_39) Ys_39) (= Xs_156 tptp.nil_nat))) (forall ((Xs_155 tptp.list_A2115238852le_alt) (Ys_38 tptp.list_A2115238852le_alt)) (=> (= Xs_155 Ys_38) (= Xs_155 (@ (@ tptp.append179082452le_alt tptp.nil_Ar1286194111le_alt) Ys_38)))) (forall ((Xs_155 tptp.list_nat) (Ys_38 tptp.list_nat)) (=> (= Xs_155 Ys_38) (= Xs_155 (@ (@ tptp.append_nat tptp.nil_nat) Ys_38)))) _let_80 (forall ((Ys_37 tptp.list_nat) (Zs_3 tptp.list_nat) (X_103 tptp.nat) (Xs_154 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X_103) Xs_154))) (= (= (@ (@ tptp.append_nat Ys_37) Zs_3) _let_1) (or (and (= Ys_37 tptp.nil_nat) (= Zs_3 _let_1)) (exists ((Ys_36 tptp.list_nat)) (and (= Ys_37 (@ (@ tptp.cons_nat X_103) Ys_36)) (= (@ (@ tptp.append_nat Ys_36) Zs_3) Xs_154))))))) (forall ((X_102 tptp.arrow_475358991le_alt) (Xs_153 tptp.list_A2115238852le_alt) (Ys_35 tptp.list_A2115238852le_alt) (Zs_2 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_102) Xs_153))) (= (= _let_1 (@ (@ tptp.append179082452le_alt Ys_35) Zs_2)) (or (and (= Ys_35 tptp.nil_Ar1286194111le_alt) (= _let_1 Zs_2)) (exists ((Ys_36 tptp.list_A2115238852le_alt)) (and (= (@ (@ tptp.cons_A228743023le_alt X_102) Ys_36) Ys_35) (= Xs_153 (@ (@ tptp.append179082452le_alt Ys_36) Zs_2)))))))) (forall ((X_102 tptp.nat) (Xs_153 tptp.list_nat) (Ys_35 tptp.list_nat) (Zs_2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X_102) Xs_153))) (= (= _let_1 (@ (@ tptp.append_nat Ys_35) Zs_2)) (or (and (= Ys_35 tptp.nil_nat) (= _let_1 Zs_2)) (exists ((Ys_36 tptp.list_nat)) (and (= (@ (@ tptp.cons_nat X_102) Ys_36) Ys_35) (= Xs_153 (@ (@ tptp.append_nat Ys_36) Zs_2)))))))) _let_79 (forall ((Xs_152 tptp.list_nat) (X_101 tptp.nat) (Ys_34 tptp.list_nat) (Y_42 tptp.nat)) (= (= (@ (@ tptp.append_nat Xs_152) (@ (@ tptp.cons_nat X_101) tptp.nil_nat)) (@ (@ tptp.append_nat Ys_34) (@ (@ tptp.cons_nat Y_42) tptp.nil_nat))) (and (= Xs_152 Ys_34) (= X_101 Y_42)))) (forall ((Xs_151 tptp.list_A2115238852le_alt) (Ys_33 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Xs_151))) (let ((_let_2 (@ tptp.butlas274947851le_alt (@ _let_1 Ys_33)))) (let ((_let_3 (= Ys_33 tptp.nil_Ar1286194111le_alt))) (and (=> _let_3 (= _let_2 (@ tptp.butlas274947851le_alt Xs_151))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlas274947851le_alt Ys_33))))))))) (forall ((Xs_151 tptp.list_nat) (Ys_33 tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Xs_151))) (let ((_let_2 (@ tptp.butlast_nat (@ _let_1 Ys_33)))) (let ((_let_3 (= Ys_33 tptp.nil_nat))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_nat Xs_151))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_nat Ys_33))))))))) (forall ((Xs_150 tptp.list_nat)) (=> (not (= Xs_150 tptp.nil_nat)) (=> (@ tptp.linorder_sorted_nat Xs_150) (@ tptp.linorder_sorted_nat (@ tptp.butlast_nat Xs_150))))) (forall ((Xs_149 tptp.list_A2115238852le_alt) (P_32 (-> tptp.list_A2115238852le_alt Bool))) (=> (@ P_32 tptp.nil_Ar1286194111le_alt) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt)) (=> (@ P_32 Xs_54) (@ P_32 (@ (@ tptp.append179082452le_alt Xs_54) (@ (@ tptp.cons_A228743023le_alt X_1) tptp.nil_Ar1286194111le_alt))))) (@ P_32 Xs_149)))) (forall ((Xs_149 tptp.list_nat) (P_32 (-> tptp.list_nat Bool))) (=> (@ P_32 tptp.nil_nat) (=> (forall ((X_1 tptp.nat) (Xs_54 tptp.list_nat)) (=> (@ P_32 Xs_54) (@ P_32 (@ (@ tptp.append_nat Xs_54) (@ (@ tptp.cons_nat X_1) tptp.nil_nat))))) (@ P_32 Xs_149)))) (forall ((Xs_148 tptp.list_A2115238852le_alt)) (=> (not (= Xs_148 tptp.nil_Ar1286194111le_alt)) (not (forall ((Ys_5 tptp.list_A2115238852le_alt) (Y_3 tptp.arrow_475358991le_alt)) (not (= Xs_148 (@ (@ tptp.append179082452le_alt Ys_5) (@ (@ tptp.cons_A228743023le_alt Y_3) tptp.nil_Ar1286194111le_alt)))))))) (forall ((Xs_148 tptp.list_nat)) (=> (not (= Xs_148 tptp.nil_nat)) (not (forall ((Ys_5 tptp.list_nat) (Y_3 tptp.nat)) (not (= Xs_148 (@ (@ tptp.append_nat Ys_5) (@ (@ tptp.cons_nat Y_3) tptp.nil_nat)))))))) (forall ((Xs_147 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.equal_484611810le_alt Xs_147) tptp.nil_Ar1286194111le_alt) (@ tptp.null_A1520965063le_alt Xs_147))) (forall ((Xs_147 tptp.list_nat)) (= (@ (@ tptp.equal_equal_list_nat Xs_147) tptp.nil_nat) (@ tptp.null_nat Xs_147))) _let_78 (forall ((Xs_146 tptp.list_nat) (X_100 tptp.nat) (Ys_32 tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs_146) (@ (@ tptp.cons_nat X_100) tptp.nil_nat)) Ys_32) (and (not (= Ys_32 tptp.nil_nat)) (= (@ tptp.butlast_nat Ys_32) Xs_146) (= (@ tptp.last_nat Ys_32) X_100)))) _let_77 (forall ((Xs_145 tptp.list_nat)) (=> (not (= Xs_145 tptp.nil_nat)) (= (@ (@ tptp.append_nat (@ tptp.butlast_nat Xs_145)) (@ (@ tptp.cons_nat (@ tptp.last_nat Xs_145)) tptp.nil_nat)) Xs_145))) _let_76 (forall ((X_99 tptp.arrow_475358991le_alt) (Xs_144 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_99))) (and (= (@ tptp.rotate335349260le_alt tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt) (= (@ tptp.rotate335349260le_alt (@ _let_1 Xs_144)) (@ (@ tptp.append179082452le_alt Xs_144) (@ _let_1 tptp.nil_Ar1286194111le_alt)))))) (forall ((X_99 tptp.nat) (Xs_144 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X_99))) (and (= (@ tptp.rotate335349260le_alt tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt) (= (@ tptp.rotate1_nat (@ _let_1 Xs_144)) (@ (@ tptp.append_nat Xs_144) (@ _let_1 tptp.nil_nat)))))) (forall ((Xs_143 tptp.list_A2115238852le_alt) (X_98 tptp.arrow_475358991le_alt)) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.append179082452le_alt Xs_143) (@ (@ tptp.cons_A228743023le_alt X_98) tptp.nil_Ar1286194111le_alt))) X_98)) (forall ((Xs_143 tptp.list_nat) (X_98 tptp.nat)) (= (@ tptp.last_nat (@ (@ tptp.append_nat Xs_143) (@ (@ tptp.cons_nat X_98) tptp.nil_nat))) X_98)) _let_75 (forall ((Ws tptp.list_nat)) (=> (not (@ tptp.distinct_nat Ws)) (exists ((Xs_54 tptp.list_nat) (Ys_5 tptp.list_nat) (Zs_1 tptp.list_nat) (Y_3 tptp.nat)) (let ((_let_1 (@ tptp.append_nat (@ (@ tptp.cons_nat Y_3) tptp.nil_nat)))) (= Ws (@ (@ tptp.append_nat Xs_54) (@ _let_1 (@ (@ tptp.append_nat Ys_5) (@ _let_1 Zs_1))))))))) (forall ((I_28 tptp.nat) (X_97 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ (@ tptp.replic1511538809le_alt I_28) X_97))) (let ((_let_2 (@ tptp.cons_A228743023le_alt X_97))) (= (@ (@ tptp.append179082452le_alt _let_1) (@ _let_2 tptp.nil_Ar1286194111le_alt)) (@ _let_2 _let_1))))) (forall ((I_28 tptp.nat) (X_97 tptp.nat)) (let ((_let_1 (@ (@ tptp.replicate_nat I_28) X_97))) (let ((_let_2 (@ tptp.cons_nat X_97))) (= (@ (@ tptp.append_nat _let_1) (@ _let_2 tptp.nil_nat)) (@ _let_2 _let_1))))) _let_74 (forall ((X_96 tptp.nat) (Xs_142 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X_96))) (= (@ tptp.rev_nat (@ _let_1 Xs_142)) (@ (@ tptp.append_nat (@ tptp.rev_nat Xs_142)) (@ _let_1 tptp.nil_nat))))) (forall ((Xs_141 tptp.list_nat) (Ys_31 tptp.list_nat)) (= (= (@ tptp.rev_nat Xs_141) (@ tptp.rev_nat Ys_31)) (= Xs_141 Ys_31))) (forall ((Xs_141 tptp.list_A2115238852le_alt) (Ys_31 tptp.list_A2115238852le_alt)) (= (= (@ tptp.rev_Ar1106406943le_alt Xs_141) (@ tptp.rev_Ar1106406943le_alt Ys_31)) (= Xs_141 Ys_31))) (forall ((Xs_140 tptp.list_nat) (Ys_30 tptp.list_nat)) (= (= (@ tptp.rev_nat Xs_140) Ys_30) (= Xs_140 (@ tptp.rev_nat Ys_30)))) _let_73 (forall ((N_53 tptp.nat) (X_95 tptp.nat)) (let ((_let_1 (@ (@ tptp.replicate_nat N_53) X_95))) (= (@ tptp.rev_nat _let_1) _let_1))) (forall ((N_53 tptp.nat) (X_95 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ (@ tptp.replic1511538809le_alt N_53) X_95))) (= (@ tptp.rev_Ar1106406943le_alt _let_1) _let_1))) (forall ((Xs_139 tptp.list_nat)) (= (@ tptp.rev_nat (@ tptp.rev_nat Xs_139)) Xs_139)) (forall ((Xs_139 tptp.list_A2115238852le_alt)) (= (@ tptp.rev_Ar1106406943le_alt (@ tptp.rev_Ar1106406943le_alt Xs_139)) Xs_139)) (forall ((X_94 tptp.list_A2115238852le_alt) (Y_41 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.equal_484611810le_alt X_94) Y_41) (= X_94 Y_41))) (forall ((Xs_138 tptp.list_A2115238852le_alt)) (= (= (@ tptp.rev_Ar1106406943le_alt Xs_138) tptp.nil_Ar1286194111le_alt) (= Xs_138 tptp.nil_Ar1286194111le_alt))) (forall ((Xs_138 tptp.list_nat)) (= (= (@ tptp.rev_nat Xs_138) tptp.nil_nat) (= Xs_138 tptp.nil_nat))) (forall ((Xs_137 tptp.list_A2115238852le_alt)) (= (= tptp.nil_Ar1286194111le_alt (@ tptp.rev_Ar1106406943le_alt Xs_137)) (= Xs_137 tptp.nil_Ar1286194111le_alt))) (forall ((Xs_137 tptp.list_nat)) (= (= tptp.nil_nat (@ tptp.rev_nat Xs_137)) (= Xs_137 tptp.nil_nat))) _let_72 (= (@ tptp.rev_nat tptp.nil_nat) tptp.nil_nat) (forall ((Xs_136 tptp.list_nat) (Ys_29 tptp.list_nat)) (= (@ tptp.rev_nat (@ (@ tptp.append_nat Xs_136) Ys_29)) (@ (@ tptp.append_nat (@ tptp.rev_nat Ys_29)) (@ tptp.rev_nat Xs_136)))) (forall ((Xs_136 tptp.list_A2115238852le_alt) (Ys_29 tptp.list_A2115238852le_alt)) (= (@ tptp.rev_Ar1106406943le_alt (@ (@ tptp.append179082452le_alt Xs_136) Ys_29)) (@ (@ tptp.append179082452le_alt (@ tptp.rev_Ar1106406943le_alt Ys_29)) (@ tptp.rev_Ar1106406943le_alt Xs_136)))) _let_70 (forall ((Xs_135 tptp.list_nat)) (= (@ tptp.distinct_nat (@ tptp.rev_nat Xs_135)) (@ tptp.distinct_nat Xs_135))) (forall ((N_52 tptp.nat) (X_93 tptp.arrow_475358991le_alt) (K_8 tptp.nat)) (let ((_let_1 (@ (@ tptp.replic1511538809le_alt N_52) X_93))) (let ((_let_2 (@ (@ tptp.replic1511538809le_alt K_8) X_93))) (= (@ (@ tptp.append179082452le_alt _let_1) _let_2) (@ (@ tptp.append179082452le_alt _let_2) _let_1))))) (forall ((Xs_134 tptp.list_A2115238852le_alt)) (= (= (@ tptp.rotate335349260le_alt Xs_134) tptp.nil_Ar1286194111le_alt) (= Xs_134 tptp.nil_Ar1286194111le_alt))) (forall ((Xs_134 tptp.list_nat)) (= (= (@ tptp.rotate1_nat Xs_134) tptp.nil_nat) (= Xs_134 tptp.nil_nat))) (forall ((X_92 tptp.nat) (A_87 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat X_92) A_87) (@ A_87 X_92))) (forall ((X_92 tptp.int) (A_87 (-> tptp.int Bool))) (= (@ (@ tptp.member_int X_92) A_87) (@ A_87 X_92))) (forall ((P_31 (-> tptp.nat Bool))) (= (@ tptp.collect_nat P_31) P_31)) _let_69 _let_68 (forall ((X_91 tptp.nat) (Xs_132 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X_91) tptp.nil_nat))) (= (= _let_1 (@ tptp.rev_nat Xs_132)) (= Xs_132 _let_1)))) (forall ((Xs_131 tptp.list_A2115238852le_alt) (X_90 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_90) tptp.nil_Ar1286194111le_alt))) (= (= (@ tptp.rev_Ar1106406943le_alt Xs_131) _let_1) (= Xs_131 _let_1)))) (forall ((Xs_131 tptp.list_nat) (X_90 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat X_90) tptp.nil_nat))) (= (= (@ tptp.rev_nat Xs_131) _let_1) (= Xs_131 _let_1)))) (forall ((N_51 tptp.nat) (X_89 tptp.arrow_475358991le_alt) (Xs_130 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt (@ (@ tptp.replic1511538809le_alt N_51) X_89)))) (let ((_let_2 (@ tptp.cons_A228743023le_alt X_89))) (= (@ _let_1 (@ _let_2 Xs_130)) (@ _let_2 (@ _let_1 Xs_130)))))) _let_67 (forall ((X_88 tptp.nat) (Xs_129 tptp.list_nat)) (=> (= Xs_129 tptp.nil_nat) (= (@ tptp.last_nat (@ (@ tptp.cons_nat X_88) Xs_129)) X_88))) _let_66 (forall ((X_87 tptp.nat) (Xs_128 tptp.list_nat)) (=> (not (= Xs_128 tptp.nil_nat)) (= (@ tptp.last_nat (@ (@ tptp.cons_nat X_87) Xs_128)) (@ tptp.last_nat Xs_128)))) (forall ((X_86 tptp.arrow_475358991le_alt) (Xs_127 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.last_A1217315288le_alt (@ (@ tptp.cons_A228743023le_alt X_86) Xs_127)))) (let ((_let_2 (= Xs_127 tptp.nil_Ar1286194111le_alt))) (and (=> _let_2 (= _let_1 X_86)) (=> (not _let_2) (= _let_1 (@ tptp.last_A1217315288le_alt Xs_127))))))) (forall ((X_86 tptp.nat) (Xs_127 tptp.list_nat)) (let ((_let_1 (@ tptp.last_nat (@ (@ tptp.cons_nat X_86) Xs_127)))) (let ((_let_2 (= Xs_127 tptp.nil_nat))) (and (=> _let_2 (= _let_1 X_86)) (=> (not _let_2) (= _let_1 (@ tptp.last_nat Xs_127))))))) (forall ((Xs_126 tptp.list_A2115238852le_alt) (Ys_28 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.last_A1217315288le_alt (@ (@ tptp.append179082452le_alt Xs_126) Ys_28)))) (let ((_let_2 (= Ys_28 tptp.nil_Ar1286194111le_alt))) (and (=> _let_2 (= _let_1 (@ tptp.last_A1217315288le_alt Xs_126))) (=> (not _let_2) (= _let_1 (@ tptp.last_A1217315288le_alt Ys_28))))))) (forall ((Xs_126 tptp.list_nat) (Ys_28 tptp.list_nat)) (let ((_let_1 (@ tptp.last_nat (@ (@ tptp.append_nat Xs_126) Ys_28)))) (let ((_let_2 (= Ys_28 tptp.nil_nat))) (and (=> _let_2 (= _let_1 (@ tptp.last_nat Xs_126))) (=> (not _let_2) (= _let_1 (@ tptp.last_nat Ys_28))))))) (forall ((Xs_125 tptp.list_A2115238852le_alt) (Ys_27 tptp.list_A2115238852le_alt)) (=> (not (= Ys_27 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.append179082452le_alt Xs_125) Ys_27)) (@ tptp.last_A1217315288le_alt Ys_27)))) (forall ((Xs_125 tptp.list_nat) (Ys_27 tptp.list_nat)) (=> (not (= Ys_27 tptp.nil_nat)) (= (@ tptp.last_nat (@ (@ tptp.append_nat Xs_125) Ys_27)) (@ tptp.last_nat Ys_27)))) (forall ((Xs_124 tptp.list_A2115238852le_alt) (Ys_26 tptp.list_A2115238852le_alt)) (=> (= Ys_26 tptp.nil_Ar1286194111le_alt) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.append179082452le_alt Xs_124) Ys_26)) (@ tptp.last_A1217315288le_alt Xs_124)))) (forall ((Xs_124 tptp.list_nat) (Ys_26 tptp.list_nat)) (=> (= Ys_26 tptp.nil_nat) (= (@ tptp.last_nat (@ (@ tptp.append_nat Xs_124) Ys_26)) (@ tptp.last_nat Xs_124)))) _let_65 (forall ((Xs_123 tptp.list_nat) (Y_40 tptp.nat) (Ys_25 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat Y_40))) (= (= (@ tptp.rev_nat Xs_123) (@ _let_1 Ys_25)) (= Xs_123 (@ (@ tptp.append_nat (@ tptp.rev_nat Ys_25)) (@ _let_1 tptp.nil_nat)))))) (forall ((Xs_122 tptp.list_A2115238852le_alt)) (=> (not (= Xs_122 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.last_A1217315288le_alt (@ tptp.rev_Ar1106406943le_alt Xs_122)) (@ tptp.hd_Arr1965683346le_alt Xs_122)))) (forall ((Xs_122 tptp.list_nat)) (=> (not (= Xs_122 tptp.nil_nat)) (= (@ tptp.last_nat (@ tptp.rev_nat Xs_122)) (@ tptp.hd_nat Xs_122)))) _let_64 (forall ((Xs_121 tptp.list_nat)) (=> (not (= Xs_121 tptp.nil_nat)) (= (@ tptp.hd_nat (@ tptp.rev_nat Xs_121)) (@ tptp.last_nat Xs_121)))) _let_63 (forall ((X_85 tptp.list_A2115238852le_alt)) (@ (@ tptp.equal_484611810le_alt X_85) X_85)) (forall ((X_84 tptp.list_A2115238852le_alt) (Y_39 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.equal_484611810le_alt X_84) Y_39) (= X_84 Y_39))) (= tptp.fequal781288069le_alt tptp.equal_484611810le_alt) (forall ((Ys_24 tptp.list_A2115238852le_alt) (Xs_120 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.append179082452le_alt Xs_120) Ys_24)))) (let ((_let_2 (= Xs_120 tptp.nil_Ar1286194111le_alt))) (and (=> _let_2 (= _let_1 (@ tptp.hd_Arr1965683346le_alt Ys_24))) (=> (not _let_2) (= _let_1 (@ tptp.hd_Arr1965683346le_alt Xs_120))))))) (forall ((Ys_24 tptp.list_nat) (Xs_120 tptp.list_nat)) (let ((_let_1 (@ tptp.hd_nat (@ (@ tptp.append_nat Xs_120) Ys_24)))) (let ((_let_2 (= Xs_120 tptp.nil_nat))) (and (=> _let_2 (= _let_1 (@ tptp.hd_nat Ys_24))) (=> (not _let_2) (= _let_1 (@ tptp.hd_nat Xs_120))))))) (forall ((Ys_23 tptp.list_A2115238852le_alt) (Xs_119 tptp.list_A2115238852le_alt)) (=> (not (= Xs_119 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.append179082452le_alt Xs_119) Ys_23)) (@ tptp.hd_Arr1965683346le_alt Xs_119)))) (forall ((Ys_23 tptp.list_nat) (Xs_119 tptp.list_nat)) (=> (not (= Xs_119 tptp.nil_nat)) (= (@ tptp.hd_nat (@ (@ tptp.append_nat Xs_119) Ys_23)) (@ tptp.hd_nat Xs_119)))) _let_62 (forall ((Xs_118 tptp.list_nat)) (=> (not (= Xs_118 tptp.nil_nat)) (= (@ tptp.rotate1_nat Xs_118) (@ (@ tptp.append_nat (@ tptp.tl_nat Xs_118)) (@ (@ tptp.cons_nat (@ tptp.hd_nat Xs_118)) tptp.nil_nat))))) _let_61 (= (@ tptp.tl_Arr465451158le_alt tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt) (= (@ tptp.tl_nat tptp.nil_nat) tptp.nil_nat) _let_60 _let_59 (forall ((Xs_114 tptp.list_nat)) (=> (@ tptp.linorder_sorted_nat Xs_114) (@ tptp.linorder_sorted_nat (@ tptp.tl_nat Xs_114)))) _let_58 (forall ((Ys_22 tptp.list_nat) (Xs_113 tptp.list_nat)) (=> (not (= Xs_113 tptp.nil_nat)) (= (@ tptp.tl_nat (@ (@ tptp.append_nat Xs_113) Ys_22)) (@ (@ tptp.append_nat (@ tptp.tl_nat Xs_113)) Ys_22)))) (forall ((P_30 (-> tptp.arrow_475358991le_alt Bool)) (Xs_112 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.dropWh1316781920le_alt P_30) Xs_112))) (=> (not (= _let_1 tptp.nil_Ar1286194111le_alt)) (not (@ P_30 (@ tptp.hd_Arr1965683346le_alt _let_1)))))) (forall ((P_30 (-> tptp.nat Bool)) (Xs_112 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.dropWhile_nat P_30) Xs_112))) (=> (not (= _let_1 tptp.nil_nat)) (not (@ P_30 (@ tptp.hd_nat _let_1)))))) (forall ((Y_38 tptp.arrow_475358991le_alt)) (not (@ (@ tptp.member1504968148le_alt tptp.nil_Ar1286194111le_alt) Y_38))) (forall ((Y_38 tptp.nat)) (not (@ (@ tptp.member_nat_1 tptp.nil_nat) Y_38))) (forall ((P_29 (-> tptp.arrow_475358991le_alt Bool))) (not (@ (@ tptp.list_e239244930le_alt P_29) tptp.nil_Ar1286194111le_alt))) (forall ((P_29 (-> tptp.nat Bool))) (not (@ (@ tptp.list_ex1_nat P_29) tptp.nil_nat))) (forall ((X_81 tptp.arrow_475358991le_alt) (Xs_111 tptp.list_A2115238852le_alt)) (@ (@ tptp.listMe78047147le_alt X_81) (@ (@ tptp.cons_A228743023le_alt X_81) Xs_111))) (forall ((X_80 tptp.arrow_475358991le_alt) (Xs_110 tptp.list_A2115238852le_alt) (Y_37 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.member1504968148le_alt (@ (@ tptp.cons_A228743023le_alt X_80) Xs_110)) Y_37) (or (= X_80 Y_37) (@ (@ tptp.member1504968148le_alt Xs_110) Y_37)))) (forall ((Y_36 tptp.arrow_475358991le_alt) (X_79 tptp.arrow_475358991le_alt) (Xs_109 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.listMe78047147le_alt X_79))) (=> (@ _let_1 Xs_109) (@ _let_1 (@ (@ tptp.cons_A228743023le_alt Y_36) Xs_109))))) (forall ((X_78 tptp.arrow_475358991le_alt) (N_50 tptp.nat)) (=> (not (= N_50 tptp.zero_zero_nat)) (= (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.replic1511538809le_alt N_50) X_78)) X_78))) (forall ((X_77 tptp.arrow_475358991le_alt) (N_49 tptp.nat)) (=> (not (= N_49 tptp.zero_zero_nat)) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.replic1511538809le_alt N_49) X_77)) X_77))) (forall ((M_5 tptp.nat) (X_76 tptp.arrow_475358991le_alt) (N_48 tptp.nat) (Y_35 tptp.arrow_475358991le_alt)) (= (= (@ (@ tptp.replic1511538809le_alt M_5) X_76) (@ (@ tptp.replic1511538809le_alt N_48) Y_35)) (and (= M_5 N_48) (=> (not (= M_5 tptp.zero_zero_nat)) (= X_76 Y_35))))) (forall ((Xs_108 tptp.list_A2115238852le_alt) (P_28 (-> tptp.arrow_475358991le_alt Bool)) (X_75 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_75) Xs_108))) (let ((_let_2 (@ tptp.dropWh1316781920le_alt P_28))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ P_28 X_75))) (and (=> _let_4 (= _let_3 (@ _let_2 Xs_108))) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((P_27 (-> tptp.arrow_475358991le_alt Bool))) (= (@ (@ tptp.dropWh1316781920le_alt P_27) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)) (forall ((P_27 (-> tptp.nat Bool))) (= (@ (@ tptp.dropWhile_nat P_27) tptp.nil_nat) tptp.nil_nat)) (forall ((P_26 (-> tptp.arrow_475358991le_alt Bool)) (Xs_107 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_107) (@ tptp.distin236324274le_alt (@ (@ tptp.dropWh1316781920le_alt P_26) Xs_107)))) (forall ((P_25 (-> tptp.nat Bool)) (Xs_106 tptp.list_nat)) (=> (@ tptp.linorder_sorted_nat Xs_106) (@ tptp.linorder_sorted_nat (@ (@ tptp.dropWhile_nat P_25) Xs_106)))) (forall ((X_74 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.replic1511538809le_alt tptp.zero_zero_nat) X_74) tptp.nil_Ar1286194111le_alt)) (forall ((X_74 tptp.nat)) (= (@ (@ tptp.replicate_nat tptp.zero_zero_nat) X_74) tptp.nil_nat)) (forall ((N_47 tptp.nat) (X_73 tptp.arrow_475358991le_alt)) (= (= tptp.nil_Ar1286194111le_alt (@ (@ tptp.replic1511538809le_alt N_47) X_73)) (= N_47 tptp.zero_zero_nat))) (forall ((N_47 tptp.nat) (X_73 tptp.nat)) (= (= tptp.nil_nat (@ (@ tptp.replicate_nat N_47) X_73)) (= N_47 tptp.zero_zero_nat))) (forall ((N_46 tptp.nat) (X_72 tptp.arrow_475358991le_alt)) (= (= (@ (@ tptp.replic1511538809le_alt N_46) X_72) tptp.nil_Ar1286194111le_alt) (= N_46 tptp.zero_zero_nat))) (forall ((N_46 tptp.nat) (X_72 tptp.nat)) (= (= (@ (@ tptp.replicate_nat N_46) X_72) tptp.nil_nat) (= N_46 tptp.zero_zero_nat))) (forall ((X_71 tptp.arrow_475358991le_alt) (A_86 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt X_71) tptp.nil_Ar1286194111le_alt))) (let ((_let_2 (@ (@ tptp.sublis2047953604le_alt _let_1) A_86))) (let ((_let_3 (@ (@ tptp.member_nat tptp.zero_zero_nat) A_86))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_Ar1286194111le_alt))))))) (forall ((X_71 tptp.nat) (A_86 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.cons_nat X_71) tptp.nil_nat))) (let ((_let_2 (@ (@ tptp.sublist_nat _let_1) A_86))) (let ((_let_3 (@ (@ tptp.member_nat tptp.zero_zero_nat) A_86))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))) (forall ((P_24 (-> tptp.arrow_475358991le_alt Bool)) (Xs_105 tptp.list_A2115238852le_alt) (Y_34 tptp.arrow_475358991le_alt) (Ys_21 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.cons_A228743023le_alt Y_34) Ys_21))) (= (= (@ (@ tptp.dropWh1316781920le_alt P_24) Xs_105) _let_1) (and (= Xs_105 (@ (@ tptp.append179082452le_alt (@ (@ tptp.takeWh1696291512le_alt P_24) Xs_105)) _let_1)) (not (@ P_24 Y_34)))))) (forall ((Fa_1 (-> tptp.arrow_475358991le_alt tptp.nat))) (= (@ (@ tptp.list_s250295873le_alt Fa_1) tptp.nil_Ar1286194111le_alt) tptp.zero_zero_nat)) (forall ((Fa_1 (-> tptp.nat tptp.nat))) (= (@ (@ tptp.list_size_nat Fa_1) tptp.nil_nat) tptp.zero_zero_nat)) (forall ((A1_1 tptp.arrow_475358991le_alt) (A2_1 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.listMe78047147le_alt A1_1) A2_1) (or (exists ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt)) (and (= A1_1 X_1) (= A2_1 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)))) (exists ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt) (Y_3 tptp.arrow_475358991le_alt)) (and (= A1_1 X_1) (= A2_1 (@ (@ tptp.cons_A228743023le_alt Y_3) Xs_54)) (@ (@ tptp.listMe78047147le_alt X_1) Xs_54)))))) (forall ((X_70 tptp.int)) (= (= tptp.zero_zero_int X_70) (= X_70 tptp.zero_zero_int))) (forall ((X_70 tptp.nat)) (= (= tptp.zero_zero_nat X_70) (= X_70 tptp.zero_zero_nat))) (forall ((Xs_104 tptp.list_nat)) (=> (not (= Xs_104 tptp.nil_nat)) (= (@ tptp.hd_nat Xs_104) (@ (@ tptp.nth_nat Xs_104) tptp.zero_zero_nat)))) (forall ((Xs_104 tptp.list_A2115238852le_alt)) (=> (not (= Xs_104 tptp.nil_Ar1286194111le_alt)) (= (@ tptp.hd_Arr1965683346le_alt Xs_104) (@ (@ tptp.nth_Ar125878976le_alt Xs_104) tptp.zero_zero_nat)))) (forall ((P_23 (-> tptp.nat Bool))) (= (@ (@ tptp.takeWhile_nat P_23) tptp.nil_nat) tptp.nil_nat)) (forall ((P_23 (-> tptp.arrow_475358991le_alt Bool))) (= (@ (@ tptp.takeWh1696291512le_alt P_23) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)) (forall ((P_22 (-> tptp.arrow_475358991le_alt Bool)) (Xs_103 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_103) (@ tptp.distin236324274le_alt (@ (@ tptp.takeWh1696291512le_alt P_22) Xs_103)))) (forall ((P_21 (-> tptp.nat Bool)) (Xs_102 tptp.list_nat)) (=> (@ tptp.linorder_sorted_nat Xs_102) (@ tptp.linorder_sorted_nat (@ (@ tptp.takeWhile_nat P_21) Xs_102)))) (forall ((A_85 (-> tptp.nat Bool))) (= (@ (@ tptp.sublist_nat tptp.nil_nat) A_85) tptp.nil_nat)) (forall ((A_85 (-> tptp.nat Bool))) (= (@ (@ tptp.sublis2047953604le_alt tptp.nil_Ar1286194111le_alt) A_85) tptp.nil_Ar1286194111le_alt)) (forall ((I_27 (-> tptp.nat Bool)) (Xs_101 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_101) (@ tptp.distin236324274le_alt (@ (@ tptp.sublis2047953604le_alt Xs_101) I_27)))) (forall ((X_69 tptp.nat) (Xs_100 tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X_69) Xs_100)) tptp.zero_zero_nat) X_69)) _let_57 (forall ((Xs_99 tptp.list_nat) (P_20 (-> tptp.nat Bool)) (X_68 tptp.nat)) (let ((_let_1 (@ tptp.cons_nat X_68))) (let ((_let_2 (@ tptp.takeWhile_nat P_20))) (let ((_let_3 (@ _let_2 (@ _let_1 Xs_99)))) (let ((_let_4 (@ P_20 X_68))) (and (=> _let_4 (= _let_3 (@ _let_1 (@ _let_2 Xs_99)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))) (forall ((Xs_99 tptp.list_A2115238852le_alt) (P_20 (-> tptp.arrow_475358991le_alt Bool)) (X_68 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_68))) (let ((_let_2 (@ tptp.takeWh1696291512le_alt P_20))) (let ((_let_3 (@ _let_2 (@ _let_1 Xs_99)))) (let ((_let_4 (@ P_20 X_68))) (and (=> _let_4 (= _let_3 (@ _let_1 (@ _let_2 Xs_99)))) (=> (not _let_4) (= _let_3 tptp.nil_Ar1286194111le_alt)))))))) (forall ((Xs_98 tptp.list_A2115238852le_alt) (L_1 tptp.list_A2115238852le_alt) (P_19 (-> tptp.arrow_475358991le_alt Bool)) (X_67 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.takeWh1696291512le_alt P_19))) (=> (not (@ P_19 X_67)) (= (@ _let_1 (@ (@ tptp.append179082452le_alt Xs_98) (@ (@ tptp.cons_A228743023le_alt X_67) L_1))) (@ _let_1 Xs_98))))) (forall ((P_18 (-> tptp.arrow_475358991le_alt Bool)) (Xs_97 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.append179082452le_alt (@ (@ tptp.takeWh1696291512le_alt P_18) Xs_97)) (@ (@ tptp.dropWh1316781920le_alt P_18) Xs_97)) Xs_97)) (forall ((Xs_96 tptp.list_nat) (X_66 tptp.nat) (Ys_20 tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.append_nat Xs_96) (@ (@ tptp.cons_nat X_66) Ys_20))) (@ tptp.size_size_list_nat Xs_96)) X_66)) (forall ((Xs_96 tptp.list_A2115238852le_alt) (X_66 tptp.arrow_475358991le_alt) (Ys_20 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.append179082452le_alt Xs_96) (@ (@ tptp.cons_A228743023le_alt X_66) Ys_20))) (@ tptp.size_s1858781230le_alt Xs_96)) X_66)) (forall ((Y_33 tptp.int) (Xs_95 tptp.list_int)) (let ((_let_1 (@ (@ (@ tptp.foldr_int_int tptp.ord_max_int) Xs_95) Y_33))) (let ((_let_2 (= Xs_95 tptp.nil_int))) (=> (@ tptp.linorder_sorted_int (@ tptp.rev_int Xs_95)) (and (=> _let_2 (= _let_1 Y_33)) (=> (not _let_2) (= _let_1 (@ (@ tptp.ord_max_int (@ (@ tptp.nth_int Xs_95) tptp.zero_zero_nat)) Y_33)))))))) (forall ((Y_33 tptp.nat) (Xs_95 tptp.list_nat)) (let ((_let_1 (@ (@ (@ tptp.foldr_nat_nat tptp.ord_max_nat) Xs_95) Y_33))) (let ((_let_2 (= Xs_95 tptp.nil_nat))) (=> (@ tptp.linorder_sorted_nat (@ tptp.rev_nat Xs_95)) (and (=> _let_2 (= _let_1 Y_33)) (=> (not _let_2) (= _let_1 (@ (@ tptp.ord_max_nat (@ (@ tptp.nth_nat Xs_95) tptp.zero_zero_nat)) Y_33)))))))) (forall ((Xs_94 tptp.list_A2115238852le_alt) (Ys_19 tptp.list_nat) (P_17 (-> tptp.list_A2115238852le_alt tptp.list_nat Bool))) (=> (@ (@ P_17 tptp.nil_Ar1286194111le_alt) tptp.nil_nat) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt)) (@ (@ P_17 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)) tptp.nil_nat)) (=> (forall ((Y_3 tptp.nat) (Ys_5 tptp.list_nat)) (@ (@ P_17 tptp.nil_Ar1286194111le_alt) (@ (@ tptp.cons_nat Y_3) Ys_5))) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt) (Y_3 tptp.nat) (Ys_5 tptp.list_nat)) (=> (@ (@ P_17 Xs_54) Ys_5) (@ (@ P_17 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)) (@ (@ tptp.cons_nat Y_3) Ys_5)))) (@ (@ P_17 Xs_94) Ys_19)))))) (forall ((Xs_94 tptp.list_nat) (Ys_19 tptp.list_A2115238852le_alt) (P_17 (-> tptp.list_nat tptp.list_A2115238852le_alt Bool))) (=> (@ (@ P_17 tptp.nil_nat) tptp.nil_Ar1286194111le_alt) (=> (forall ((X_1 tptp.nat) (Xs_54 tptp.list_nat)) (@ (@ P_17 (@ (@ tptp.cons_nat X_1) Xs_54)) tptp.nil_Ar1286194111le_alt)) (=> (forall ((Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (@ (@ P_17 tptp.nil_nat) (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5))) (=> (forall ((X_1 tptp.nat) (Xs_54 tptp.list_nat) (Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (=> (@ (@ P_17 Xs_54) Ys_5) (@ (@ P_17 (@ (@ tptp.cons_nat X_1) Xs_54)) (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5)))) (@ (@ P_17 Xs_94) Ys_19)))))) (forall ((F_5 (-> tptp.arrow_475358991le_alt tptp.option_nat))) (= (@ (@ tptp.map_fi312151301lt_nat F_5) tptp.nil_Ar1286194111le_alt) tptp.nil_nat)) (forall ((F_5 (-> tptp.nat tptp.option514678660le_alt))) (= (@ (@ tptp.map_fi1462697295le_alt F_5) tptp.nil_nat) tptp.nil_Ar1286194111le_alt)) (forall ((R_2 (-> tptp.nat tptp.nat Bool))) (@ (@ (@ tptp.listrelp_nat R_2) tptp.nil_nat) tptp.nil_nat)) (forall ((R_2 (-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool))) (@ (@ (@ tptp.listre1213162009le_alt R_2) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)) (forall ((Xs_93 tptp.list_A2115238852le_alt) (Ys_18 tptp.list_A2115238852le_alt) (R_1 (-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool)) (X_65 tptp.arrow_475358991le_alt) (Y_32 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.listre1213162009le_alt R_1))) (=> (@ (@ R_1 X_65) Y_32) (=> (@ (@ _let_1 Xs_93) Ys_18) (@ (@ _let_1 (@ (@ tptp.cons_A228743023le_alt X_65) Xs_93)) (@ (@ tptp.cons_A228743023le_alt Y_32) Ys_18)))))) (forall ((Xs_92 tptp.list_nat)) (= (@ (@ tptp.sublist_nat Xs_92) tptp.bot_bot_nat_o) tptp.nil_nat)) (forall ((Xs_92 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.sublis2047953604le_alt Xs_92) tptp.bot_bot_nat_o) tptp.nil_Ar1286194111le_alt)) (forall ((Xs_91 tptp.list_A2115238852le_alt) (Ys_17 tptp.list_A2115238852le_alt)) (=> (not (= (@ tptp.size_s1858781230le_alt Xs_91) (@ tptp.size_s1858781230le_alt Ys_17))) (not (= Xs_91 Ys_17)))) (forall ((Xs_90 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rev_nat Xs_90)) (@ tptp.size_size_list_nat Xs_90))) (forall ((Xs_90 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ tptp.rev_Ar1106406943le_alt Xs_90)) (@ tptp.size_s1858781230le_alt Xs_90))) (forall ((N_45 tptp.nat) (X_64 tptp.arrow_475358991le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ tptp.replic1511538809le_alt N_45) X_64)) N_45)) _let_56 (forall ((F_4 (-> tptp.nat tptp.nat tptp.nat)) (X_63 tptp.nat) (Xs_88 tptp.list_nat) (A_84 tptp.nat)) (let ((_let_1 (@ tptp.foldr_nat_nat F_4))) (= (@ (@ _let_1 (@ (@ tptp.cons_nat X_63) Xs_88)) A_84) (@ (@ F_4 X_63) (@ (@ _let_1 Xs_88) A_84))))) (forall ((F_3 (-> tptp.nat tptp.nat tptp.nat)) (A_83 tptp.nat)) (= (@ (@ (@ tptp.foldr_nat_nat F_3) tptp.nil_nat) A_83) A_83)) (forall ((F_2 (-> tptp.nat tptp.nat tptp.nat)) (Xs_87 tptp.list_nat) (Ys_16 tptp.list_nat) (A_82 tptp.nat)) (let ((_let_1 (@ tptp.foldr_nat_nat F_2))) (= (@ (@ _let_1 (@ (@ tptp.append_nat Xs_87) Ys_16)) A_82) (@ (@ _let_1 Xs_87) (@ (@ _let_1 Ys_16) A_82))))) (forall ((Xs_86 tptp.list_nat)) (= (= (@ tptp.size_size_list_nat Xs_86) tptp.zero_zero_nat) (= Xs_86 tptp.nil_nat))) (forall ((Xs_86 tptp.list_A2115238852le_alt)) (= (= (@ tptp.size_s1858781230le_alt Xs_86) tptp.zero_zero_nat) (= Xs_86 tptp.nil_Ar1286194111le_alt))) _let_55 _let_54 (forall ((P_16 (-> tptp.list_A2115238852le_alt tptp.list_nat Bool)) (Xs_85 tptp.list_A2115238852le_alt) (Ys_15 tptp.list_nat)) (=> (= (@ tptp.size_s1858781230le_alt Xs_85) (@ tptp.size_size_list_nat Ys_15)) (=> (@ (@ P_16 tptp.nil_Ar1286194111le_alt) tptp.nil_nat) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt) (Y_3 tptp.nat) (Ys_5 tptp.list_nat)) (=> (= (@ tptp.size_s1858781230le_alt Xs_54) (@ tptp.size_size_list_nat Ys_5)) (=> (@ (@ P_16 Xs_54) Ys_5) (@ (@ P_16 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)) (@ (@ tptp.cons_nat Y_3) Ys_5))))) (@ (@ P_16 Xs_85) Ys_15))))) (forall ((P_16 (-> tptp.list_nat tptp.list_A2115238852le_alt Bool)) (Xs_85 tptp.list_nat) (Ys_15 tptp.list_A2115238852le_alt)) (=> (= (@ tptp.size_size_list_nat Xs_85) (@ tptp.size_s1858781230le_alt Ys_15)) (=> (@ (@ P_16 tptp.nil_nat) tptp.nil_Ar1286194111le_alt) (=> (forall ((X_1 tptp.nat) (Xs_54 tptp.list_nat) (Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (=> (= (@ tptp.size_size_list_nat Xs_54) (@ tptp.size_s1858781230le_alt Ys_5)) (=> (@ (@ P_16 Xs_54) Ys_5) (@ (@ P_16 (@ (@ tptp.cons_nat X_1) Xs_54)) (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5))))) (@ (@ P_16 Xs_85) Ys_15))))) (forall ((P_16 (-> tptp.list_A2115238852le_alt tptp.list_A2115238852le_alt Bool)) (Xs_85 tptp.list_A2115238852le_alt) (Ys_15 tptp.list_A2115238852le_alt)) (=> (= (@ tptp.size_s1858781230le_alt Xs_85) (@ tptp.size_s1858781230le_alt Ys_15)) (=> (@ (@ P_16 tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt) (=> (forall ((X_1 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt) (Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (=> (= (@ tptp.size_s1858781230le_alt Xs_54) (@ tptp.size_s1858781230le_alt Ys_5)) (=> (@ (@ P_16 Xs_54) Ys_5) (@ (@ P_16 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)) (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5))))) (@ (@ P_16 Xs_85) Ys_15))))) (forall ((A_81 tptp.int)) (not (@ (@ tptp.member_int A_81) tptp.bot_bot_int_o))) (forall ((A_81 tptp.nat)) (not (@ (@ tptp.member_nat A_81) tptp.bot_bot_nat_o))) (forall ((X_1 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_1) tptp.bot_bot_o)) (forall ((X_62 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_62) tptp.bot_bot_o)) (forall ((N_44 tptp.nat)) (exists ((Xs_54 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt Xs_54) N_44))) (forall ((R (-> tptp.nat tptp.nat Bool)) (A1 tptp.list_nat) (A2 tptp.list_nat)) (= (@ (@ (@ tptp.listrelp_nat R) A1) A2) (or (and (= A1 tptp.nil_nat) (= A2 tptp.nil_nat)) (exists ((X_1 tptp.nat) (Y_3 tptp.nat) (Xs_54 tptp.list_nat) (Ys_5 tptp.list_nat)) (and (= A1 (@ (@ tptp.cons_nat X_1) Xs_54)) (= A2 (@ (@ tptp.cons_nat Y_3) Ys_5)) (@ (@ R X_1) Y_3) (@ (@ (@ tptp.listrelp_nat R) Xs_54) Ys_5)))))) (forall ((R (-> tptp.arrow_475358991le_alt tptp.arrow_475358991le_alt Bool)) (A1 tptp.list_A2115238852le_alt) (A2 tptp.list_A2115238852le_alt)) (= (@ (@ (@ tptp.listre1213162009le_alt R) A1) A2) (or (and (= A1 tptp.nil_Ar1286194111le_alt) (= A2 tptp.nil_Ar1286194111le_alt)) (exists ((X_1 tptp.arrow_475358991le_alt) (Y_3 tptp.arrow_475358991le_alt) (Xs_54 tptp.list_A2115238852le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (and (= A1 (@ (@ tptp.cons_A228743023le_alt X_1) Xs_54)) (= A2 (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5)) (@ (@ R X_1) Y_3) (@ (@ (@ tptp.listre1213162009le_alt R) Xs_54) Ys_5)))))) (forall ((A_80 tptp.int) (A_79 (-> tptp.int Bool))) (=> (= A_79 tptp.bot_bot_int_o) (not (@ (@ tptp.member_int A_80) A_79)))) (forall ((A_80 tptp.nat) (A_79 (-> tptp.nat Bool))) (=> (= A_79 tptp.bot_bot_nat_o) (not (@ (@ tptp.member_nat A_80) A_79)))) (forall ((P_15 (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P_15) tptp.bot_bot_nat_o) (forall ((X_1 tptp.nat)) (not (@ P_15 X_1))))) (forall ((C_36 tptp.int)) (not (@ (@ tptp.member_int C_36) tptp.bot_bot_int_o))) (forall ((C_36 tptp.nat)) (not (@ (@ tptp.member_nat C_36) tptp.bot_bot_nat_o))) (forall ((P_14 (-> tptp.nat Bool))) (= (= tptp.bot_bot_nat_o (@ tptp.collect_nat P_14)) (forall ((X_1 tptp.nat)) (not (@ P_14 X_1))))) (forall ((A_78 (-> tptp.int Bool))) (= (exists ((X_1 tptp.int)) (@ (@ tptp.member_int X_1) A_78)) (not (= A_78 tptp.bot_bot_int_o)))) (forall ((A_78 (-> tptp.nat Bool))) (= (exists ((X_1 tptp.nat)) (@ (@ tptp.member_nat X_1) A_78)) (not (= A_78 tptp.bot_bot_nat_o)))) (forall ((A_77 (-> tptp.int Bool))) (= (forall ((X_1 tptp.int)) (not (@ (@ tptp.member_int X_1) A_77))) (= A_77 tptp.bot_bot_int_o))) (forall ((A_77 (-> tptp.nat Bool))) (= (forall ((X_1 tptp.nat)) (not (@ (@ tptp.member_nat X_1) A_77))) (= A_77 tptp.bot_bot_nat_o))) _let_52 (forall ((A_76 (-> tptp.int Bool))) (=> (forall ((Y_3 tptp.int)) (not (@ (@ tptp.member_int Y_3) A_76))) (= A_76 tptp.bot_bot_int_o))) (forall ((A_76 (-> tptp.nat Bool))) (=> (forall ((Y_3 tptp.nat)) (not (@ (@ tptp.member_nat Y_3) A_76))) (= A_76 tptp.bot_bot_nat_o))) _let_51 (forall ((X_61 tptp.int) (Y_31 tptp.int) (Z_8 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int X_61))) (= (@ (@ tptp.ord_max_int (@ _let_1 Y_31)) Z_8) (@ _let_1 (@ (@ tptp.ord_max_int Y_31) Z_8))))) (forall ((X_61 tptp.nat) (Y_31 tptp.nat) (Z_8 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat X_61))) (= (@ (@ tptp.ord_max_nat (@ _let_1 Y_31)) Z_8) (@ _let_1 (@ (@ tptp.ord_max_nat Y_31) Z_8))))) (forall ((A_75 tptp.int) (B_47 tptp.int) (C_35 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A_75))) (= (@ (@ tptp.ord_max_int (@ _let_1 B_47)) C_35) (@ _let_1 (@ (@ tptp.ord_max_int B_47) C_35))))) (forall ((A_75 tptp.nat) (B_47 tptp.nat) (C_35 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A_75))) (= (@ (@ tptp.ord_max_nat (@ _let_1 B_47)) C_35) (@ _let_1 (@ (@ tptp.ord_max_nat B_47) C_35))))) (forall ((X_60 tptp.int) (Y_30 tptp.int) (Z_7 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int X_60))) (let ((_let_2 (@ tptp.ord_max_int Y_30))) (= (@ _let_1 (@ _let_2 Z_7)) (@ _let_2 (@ _let_1 Z_7)))))) (forall ((X_60 tptp.nat) (Y_30 tptp.nat) (Z_7 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat X_60))) (let ((_let_2 (@ tptp.ord_max_nat Y_30))) (= (@ _let_1 (@ _let_2 Z_7)) (@ _let_2 (@ _let_1 Z_7)))))) (forall ((B_46 tptp.int) (A_74 tptp.int) (C_34 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int B_46))) (let ((_let_2 (@ tptp.ord_max_int A_74))) (= (@ _let_1 (@ _let_2 C_34)) (@ _let_2 (@ _let_1 C_34)))))) (forall ((B_46 tptp.nat) (A_74 tptp.nat) (C_34 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat B_46))) (let ((_let_2 (@ tptp.ord_max_nat A_74))) (= (@ _let_1 (@ _let_2 C_34)) (@ _let_2 (@ _let_1 C_34)))))) (forall ((A_73 tptp.int)) (= (@ (@ tptp.ord_max_int A_73) A_73) A_73)) (forall ((A_73 tptp.nat)) (= (@ (@ tptp.ord_max_nat A_73) A_73) A_73)) (forall ((A_72 tptp.int) (B_45 tptp.int)) (= (@ (@ tptp.ord_max_int A_72) B_45) (@ (@ tptp.ord_max_int B_45) A_72))) (forall ((A_72 tptp.nat) (B_45 tptp.nat)) (= (@ (@ tptp.ord_max_nat A_72) B_45) (@ (@ tptp.ord_max_nat B_45) A_72))) (forall ((X_59 tptp.int) (Y_29 tptp.int)) (= (@ (@ tptp.ord_max_int X_59) Y_29) (@ (@ tptp.ord_max_int Y_29) X_59))) (forall ((X_59 tptp.nat) (Y_29 tptp.nat)) (= (@ (@ tptp.ord_max_nat X_59) Y_29) (@ (@ tptp.ord_max_nat Y_29) X_59))) (forall ((A_71 tptp.int) (B_44 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A_71))) (let ((_let_2 (@ _let_1 B_44))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A_71 tptp.nat) (B_44 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A_71))) (let ((_let_2 (@ _let_1 B_44))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X_58 tptp.int) (Y_28 tptp.int)) (let ((_let_1 (@ tptp.ord_max_int X_58))) (let ((_let_2 (@ _let_1 Y_28))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X_58 tptp.nat) (Y_28 tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat X_58))) (let ((_let_2 (@ _let_1 Y_28))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X_57 tptp.int)) (= (@ (@ tptp.ord_max_int X_57) X_57) X_57)) (forall ((X_57 tptp.nat)) (= (@ (@ tptp.ord_max_nat X_57) X_57) X_57)) (forall ((P_13 (-> tptp.arrow_475358991le_alt Bool)) (Xs_84 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.dropWh1316781920le_alt P_13) Xs_84) (@ (@ tptp.drop_A1346709759le_alt (@ tptp.size_s1858781230le_alt (@ (@ tptp.takeWh1696291512le_alt P_13) Xs_84))) Xs_84))) (forall ((P_12 (-> tptp.nat Bool)) (Xs_83 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat (@ (@ tptp.takeWhile_nat P_12) Xs_83)))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_nat Xs_83)) (not (@ P_12 (@ (@ tptp.nth_nat Xs_83) _let_1)))))) (forall ((P_12 (-> tptp.arrow_475358991le_alt Bool)) (Xs_83 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt (@ (@ tptp.takeWh1696291512le_alt P_12) Xs_83)))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_s1858781230le_alt Xs_83)) (not (@ P_12 (@ (@ tptp.nth_Ar125878976le_alt Xs_83) _let_1)))))) (forall ((J_7 tptp.nat) (P_11 (-> tptp.nat Bool)) (Xs_82 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.takeWhile_nat P_11) Xs_82))) (=> (@ (@ tptp.ord_less_nat J_7) (@ tptp.size_size_list_nat _let_1)) (= (@ (@ tptp.nth_nat _let_1) J_7) (@ (@ tptp.nth_nat Xs_82) J_7))))) (forall ((J_7 tptp.nat) (P_11 (-> tptp.arrow_475358991le_alt Bool)) (Xs_82 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.takeWh1696291512le_alt P_11) Xs_82))) (=> (@ (@ tptp.ord_less_nat J_7) (@ tptp.size_s1858781230le_alt _let_1)) (= (@ (@ tptp.nth_Ar125878976le_alt _let_1) J_7) (@ (@ tptp.nth_Ar125878976le_alt Xs_82) J_7))))) (forall ((Xs_81 tptp.list_A2115238852le_alt) (X_56 tptp.arrow_475358991le_alt) (Ys_14 tptp.list_A2115238852le_alt) (Y_27 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.append179082452le_alt Xs_81))) (= (@ (@ (@ tptp.list_u62477863le_alt (@ _let_1 (@ (@ tptp.cons_A228743023le_alt X_56) Ys_14))) (@ tptp.size_s1858781230le_alt Xs_81)) Y_27) (@ _let_1 (@ (@ tptp.cons_A228743023le_alt Y_27) Ys_14))))) (forall ((N_5 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N_5) N_5)) (forall ((N_5 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_5) tptp.zero_zero_nat))) (forall ((Xs_80 tptp.list_A2115238852le_alt) (I_26 tptp.nat) (X_55 tptp.arrow_475358991le_alt) (Y_26 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ (@ tptp.list_u62477863le_alt Xs_80) I_26))) (= (@ (@ (@ tptp.list_u62477863le_alt (@ _let_1 X_55)) I_26) Y_26) (@ _let_1 Y_26)))) (forall ((Xs_79 tptp.list_A2115238852le_alt) (X_54 tptp.arrow_475358991le_alt) (X_53 tptp.arrow_475358991le_alt) (I_25 tptp.nat) (I_24 tptp.nat)) (let ((_let_1 (@ tptp.list_u62477863le_alt Xs_79))) (=> (not (= I_25 I_24)) (= (@ (@ (@ tptp.list_u62477863le_alt (@ (@ _let_1 I_25) X_54)) I_24) X_53) (@ (@ (@ tptp.list_u62477863le_alt (@ (@ _let_1 I_24) X_53)) I_25) X_54))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ (@ P N_5) M))) (=> (=> (@ (@ tptp.ord_less_nat M) N_5) _let_1) (=> (=> (= M N_5) _let_1) (=> (=> (@ (@ tptp.ord_less_nat N_5) M) _let_1) _let_1))))) (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))) (forall ((N_5 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N_5) M) (not (= M N_5)))) (forall ((N_5 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_5) N_5))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((M tptp.nat) (N_5 tptp.nat)) (= (not (= M N_5)) (or (@ (@ tptp.ord_less_nat M) N_5) (@ (@ tptp.ord_less_nat N_5) M)))) (forall ((N_5 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_5) N_5))) (forall ((N_5 tptp.nat)) (=> (not (= N_5 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5))) (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N_5) (not (= N_5 tptp.zero_zero_nat)))) (forall ((N_5 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_5) tptp.zero_zero_nat))) (forall ((N_5 tptp.nat)) (= (not (= N_5 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5))) (forall ((N_5 tptp.nat)) (not (@ (@ tptp.ord_less_nat N_5) tptp.zero_zero_nat))) (forall ((X_52 tptp.int)) (not (@ (@ tptp.ord_less_int X_52) X_52))) (forall ((X_52 (-> tptp.nat Bool))) (not (@ (@ tptp.ord_less_nat_o X_52) X_52))) (forall ((X_52 tptp.nat)) (not (@ (@ tptp.ord_less_nat X_52) X_52))) (forall ((X_51 tptp.int) (Y_25 tptp.int)) (= (not (= X_51 Y_25)) (or (@ (@ tptp.ord_less_int X_51) Y_25) (@ (@ tptp.ord_less_int Y_25) X_51)))) (forall ((X_51 tptp.nat) (Y_25 tptp.nat)) (= (not (= X_51 Y_25)) (or (@ (@ tptp.ord_less_nat X_51) Y_25) (@ (@ tptp.ord_less_nat Y_25) X_51)))) (forall ((X_50 tptp.int) (Y_24 tptp.int)) (= (not (@ (@ tptp.ord_less_int X_50) Y_24)) (or (@ (@ tptp.ord_less_int Y_24) X_50) (= X_50 Y_24)))) (forall ((X_50 tptp.nat) (Y_24 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X_50) Y_24)) (or (@ (@ tptp.ord_less_nat Y_24) X_50) (= X_50 Y_24)))) (forall ((X_49 tptp.int) (Y_23 tptp.int)) (or (@ (@ tptp.ord_less_int X_49) Y_23) (= X_49 Y_23) (@ (@ tptp.ord_less_int Y_23) X_49))) (forall ((X_49 tptp.nat) (Y_23 tptp.nat)) (or (@ (@ tptp.ord_less_nat X_49) Y_23) (= X_49 Y_23) (@ (@ tptp.ord_less_nat Y_23) X_49))) (forall ((Y_22 tptp.int) (X_48 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y_22) X_48)) (= (not (@ (@ tptp.ord_less_int X_48) Y_22)) (= X_48 Y_22)))) (forall ((Y_22 tptp.nat) (X_48 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y_22) X_48)) (= (not (@ (@ tptp.ord_less_nat X_48) Y_22)) (= X_48 Y_22)))) (forall ((X_47 tptp.int) (Y_21 tptp.int)) (=> (not (= X_47 Y_21)) (=> (not (@ (@ tptp.ord_less_int X_47) Y_21)) (@ (@ tptp.ord_less_int Y_21) X_47)))) (forall ((X_47 tptp.nat) (Y_21 tptp.nat)) (=> (not (= X_47 Y_21)) (=> (not (@ (@ tptp.ord_less_nat X_47) Y_21)) (@ (@ tptp.ord_less_nat Y_21) X_47)))) (forall ((X_46 tptp.int) (Y_20 tptp.int)) (=> (@ (@ tptp.ord_less_int X_46) Y_20) (not (= X_46 Y_20)))) (forall ((X_46 (-> tptp.nat Bool)) (Y_20 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(@ tptp.ord_less_int A_66))) (=> (@ _let_1 B_39) (=> (= B_39 C_31) (@ _let_1 C_31))))) (forall ((C_31 (-> tptp.nat Bool)) (A_66 (-> tptp.nat Bool)) (B_39 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_nat_o A_66))) (=> (@ _let_1 B_39) (=> (= B_39 C_31) (@ _let_1 C_31))))) (forall ((C_31 tptp.nat) (A_66 tptp.nat) (B_39 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A_66))) (=> (@ _let_1 B_39) (=> (= B_39 C_31) (@ _let_1 C_31))))) (forall ((C_30 tptp.int) (B_38 tptp.int) (A_65 tptp.int)) (=> (@ (@ tptp.ord_less_int B_38) A_65) (=> (= B_38 C_30) (@ (@ tptp.ord_less_int C_30) A_65)))) (forall ((C_30 (-> tptp.nat Bool)) (B_38 (-> tptp.nat Bool)) (A_65 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o B_38) A_65) (=> (= B_38 C_30) (@ (@ tptp.ord_less_nat_o C_30) A_65)))) (forall ((C_30 tptp.nat) (B_38 tptp.nat) (A_65 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B_38) A_65) (=> (= B_38 C_30) (@ (@ tptp.ord_less_nat C_30) A_65)))) (forall ((Z_6 tptp.int) (X_40 tptp.int) (Y_14 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X_40))) (=> (@ _let_1 Y_14) (=> (@ (@ tptp.ord_less_int Y_14) Z_6) (@ _let_1 Z_6))))) (forall ((Z_6 (-> tptp.nat Bool)) (X_40 (-> tptp.nat Bool)) (Y_14 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_nat_o X_40))) (=> (@ _let_1 Y_14) (=> (@ (@ tptp.ord_less_nat_o Y_14) Z_6) (@ _let_1 Z_6))))) _let_49 (forall ((Z_5 tptp.int) (Y_13 tptp.int) (X_39 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z_5))) (=> (@ (@ tptp.ord_less_int Y_13) X_39) (=> (@ _let_1 Y_13) (@ _let_1 X_39))))) (forall ((Z_5 (-> tptp.nat Bool)) (Y_13 (-> tptp.nat Bool)) (X_39 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_nat_o Z_5))) (=> (@ (@ tptp.ord_less_nat_o Y_13) X_39) (=> (@ _let_1 Y_13) (@ _let_1 X_39))))) (forall ((Z_5 tptp.nat) (Y_13 tptp.nat) (X_39 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z_5))) (=> (@ (@ tptp.ord_less_nat Y_13) X_39) (=> (@ _let_1 Y_13) (@ _let_1 X_39))))) (forall ((X_38 tptp.int) (Y_12 tptp.int)) (=> (@ (@ tptp.ord_less_int X_38) Y_12) (not (@ (@ tptp.ord_less_int Y_12) X_38)))) (forall ((X_38 (-> tptp.nat Bool)) (Y_12 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat_o X_38) Y_12) (not (@ (@ tptp.ord_less_nat_o Y_12) X_38)))) (forall ((X_38 tptp.nat) (Y_12 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X_38) Y_12) (not (@ (@ tptp.ord_less_nat Y_12) X_38)))) (forall ((X_37 tptp.int) (Y_11 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X_37) Y_11)) (=> (not (= X_37 Y_11)) (@ (@ tptp.ord_less_int Y_11) X_37)))) (forall ((X_37 tptp.nat) (Y_11 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X_37) Y_11)) (=> (not (= X_37 Y_11)) (@ (@ tptp.ord_less_nat Y_11) X_37)))) (forall ((Ys_13 tptp.list_A2115238852le_alt) (X_36 tptp.arrow_475358991le_alt) (I_23 tptp.nat) (Xs_78 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_23) (@ tptp.size_s1858781230le_alt Xs_78)) (= (@ (@ (@ tptp.list_u62477863le_alt (@ (@ tptp.append179082452le_alt Xs_78) Ys_13)) I_23) X_36) (@ (@ tptp.append179082452le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_78) I_23) X_36)) Ys_13)))) (forall ((X_35 tptp.arrow_475358991le_alt) (J_6 tptp.nat) (I_22 tptp.nat) (Xs_77 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.nth_Ar125878976le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_77) I_22) X_35)) J_6))) (let ((_let_2 (= I_22 J_6))) (=> (@ (@ tptp.ord_less_nat I_22) (@ tptp.size_s1858781230le_alt Xs_77)) (and (=> _let_2 (= _let_1 X_35)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_Ar125878976le_alt Xs_77) J_6)))))))) (forall ((X_35 tptp.nat) (J_6 tptp.nat) (I_22 tptp.nat) (Xs_77 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs_77) I_22) X_35)) J_6))) (let ((_let_2 (= I_22 J_6))) (=> (@ (@ tptp.ord_less_nat I_22) (@ tptp.size_size_list_nat Xs_77)) (and (=> _let_2 (= _let_1 X_35)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs_77) J_6)))))))) (forall ((X_34 tptp.arrow_475358991le_alt) (I_21 tptp.nat) (Xs_76 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_21) (@ tptp.size_s1858781230le_alt Xs_76)) (= (= (@ (@ (@ tptp.list_u62477863le_alt Xs_76) I_21) X_34) Xs_76) (= (@ (@ tptp.nth_Ar125878976le_alt Xs_76) I_21) X_34)))) (forall ((X_34 tptp.nat) (I_21 tptp.nat) (Xs_76 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I_21) (@ tptp.size_size_list_nat Xs_76)) (= (= (@ (@ (@ tptp.list_update_nat Xs_76) I_21) X_34) Xs_76) (= (@ (@ tptp.nth_nat Xs_76) I_21) X_34)))) (forall ((X_33 tptp.arrow_475358991le_alt) (I_20 tptp.nat) (Xs_75 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_20) (@ tptp.size_s1858781230le_alt Xs_75)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_75) I_20) X_33)) I_20) X_33))) (forall ((X_33 tptp.nat) (I_20 tptp.nat) (Xs_75 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I_20) (@ tptp.size_size_list_nat Xs_75)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs_75) I_20) X_33)) I_20) X_33))) (forall ((N_43 tptp.nat) (Xs_74 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat N_43) (@ tptp.size_s1858781230le_alt Xs_74)) (= (@ tptp.last_A1217315288le_alt (@ (@ tptp.drop_A1346709759le_alt N_43) Xs_74)) (@ tptp.last_A1217315288le_alt Xs_74)))) (forall ((A_64 Bool)) (not (@ (@ tptp.ord_less_o A_64) tptp.bot_bot_o))) (forall ((A_64 tptp.nat)) (not (@ (@ tptp.ord_less_nat A_64) tptp.bot_bot_nat))) (forall ((A_64 (-> tptp.nat Bool))) (not (@ (@ tptp.ord_less_nat_o A_64) tptp.bot_bot_nat_o))) (forall ((A_63 Bool)) (= (not (= A_63 tptp.bot_bot_o)) (@ (@ tptp.ord_less_o tptp.bot_bot_o) A_63))) (forall ((A_63 tptp.nat)) (= (not (= A_63 tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A_63))) (forall ((A_63 (-> tptp.nat Bool))) (= (not (= A_63 tptp.bot_bot_nat_o)) (@ (@ tptp.ord_less_nat_o tptp.bot_bot_nat_o) A_63))) (forall ((Xs_73 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt tptp.zero_zero_nat) Xs_73) Xs_73)) (forall ((N_42 tptp.nat)) (= (@ (@ tptp.drop_nat N_42) tptp.nil_nat) tptp.nil_nat)) (forall ((N_42 tptp.nat)) (= (@ (@ tptp.drop_A1346709759le_alt N_42) tptp.nil_Ar1286194111le_alt) tptp.nil_Ar1286194111le_alt)) (forall ((Z_4 tptp.int) (X_32 tptp.int) (Y_10 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z_4))) (= (@ _let_1 (@ (@ tptp.ord_max_int X_32) Y_10)) (or (@ _let_1 X_32) (@ _let_1 Y_10))))) (forall ((Z_4 tptp.nat) (X_32 tptp.nat) (Y_10 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z_4))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X_32) Y_10)) (or (@ _let_1 X_32) (@ _let_1 Y_10))))) (forall ((X_31 tptp.int) (Y_9 tptp.int) (Z_3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X_31) Y_9)) Z_3) (and (@ (@ tptp.ord_less_int X_31) Z_3) (@ (@ tptp.ord_less_int Y_9) Z_3)))) (forall ((X_31 tptp.nat) (Y_9 tptp.nat) (Z_3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X_31) Y_9)) Z_3) (and (@ (@ tptp.ord_less_nat X_31) Z_3) (@ (@ tptp.ord_less_nat Y_9) Z_3)))) (forall ((B_37 tptp.int) (X_30 tptp.int) (A_62 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X_30))) (=> (@ _let_1 A_62) (@ _let_1 (@ (@ tptp.ord_max_int A_62) B_37))))) (forall ((B_37 tptp.nat) (X_30 tptp.nat) (A_62 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_30))) (=> (@ _let_1 A_62) (@ _let_1 (@ (@ tptp.ord_max_nat A_62) B_37))))) (forall ((A_61 tptp.int) (X_29 tptp.int) (B_36 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X_29))) (=> (@ _let_1 B_36) (@ _let_1 (@ (@ tptp.ord_max_int A_61) B_36))))) (forall ((A_61 tptp.nat) (X_29 tptp.nat) (B_36 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X_29))) (=> (@ _let_1 B_36) (@ _let_1 (@ (@ tptp.ord_max_nat A_61) B_36))))) (forall ((I_19 tptp.nat) (Xs_72 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_72) (@ tptp.distin236324274le_alt (@ (@ tptp.drop_A1346709759le_alt I_19) Xs_72)))) (forall ((N_41 tptp.nat) (Xs_71 tptp.list_nat)) (=> (@ tptp.linorder_sorted_nat Xs_71) (@ tptp.linorder_sorted_nat (@ (@ tptp.drop_nat N_41) Xs_71)))) (forall ((Xs_70 tptp.list_nat) (K_7 tptp.nat) (X_28 tptp.nat)) (= (= (@ (@ (@ tptp.list_update_nat Xs_70) K_7) X_28) tptp.nil_nat) (= Xs_70 tptp.nil_nat))) (forall ((Xs_70 tptp.list_A2115238852le_alt) (K_7 tptp.nat) (X_28 tptp.arrow_475358991le_alt)) (= (= (@ (@ (@ tptp.list_u62477863le_alt Xs_70) K_7) X_28) tptp.nil_Ar1286194111le_alt) (= Xs_70 tptp.nil_Ar1286194111le_alt))) (forall ((I_18 tptp.nat) (V_3 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat tptp.nil_nat) I_18) V_3) tptp.nil_nat)) (forall ((I_18 tptp.nat) (V_3 tptp.arrow_475358991le_alt)) (= (@ (@ (@ tptp.list_u62477863le_alt tptp.nil_Ar1286194111le_alt) I_18) V_3) tptp.nil_Ar1286194111le_alt)) (forall ((I_17 tptp.nat) (Y_8 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat tptp.nil_nat) I_17) Y_8) tptp.nil_nat)) (forall ((I_17 tptp.nat) (Y_8 tptp.arrow_475358991le_alt)) (= (@ (@ (@ tptp.list_u62477863le_alt tptp.nil_Ar1286194111le_alt) I_17) Y_8) tptp.nil_Ar1286194111le_alt)) (forall ((Xs_69 tptp.list_A2115238852le_alt) (I_16 tptp.nat) (X_27 tptp.arrow_475358991le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_69) I_16) X_27)) (@ tptp.size_s1858781230le_alt Xs_69))) _let_48 (forall ((Xs_68 tptp.list_nat) (I_15 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs_68) I_15) (@ (@ tptp.nth_nat Xs_68) I_15)) Xs_68)) (forall ((Xs_67 tptp.list_A2115238852le_alt) (X_26 tptp.arrow_475358991le_alt) (I_14 tptp.nat) (J_5 tptp.nat)) (=> (not (= I_14 J_5)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_67) I_14) X_26)) J_5) (@ (@ tptp.nth_Ar125878976le_alt Xs_67) J_5)))) (forall ((Xs_67 tptp.list_nat) (X_26 tptp.nat) (I_14 tptp.nat) (J_5 tptp.nat)) (=> (not (= I_14 J_5)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs_67) I_14) X_26)) J_5) (@ (@ tptp.nth_nat Xs_67) J_5)))) (forall ((N_40 tptp.nat) (Xs_66 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.drop_A1346709759le_alt N_40))) (= (@ _let_1 (@ tptp.butlas274947851le_alt Xs_66)) (@ tptp.butlas274947851le_alt (@ _let_1 Xs_66))))) (forall ((N_39 tptp.nat) (Xs_65 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.drop_A1346709759le_alt N_39))) (= (@ tptp.butlas274947851le_alt (@ _let_1 Xs_65)) (@ _let_1 (@ tptp.butlas274947851le_alt Xs_65))))) (forall ((N_38 tptp.nat) (Xs_64 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.drop_A1346709759le_alt N_38))) (= (@ tptp.tl_Arr465451158le_alt (@ _let_1 Xs_64)) (@ _let_1 (@ tptp.tl_Arr465451158le_alt Xs_64))))) (forall ((N_37 tptp.nat) (Xs_63 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.drop_A1346709759le_alt N_37))) (= (@ _let_1 (@ tptp.tl_Arr465451158le_alt Xs_63)) (@ tptp.tl_Arr465451158le_alt (@ _let_1 Xs_63))))) (forall ((N_36 tptp.nat) (Xs_62 tptp.list_nat)) (=> (not (= Xs_62 tptp.nil_nat)) (=> (@ (@ tptp.ord_less_nat N_36) (@ tptp.size_size_list_nat Xs_62)) (= (@ tptp.hd_nat (@ (@ tptp.drop_nat N_36) Xs_62)) (@ (@ tptp.nth_nat Xs_62) N_36))))) _let_47 (forall ((N_35 tptp.nat) (Xs_61 tptp.list_nat) (Y_7 tptp.nat) (Ys_12 tptp.list_nat)) (=> (= (@ (@ tptp.drop_nat N_35) Xs_61) (@ (@ tptp.cons_nat Y_7) Ys_12)) (= (@ (@ tptp.nth_nat Xs_61) N_35) Y_7))) _let_46 (forall ((Xs_60 tptp.list_A2115238852le_alt) (Ys_11 tptp.list_A2115238852le_alt)) (= (= Xs_60 Ys_11) (and (= (@ tptp.size_s1858781230le_alt Xs_60) (@ tptp.size_s1858781230le_alt Ys_11)) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_s1858781230le_alt Xs_60)) (= (@ (@ tptp.nth_Ar125878976le_alt Xs_60) I_4) (@ (@ tptp.nth_Ar125878976le_alt Ys_11) I_4))))))) (forall ((Xs_60 tptp.list_nat) (Ys_11 tptp.list_nat)) (= (= Xs_60 Ys_11) (and (= (@ tptp.size_size_list_nat Xs_60) (@ tptp.size_size_list_nat Ys_11)) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_size_list_nat Xs_60)) (= (@ (@ tptp.nth_nat Xs_60) I_4) (@ (@ tptp.nth_nat Ys_11) I_4))))))) (forall ((X_25 tptp.arrow_475358991le_alt) (Xs_59 tptp.list_A2115238852le_alt) (Y_6 tptp.arrow_475358991le_alt)) (= (@ (@ (@ tptp.list_u62477863le_alt (@ (@ tptp.cons_A228743023le_alt X_25) Xs_59)) tptp.zero_zero_nat) Y_6) (@ (@ tptp.cons_A228743023le_alt Y_6) Xs_59))) (forall ((X_24 tptp.nat) (I_13 tptp.nat) (N_34 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_13) N_34) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N_34) X_24)) I_13) X_24))) (forall ((X_24 tptp.arrow_475358991le_alt) (I_13 tptp.nat) (N_34 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_13) N_34) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.replic1511538809le_alt N_34) X_24)) I_13) X_24))) (forall ((Xs_58 tptp.list_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs_58)) (not (= Xs_58 tptp.nil_nat)))) (forall ((Xs_58 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s1858781230le_alt Xs_58)) (not (= Xs_58 tptp.nil_Ar1286194111le_alt)))) (forall ((Xs_57 tptp.list_nat)) (= (@ tptp.distinct_nat Xs_57) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_size_list_nat Xs_57)) (forall ((J_2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs_57))) (=> (@ (@ tptp.ord_less_nat J_2) (@ tptp.size_size_list_nat Xs_57)) (=> (not (= I_4 J_2)) (not (= (@ _let_1 I_4) (@ _let_1 J_2))))))))))) _let_45 (forall ((J_4 tptp.nat) (I_12 tptp.nat) (Xs_56 tptp.list_nat)) (let ((_let_1 (@ tptp.nth_nat Xs_56))) (let ((_let_2 (@ tptp.size_size_list_nat Xs_56))) (=> (@ tptp.distinct_nat Xs_56) (=> (@ (@ tptp.ord_less_nat I_12) _let_2) (=> (@ (@ tptp.ord_less_nat J_4) _let_2) (= (= (@ _let_1 I_12) (@ _let_1 J_4)) (= I_12 J_4)))))))) _let_44 _let_43 (forall ((N_5 tptp.nat)) (= (@ (@ tptp.ord_max_nat N_5) tptp.zero_zero_nat) N_5)) (forall ((Xs_55 tptp.list_A2115238852le_alt) (Ys_10 tptp.list_A2115238852le_alt)) (=> (= (@ tptp.size_s1858781230le_alt Xs_55) (@ tptp.size_s1858781230le_alt Ys_10)) (=> (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_s1858781230le_alt Xs_55)) (= (@ (@ tptp.nth_Ar125878976le_alt Xs_55) I_4) (@ (@ tptp.nth_Ar125878976le_alt Ys_10) I_4)))) (= Xs_55 Ys_10)))) (forall ((Xs_55 tptp.list_nat) (Ys_10 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs_55) (@ tptp.size_size_list_nat Ys_10)) (=> (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) (@ tptp.size_size_list_nat Xs_55)) (= (@ (@ tptp.nth_nat Xs_55) I_4) (@ (@ tptp.nth_nat Ys_10) I_4)))) (= Xs_55 Ys_10)))) (forall ((P_9 (-> tptp.nat tptp.arrow_475358991le_alt Bool)) (K_6 tptp.nat)) (= (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) K_6) (@ tptp.ex2 (@ P_9 I_4)))) (exists ((Xs_54 tptp.list_A2115238852le_alt)) (and (= (@ tptp.size_s1858781230le_alt Xs_54) K_6) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) K_6) (@ (@ P_9 I_4) (@ (@ tptp.nth_Ar125878976le_alt Xs_54) I_4)))))))) (forall ((P_9 (-> tptp.nat tptp.nat Bool)) (K_6 tptp.nat)) (= (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) K_6) (@ tptp.ex1 (@ P_9 I_4)))) (exists ((Xs_54 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs_54) K_6) (forall ((I_4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_4) K_6) (@ (@ P_9 I_4) (@ (@ tptp.nth_nat Xs_54) I_4)))))))) (forall ((J_3 tptp.nat) (P_8 (-> tptp.nat Bool)) (Xs_53 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.dropWhile_nat P_8) Xs_53))) (=> (@ (@ tptp.ord_less_nat J_3) (@ tptp.size_size_list_nat _let_1)) (= (@ (@ tptp.nth_nat _let_1) J_3) (@ (@ tptp.nth_nat Xs_53) (@ (@ tptp.plus_plus_nat J_3) (@ tptp.size_size_list_nat (@ (@ tptp.takeWhile_nat P_8) Xs_53)))))))) (forall ((J_3 tptp.nat) (P_8 (-> tptp.arrow_475358991le_alt Bool)) (Xs_53 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.dropWh1316781920le_alt P_8) Xs_53))) (=> (@ (@ tptp.ord_less_nat J_3) (@ tptp.size_s1858781230le_alt _let_1)) (= (@ (@ tptp.nth_Ar125878976le_alt _let_1) J_3) (@ (@ tptp.nth_Ar125878976le_alt Xs_53) (@ (@ tptp.plus_plus_nat J_3) (@ tptp.size_s1858781230le_alt (@ (@ tptp.takeWh1696291512le_alt P_8) Xs_53)))))))) (forall ((I_11 tptp.nat) (Xs_52 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I_11) (@ tptp.size_size_list_nat Xs_52)) (= (@ (@ tptp.cons_nat (@ (@ tptp.nth_nat Xs_52) I_11)) (@ (@ tptp.drop_nat (@ tptp.suc I_11)) Xs_52)) (@ (@ tptp.drop_nat I_11) Xs_52)))) (forall ((I_11 tptp.nat) (Xs_52 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_11) (@ tptp.size_s1858781230le_alt Xs_52)) (= (@ (@ tptp.cons_A228743023le_alt (@ (@ tptp.nth_Ar125878976le_alt Xs_52) I_11)) (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc I_11)) Xs_52)) (@ (@ tptp.drop_A1346709759le_alt I_11) Xs_52)))) (forall ((P_7 (-> tptp.arrow_475358991le_alt Bool)) (Xs_51 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.list_e1252802557le_alt P_7) Xs_51) (exists ((N_7 tptp.nat)) (and (@ (@ tptp.ord_less_nat N_7) (@ tptp.size_s1858781230le_alt Xs_51)) (@ P_7 (@ (@ tptp.nth_Ar125878976le_alt Xs_51) N_7)))))) (forall ((P_7 (-> tptp.nat Bool)) (Xs_51 tptp.list_nat)) (= (@ (@ tptp.list_ex_nat P_7) Xs_51) (exists ((N_7 tptp.nat)) (and (@ (@ tptp.ord_less_nat N_7) (@ tptp.size_size_list_nat Xs_51)) (@ P_7 (@ (@ tptp.nth_nat Xs_51) N_7)))))) _let_42 (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N_5) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N_5)))) (forall ((N_5 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N_5))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))) (forall ((M tptp.nat) (K_3 tptp.nat) (N_5 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) K_3) (@ (@ tptp.plus_plus_nat N_5) K_3)) (= M N_5))) (forall ((K_3 tptp.nat) (M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K_3))) (= (= (@ _let_1 M) (@ _let_1 N_5)) (= M N_5)))) (forall ((M tptp.nat) (N_5 tptp.nat) (K_3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 N_5)) K_3) (@ _let_1 (@ (@ tptp.plus_plus_nat N_5) K_3))))) (forall ((Nat_3 tptp.nat) (Nat_2 tptp.nat)) (= (= (@ tptp.suc Nat_3) (@ tptp.suc Nat_2)) (= Nat_3 Nat_2))) _let_41 _let_40 (forall ((X tptp.nat) (Y tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (let ((_let_2 (@ tptp.plus_plus_nat Y))) (= (@ _let_1 (@ _let_2 Z_1)) (@ _let_2 (@ _let_1 Z_1)))))) _let_39 (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N_5) (@ (@ tptp.plus_plus_nat N_5) M))) (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N_5) (exists ((K_5 tptp.nat)) (= N_5 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_5)))))) _let_38 (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))) (forall ((N_5 tptp.nat)) (not (= (@ tptp.suc N_5) N_5))) (forall ((N_5 tptp.nat)) (not (= N_5 (@ tptp.suc N_5)))) _let_37 (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N_5)) (or (and (= M _let_1) (= N_5 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N_5 _let_1)))))) (forall ((B_35 tptp.nat) (A_60 tptp.nat) (C_29 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B_35) A_60) (@ (@ tptp.plus_plus_nat C_29) A_60)) (= B_35 C_29))) (forall ((B_35 tptp.int) (A_60 tptp.int) (C_29 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B_35) A_60) (@ (@ tptp.plus_plus_int C_29) A_60)) (= B_35 C_29))) (forall ((A_59 tptp.nat) (B_34 tptp.nat) (C_28 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_59))) (=> (= (@ _let_1 B_34) (@ _let_1 C_28)) (= B_34 C_28)))) (forall ((A_59 tptp.int) (B_34 tptp.int) (C_28 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_59))) (=> (= (@ _let_1 B_34) (@ _let_1 C_28)) (= B_34 C_28)))) (forall ((A_58 tptp.nat) (B_33 tptp.nat) (C_27 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_58))) (=> (= (@ _let_1 B_33) (@ _let_1 C_27)) (= B_33 C_27)))) (forall ((A_58 tptp.int) (B_33 tptp.int) (C_27 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_58))) (=> (= (@ _let_1 B_33) (@ _let_1 C_27)) (= B_33 C_27)))) (forall ((B_32 tptp.nat) (A_57 tptp.nat) (C_26 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B_32) A_57) (@ (@ tptp.plus_plus_nat C_26) A_57)) (= B_32 C_26))) (forall ((B_32 tptp.int) (A_57 tptp.int) (C_26 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B_32) A_57) (@ (@ tptp.plus_plus_int C_26) A_57)) (= B_32 C_26))) (forall ((A_56 tptp.nat) (B_31 tptp.nat) (C_25 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_56))) (= (= (@ _let_1 B_31) (@ _let_1 C_25)) (= B_31 C_25)))) (forall ((A_56 tptp.int) (B_31 tptp.int) (C_25 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_56))) (= (= (@ _let_1 B_31) (@ _let_1 C_25)) (= B_31 C_25)))) (forall ((A_55 tptp.nat) (B_30 tptp.nat) (C_24 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_55))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_30)) C_24) (@ _let_1 (@ (@ tptp.plus_plus_nat B_30) C_24))))) (forall ((A_55 tptp.int) (B_30 tptp.int) (C_24 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_55))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_30)) C_24) (@ _let_1 (@ (@ tptp.plus_plus_int B_30) C_24))))) _let_36 (forall ((A_54 tptp.int)) (= (@ (@ tptp.plus_plus_int A_54) tptp.zero_zero_int) A_54)) (forall ((A_53 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_53) tptp.zero_zero_nat) A_53)) (forall ((A_53 tptp.int)) (= (@ (@ tptp.plus_plus_int A_53) tptp.zero_zero_int) A_53)) (forall ((A_52 tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A_52) A_52)) (= A_52 tptp.zero_zero_int))) _let_35 (forall ((A_51 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_51) A_51)) (forall ((A_50 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_50) A_50)) (forall ((A_50 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_50) A_50)) (forall ((C_23 tptp.nat) (A_49 tptp.nat) (B_29 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_23))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A_49)) (@ _let_1 B_29)) (@ (@ tptp.ord_less_nat A_49) B_29)))) (forall ((C_23 tptp.int) (A_49 tptp.int) (B_29 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_23))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A_49)) (@ _let_1 B_29)) (@ (@ tptp.ord_less_int A_49) B_29)))) (forall ((A_48 tptp.nat) (C_22 tptp.nat) (B_28 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_48) C_22)) (@ (@ tptp.plus_plus_nat B_28) C_22)) (@ (@ tptp.ord_less_nat A_48) B_28))) (forall ((A_48 tptp.int) (C_22 tptp.int) (B_28 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_48) C_22)) (@ (@ tptp.plus_plus_int B_28) C_22)) (@ (@ tptp.ord_less_int A_48) B_28))) _let_34 (forall ((C_21 tptp.int) (D_6 tptp.int) (A_47 tptp.int) (B_27 tptp.int)) (=> (@ (@ tptp.ord_less_int A_47) B_27) (=> (@ (@ tptp.ord_less_int C_21) D_6) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_47) C_21)) (@ (@ tptp.plus_plus_int B_27) D_6))))) (forall ((C_20 tptp.nat) (A_46 tptp.nat) (B_26 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_20))) (=> (@ (@ tptp.ord_less_nat A_46) B_26) (@ (@ tptp.ord_less_nat (@ _let_1 A_46)) (@ _let_1 B_26))))) (forall ((C_20 tptp.int) (A_46 tptp.int) (B_26 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_20))) (=> (@ (@ tptp.ord_less_int A_46) B_26) (@ (@ tptp.ord_less_int (@ _let_1 A_46)) (@ _let_1 B_26))))) (forall ((C_19 tptp.nat) (A_45 tptp.nat) (B_25 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_45) B_25) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_45) C_19)) (@ (@ tptp.plus_plus_nat B_25) C_19)))) (forall ((C_19 tptp.int) (A_45 tptp.int) (B_25 tptp.int)) (=> (@ (@ tptp.ord_less_int A_45) B_25) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_45) C_19)) (@ (@ tptp.plus_plus_int B_25) C_19)))) (forall ((C_18 tptp.nat) (A_44 tptp.nat) (B_24 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_18))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A_44)) (@ _let_1 B_24)) (@ (@ tptp.ord_less_nat A_44) B_24)))) (forall ((C_18 tptp.int) (A_44 tptp.int) (B_24 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_18))) (= (@ (@ tptp.ord_less_int (@ _let_1 A_44)) (@ _let_1 B_24)) (@ (@ tptp.ord_less_int A_44) B_24)))) (forall ((A_43 tptp.nat) (C_17 tptp.nat) (B_23 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_43) C_17)) (@ (@ tptp.plus_plus_nat B_23) C_17)) (@ (@ tptp.ord_less_nat A_43) B_23))) (forall ((A_43 tptp.int) (C_17 tptp.int) (B_23 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_43) C_17)) (@ (@ tptp.plus_plus_int B_23) C_17)) (@ (@ tptp.ord_less_int A_43) B_23))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((Nat_2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat_2)))) (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((Nat_1 tptp.nat)) (not (= (@ tptp.suc Nat_1) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N_5 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N_5)) (@ (@ tptp.ord_less_nat N_5) (@ tptp.suc M)))) _let_33 (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N_5)) (@ (@ tptp.ord_less_nat M) N_5))) (forall ((N_5 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N_5))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N_5 M))))) (forall ((N_5 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N_5))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N_5))))) (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N_5) (@ _let_1 (@ tptp.suc N_5))))) (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N_5) (=> (not (= _let_1 N_5)) (@ (@ tptp.ord_less_nat _let_1) N_5))))) (forall ((K_3 tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K_3) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K_3)))) (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N_5)) (=> (not (@ _let_1 N_5)) (= M N_5))))) (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N_5) (@ (@ tptp.ord_less_nat M) N_5))) (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N_5)) (@ (@ tptp.ord_less_nat M) N_5))) (forall ((A_42 (-> tptp.nat Bool))) (not (@ (@ tptp.ord_less_nat_o A_42) tptp.bot_bot_nat_o))) (forall ((N_5 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N_5) N_5)) (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat) (N_5 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N_5) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N_5 tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N_5) M) (= N_5 tptp.zero_zero_nat))) (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))) (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))) (forall ((K_3 tptp.nat) (M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K_3))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N_5)) (@ (@ tptp.ord_less_nat M) N_5)))) (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (forall ((K_3 tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K_3)) (@ (@ tptp.plus_plus_nat J) K_3)))) (forall ((K_3 tptp.nat) (L tptp.nat) (I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K_3) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K_3)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((M tptp.nat) (N_5 tptp.nat) (K_3 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat K_3) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K_3) N_5)) (@ (@ tptp.ord_less_nat M) N_5)))) (forall ((I tptp.nat) (J tptp.nat) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K_3) (@ (@ tptp.ord_less_nat I) K_3))) (forall ((X_23 tptp.nat) (Y_5 tptp.nat) (Z_2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X_23) Y_5)) Z_2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X_23) Z_2)) (@ (@ tptp.plus_plus_nat Y_5) Z_2)))) (forall ((X_23 tptp.int) (Y_5 tptp.int) (Z_2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X_23) Y_5)) Z_2) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X_23) Z_2)) (@ (@ tptp.plus_plus_int Y_5) Z_2)))) (forall ((N_33 tptp.nat) (M_4 tptp.nat) (Xs_50 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt N_33) (@ (@ tptp.drop_A1346709759le_alt M_4) Xs_50)) (@ (@ tptp.drop_A1346709759le_alt (@ (@ tptp.plus_plus_nat N_33) M_4)) Xs_50))) (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N_5)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N_5)))) _let_32 (forall ((Fa (-> tptp.arrow_475358991le_alt tptp.nat)) (A_40 tptp.arrow_475358991le_alt) (List tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.list_s250295873le_alt Fa))) (= (@ _let_1 (@ (@ tptp.cons_A228743023le_alt A_40) List)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ Fa A_40)) (@ _let_1 List))) (@ tptp.suc tptp.zero_zero_nat))))) (forall ((P_6 (-> tptp.arrow_475358991le_alt Bool)) (X_22 tptp.arrow_475358991le_alt) (Xs_49 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.list_e1252802557le_alt P_6))) (= (@ _let_1 (@ (@ tptp.cons_A228743023le_alt X_22) Xs_49)) (or (@ P_6 X_22) (@ _let_1 Xs_49))))) (forall ((P_5 (-> tptp.nat Bool))) (not (@ (@ tptp.list_ex_nat P_5) tptp.nil_nat))) (forall ((P_5 (-> tptp.arrow_475358991le_alt Bool))) (not (@ (@ tptp.list_e1252802557le_alt P_5) tptp.nil_Ar1286194111le_alt))) (forall ((P_4 (-> tptp.arrow_475358991le_alt Bool)) (Xs_48 tptp.list_A2115238852le_alt) (Ys_9 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.list_e1252802557le_alt P_4))) (= (@ _let_1 (@ (@ tptp.append179082452le_alt Xs_48) Ys_9)) (or (@ _let_1 Xs_48) (@ _let_1 Ys_9))))) (forall ((A_39 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A_39) A_39)) (@ _let_1 A_39)))) (forall ((A_38 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_38) A_38)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_38) tptp.zero_zero_int))) (forall ((B_22 tptp.nat) (A_37 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_37) (=> (@ _let_1 B_22) (@ _let_1 (@ (@ tptp.plus_plus_nat A_37) B_22)))))) (forall ((B_22 tptp.int) (A_37 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A_37) (=> (@ _let_1 B_22) (@ _let_1 (@ (@ tptp.plus_plus_int A_37) B_22)))))) (forall ((B_21 tptp.nat) (A_36 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_36) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B_21) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_36) B_21)) tptp.zero_zero_nat)))) (forall ((B_21 tptp.int) (A_36 tptp.int)) (=> (@ (@ tptp.ord_less_int A_36) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B_21) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_36) B_21)) tptp.zero_zero_int)))) (forall ((P_3 (-> tptp.nat Bool)) (Xs_47 tptp.list_nat)) (let ((_let_1 (@ tptp.list_ex_nat P_3))) (= (@ _let_1 (@ tptp.rev_nat Xs_47)) (@ _let_1 Xs_47)))) (forall ((P_3 (-> tptp.arrow_475358991le_alt Bool)) (Xs_47 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.list_e1252802557le_alt P_3))) (= (@ _let_1 (@ tptp.rev_Ar1106406943le_alt Xs_47)) (@ _let_1 Xs_47)))) (forall ((N_5 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (exists ((M_1 tptp.nat)) (= N_5 (@ tptp.suc M_1))))) _let_31 (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N_5)) (or (= M tptp.zero_zero_nat) (exists ((J_2 tptp.nat)) (and (= M (@ tptp.suc J_2)) (@ (@ tptp.ord_less_nat J_2) N_5)))))) (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N_5)) (or (@ _let_1 M) (@ _let_1 N_5))))) (forall ((X_21 tptp.nat) (Xs_46 tptp.list_nat) (N_32 tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X_21) Xs_46)) (@ tptp.suc N_32)) (@ (@ tptp.nth_nat Xs_46) N_32))) _let_30 (forall ((Xs_45 tptp.list_A2115238852le_alt) (Ys_8 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ tptp.append179082452le_alt Xs_45) Ys_8)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1858781230le_alt Xs_45)) (@ tptp.size_s1858781230le_alt Ys_8)))) (forall ((N_31 tptp.nat) (X_20 tptp.arrow_475358991le_alt) (Xs_44 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc N_31)) (@ (@ tptp.cons_A228743023le_alt X_20) Xs_44)) (@ (@ tptp.drop_A1346709759le_alt N_31) Xs_44))) (forall ((X_19 tptp.arrow_475358991le_alt) (Xs_43 tptp.list_A2115238852le_alt) (I_10 tptp.nat) (Y_4 tptp.arrow_475358991le_alt)) (let ((_let_1 (@ tptp.cons_A228743023le_alt X_19))) (= (@ (@ (@ tptp.list_u62477863le_alt (@ _let_1 Xs_43)) (@ tptp.suc I_10)) Y_4) (@ _let_1 (@ (@ (@ tptp.list_u62477863le_alt Xs_43) I_10) Y_4))))) (forall ((N_30 tptp.nat) (X_18 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.replic1511538809le_alt (@ tptp.suc N_30)) X_18) (@ (@ tptp.cons_A228743023le_alt X_18) (@ (@ tptp.replic1511538809le_alt N_30) X_18)))) (forall ((N_29 tptp.nat) (M_3 tptp.nat) (X_17 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.replic1511538809le_alt (@ (@ tptp.plus_plus_nat N_29) M_3)) X_17) (@ (@ tptp.append179082452le_alt (@ (@ tptp.replic1511538809le_alt N_29) X_17)) (@ (@ tptp.replic1511538809le_alt M_3) X_17)))) (forall ((N_28 tptp.nat) (Xs_42 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc N_28)) Xs_42) (@ (@ tptp.drop_A1346709759le_alt N_28) (@ tptp.tl_Arr465451158le_alt Xs_42)))) (forall ((Xs_41 tptp.list_A2115238852le_alt) (Ys_7 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ (@ tptp.splice1520898450le_alt Xs_41) Ys_7)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1858781230le_alt Xs_41)) (@ tptp.size_s1858781230le_alt Ys_7)))) (forall ((Xs_40 tptp.list_nat) (Ys_6 tptp.list_nat) (N_27 tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.append_nat Xs_40) Ys_6)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat Xs_40)) N_27)) (@ (@ tptp.nth_nat Ys_6) N_27))) (forall ((Xs_40 tptp.list_A2115238852le_alt) (Ys_6 tptp.list_A2115238852le_alt) (N_27 tptp.nat)) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.append179082452le_alt Xs_40) Ys_6)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1858781230le_alt Xs_40)) N_27)) (@ (@ tptp.nth_Ar125878976le_alt Ys_6) N_27))) (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N_5) (exists ((K_5 tptp.nat)) (= N_5 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_5)))))) (forall ((Xs_39 tptp.list_A2115238852le_alt) (N_26 tptp.nat)) (= (= (@ tptp.size_s1858781230le_alt Xs_39) (@ tptp.suc N_26)) (exists ((Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (and (= Xs_39 (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5)) (= (@ tptp.size_s1858781230le_alt Ys_5) N_26))))) (forall ((N_25 tptp.nat) (Xs_38 tptp.list_A2115238852le_alt)) (= (= (@ tptp.suc N_25) (@ tptp.size_s1858781230le_alt Xs_38)) (exists ((Y_3 tptp.arrow_475358991le_alt) (Ys_5 tptp.list_A2115238852le_alt)) (and (= Xs_38 (@ (@ tptp.cons_A228743023le_alt Y_3) Ys_5)) (= (@ tptp.size_s1858781230le_alt Ys_5) N_25))))) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K_5 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_5) (= (@ (@ tptp.plus_plus_nat I) K_5) J))))) (forall ((C_16 tptp.int) (A_35 (-> tptp.int Bool)) (B_20 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_16))) (=> (@ (@ tptp.ord_less_int_o A_35) B_20) (=> (@ _let_1 A_35) (@ _let_1 B_20))))) (forall ((C_16 tptp.nat) (A_35 (-> tptp.nat Bool)) (B_20 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_16))) (=> (@ (@ tptp.ord_less_nat_o A_35) B_20) (=> (@ _let_1 A_35) (@ _let_1 B_20))))) (forall ((N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (exists ((M_1 tptp.nat)) (= N_5 (@ tptp.suc M_1))))) (forall ((N_24 tptp.nat) (N_23 tptp.nat) (F_1 (-> tptp.nat tptp.nat))) (=> (forall ((N_7 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F_1 N_7)) (@ F_1 (@ tptp.suc N_7)))) (=> (@ (@ tptp.ord_less_nat N_24) N_23) (@ (@ tptp.ord_less_nat (@ F_1 N_24)) (@ F_1 N_23))))) (forall ((N_22 tptp.nat) (M_2 tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((N_7 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N_7)) (@ F (@ tptp.suc N_7)))) (= (@ (@ tptp.ord_less_nat (@ F N_22)) (@ F M_2)) (@ (@ tptp.ord_less_nat N_22) M_2)))) (forall ((A_34 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_34) A_34)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_34) tptp.zero_zero_int))) (forall ((B_19 tptp.int) (C_15 tptp.int) (A_33 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B_19))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_33) (=> (@ _let_1 C_15) (@ _let_1 (@ (@ tptp.plus_plus_int A_33) C_15)))))) (forall ((B_19 tptp.nat) (C_15 tptp.nat) (A_33 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B_19))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_33) (=> (@ _let_1 C_15) (@ _let_1 (@ (@ tptp.plus_plus_nat A_33) C_15)))))) (forall ((A_32 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A_32) A_32) tptp.zero_zero_int) (= A_32 tptp.zero_zero_int))) _let_29 (forall ((I tptp.nat) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K_3) (not (forall ((J_2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_2) (not (= K_3 (@ tptp.suc J_2)))))))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat tptp.nat)) (not (= Y (@ tptp.suc Nat))))))) (forall ((N_5 tptp.nat)) (=> (not (= N_5 tptp.zero_zero_nat)) (exists ((M_1 tptp.nat)) (= N_5 (@ tptp.suc M_1))))) (forall ((N_5 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N_7 tptp.nat)) (=> (@ P N_7) (@ P (@ tptp.suc N_7)))) (@ P N_5)))) (forall ((P (-> tptp.nat Bool)) (K_3 tptp.nat)) (=> (@ P K_3) (=> (forall ((N_7 tptp.nat)) (=> (@ P (@ tptp.suc N_7)) (@ P N_7))) (@ P tptp.zero_zero_nat)))) (forall ((N_21 tptp.nat) (Xs_37 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat N_21) (@ tptp.size_s1858781230le_alt Xs_37)) (= (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt N_21) Xs_37)) (@ (@ tptp.cons_A228743023le_alt (@ tptp.hd_Arr1965683346le_alt (@ (@ tptp.drop_A1346709759le_alt N_21) Xs_37))) tptp.nil_Ar1286194111le_alt)) (@ (@ tptp.take_A614047655le_alt (@ tptp.suc N_21)) Xs_37)))) (forall ((N_20 tptp.nat) (Xs_36 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.take_A614047655le_alt N_20) (@ tptp.tl_Arr465451158le_alt Xs_36)) (@ tptp.tl_Arr465451158le_alt (@ (@ tptp.take_A614047655le_alt (@ tptp.suc N_20)) Xs_36)))) _let_28 (forall ((I_9 tptp.nat) (Xs_35 tptp.list_A2115238852le_alt)) (=> (@ tptp.distin236324274le_alt Xs_35) (@ tptp.distin236324274le_alt (@ (@ tptp.take_A614047655le_alt I_9) Xs_35)))) (forall ((P_2 (-> tptp.arrow_475358991le_alt Bool)) (Xs_34 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ (@ tptp.takeWh1696291512le_alt P_2) Xs_34))) (= _let_1 (@ (@ tptp.take_A614047655le_alt (@ tptp.size_s1858781230le_alt _let_1)) Xs_34)))) _let_27 _let_26 (forall ((N_16 tptp.nat) (Xs_31 tptp.list_A2115238852le_alt)) (= (= (@ (@ tptp.take_A614047655le_alt N_16) Xs_31) tptp.nil_Ar1286194111le_alt) (or (= N_16 tptp.zero_zero_nat) (= Xs_31 tptp.nil_Ar1286194111le_alt)))) (forall ((Xs_30 tptp.list_A2115238852le_alt)) (= (@ (@ tptp.take_A614047655le_alt tptp.zero_zero_nat) Xs_30) tptp.nil_Ar1286194111le_alt)) _let_25 _let_24 (forall ((N_15 tptp.nat) (Xs_27 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.take_A614047655le_alt N_15))) (=> (@ (@ tptp.ord_less_nat N_15) (@ tptp.size_s1858781230le_alt Xs_27)) (= (@ _let_1 (@ tptp.butlas274947851le_alt Xs_27)) (@ _let_1 Xs_27))))) (forall ((N_14 tptp.nat) (Xs_26 tptp.list_A2115238852le_alt)) (=> (not (= Xs_26 tptp.nil_Ar1286194111le_alt)) (= (@ (@ tptp.take_A614047655le_alt (@ tptp.suc N_14)) Xs_26) (@ (@ tptp.cons_A228743023le_alt (@ tptp.hd_Arr1965683346le_alt Xs_26)) (@ (@ tptp.take_A614047655le_alt N_14) (@ tptp.tl_Arr465451158le_alt Xs_26)))))) (forall ((I_7 tptp.nat) (Xs_25 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_7) (@ tptp.size_s1858781230le_alt Xs_25)) (= (@ (@ tptp.take_A614047655le_alt (@ tptp.suc I_7)) Xs_25) (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt I_7) Xs_25)) (@ (@ tptp.cons_A228743023le_alt (@ (@ tptp.nth_Ar125878976le_alt Xs_25) I_7)) tptp.nil_Ar1286194111le_alt))))) (forall ((I_6 tptp.nat) (Xs_24 tptp.list_A2115238852le_alt)) (=> (@ (@ tptp.ord_less_nat I_6) (@ tptp.size_s1858781230le_alt Xs_24)) (= Xs_24 (@ (@ tptp.append179082452le_alt (@ (@ tptp.take_A614047655le_alt I_6) Xs_24)) (@ (@ tptp.cons_A228743023le_alt (@ (@ tptp.nth_Ar125878976le_alt Xs_24) I_6)) (@ (@ tptp.drop_A1346709759le_alt (@ tptp.suc I_6)) Xs_24)))))) _let_23 (forall ((P_1 (-> tptp.arrow_475358991le_alt Bool)) (Xs_22 tptp.list_A2115238852le_alt) (N_13 tptp.nat)) (=> (forall ((I_4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_4))) (=> (@ _let_1 N_13) (=> (@ _let_1 (@ tptp.size_s1858781230le_alt Xs_22)) (@ P_1 (@ (@ tptp.nth_Ar125878976le_alt Xs_22) I_4)))))) (=> (=> (@ (@ tptp.ord_less_nat N_13) (@ tptp.size_s1858781230le_alt Xs_22)) (not (@ P_1 (@ (@ tptp.nth_Ar125878976le_alt Xs_22) N_13)))) (= (@ (@ tptp.takeWh1696291512le_alt P_1) Xs_22) (@ (@ tptp.take_A614047655le_alt N_13) Xs_22))))) (forall ((Z_1 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z_1))))) (forall ((Y tptp.nat) (X tptp.nat) (Z_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z_1) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z_1))))) (forall ((A_30 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_30) A_30)) (forall ((A_30 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_30) A_30)) (forall ((A_29 tptp.int)) (= (@ (@ tptp.plus_plus_int A_29) tptp.zero_zero_int) A_29)) (forall ((A_29 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_29) tptp.zero_zero_nat) A_29)) (forall ((A_28 tptp.int) (B_18 tptp.int) (C_14 tptp.int) (D_5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_28))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_18)) (@ (@ tptp.plus_plus_int C_14) D_5)) (@ (@ tptp.plus_plus_int (@ _let_1 C_14)) (@ (@ tptp.plus_plus_int B_18) D_5))))) (forall ((A_28 tptp.nat) (B_18 tptp.nat) (C_14 tptp.nat) (D_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_28))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_18)) (@ (@ tptp.plus_plus_nat C_14) D_5)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_14)) (@ (@ tptp.plus_plus_nat B_18) D_5))))) (forall ((A_27 tptp.int) (B_17 tptp.int) (C_13 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_27))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_17)) C_13) (@ (@ tptp.plus_plus_int (@ _let_1 C_13)) B_17)))) (forall ((A_27 tptp.nat) (B_17 tptp.nat) (C_13 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_27))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_17)) C_13) (@ (@ tptp.plus_plus_nat (@ _let_1 C_13)) B_17)))) (forall ((A_26 tptp.int) (B_16 tptp.int) (C_12 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_26))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_16)) C_12) (@ _let_1 (@ (@ tptp.plus_plus_int B_16) C_12))))) (forall ((A_26 tptp.nat) (B_16 tptp.nat) (C_12 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_26))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_16)) C_12) (@ _let_1 (@ (@ tptp.plus_plus_nat B_16) C_12))))) (forall ((A_25 tptp.int) (C_11 tptp.int) (D_4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_25))) (= (@ _let_1 (@ (@ tptp.plus_plus_int C_11) D_4)) (@ (@ tptp.plus_plus_int (@ _let_1 C_11)) D_4)))) (forall ((A_25 tptp.nat) (C_11 tptp.nat) (D_4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_25))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat C_11) D_4)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_11)) D_4)))) (forall ((A_24 tptp.int) (C_10 tptp.int) (D_3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_24))) (let ((_let_2 (@ tptp.plus_plus_int C_10))) (= (@ _let_1 (@ _let_2 D_3)) (@ _let_2 (@ _let_1 D_3)))))) (forall ((A_24 tptp.nat) (C_10 tptp.nat) (D_3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_24))) (let ((_let_2 (@ tptp.plus_plus_nat C_10))) (= (@ _let_1 (@ _let_2 D_3)) (@ _let_2 (@ _let_1 D_3)))))) (forall ((A_23 tptp.int) (C_9 tptp.int)) (= (@ (@ tptp.plus_plus_int A_23) C_9) (@ (@ tptp.plus_plus_int C_9) A_23))) (forall ((A_23 tptp.nat) (C_9 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_23) C_9) (@ (@ tptp.plus_plus_nat C_9) A_23))) (forall ((B_15 tptp.int) (A_22 tptp.int)) (= (= B_15 (@ (@ tptp.plus_plus_int B_15) A_22)) (= A_22 tptp.zero_zero_int))) (forall ((B_15 tptp.nat) (A_22 tptp.nat)) (= (= B_15 (@ (@ tptp.plus_plus_nat B_15) A_22)) (= A_22 tptp.zero_zero_nat))) (forall ((N_12 tptp.nat) (Xs_21 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt Xs_21))) (=> (@ (@ tptp.ord_less_nat N_12) _let_1) (= (@ (@ tptp.nth_Ar125878976le_alt (@ tptp.rev_Ar1106406943le_alt Xs_21)) N_12) (@ (@ tptp.nth_Ar125878976le_alt Xs_21) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N_12))))))) (forall ((I_3 tptp.nat) (K_4 tptp.nat) (X_15 tptp.arrow_475358991le_alt)) (= (@ (@ tptp.drop_A1346709759le_alt I_3) (@ (@ tptp.replic1511538809le_alt K_4) X_15)) (@ (@ tptp.replic1511538809le_alt (@ (@ tptp.minus_minus_nat K_4) I_3)) X_15))) (forall ((M tptp.nat) (K_3 tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K_3)) (@ (@ tptp.plus_plus_nat N_5) K_3)) (@ (@ tptp.minus_minus_nat M) N_5))) (forall ((K_3 tptp.nat) (M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K_3))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N_5)) (@ (@ tptp.minus_minus_nat M) N_5)))) (forall ((I tptp.nat) (J tptp.nat) (K_3 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K_3) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K_3))))) _let_22 (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N_5)) N_5) M)) (forall ((A_21 tptp.int) (B_14 tptp.int) (C_8 tptp.int) (D_2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_21) B_14) (@ (@ tptp.minus_minus_int C_8) D_2)) (= (@ (@ tptp.ord_less_int A_21) B_14) (@ (@ tptp.ord_less_int C_8) D_2)))) (forall ((A_20 tptp.int) (B_13 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_20) B_13)) B_13) A_20)) (forall ((A_19 tptp.int) (B_12 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_19) B_12)) B_12) A_19)) (forall ((N_5 tptp.nat) (J tptp.nat) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K_3) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N_5)) K_3))) (forall ((L tptp.nat) (M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N_5) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N_5)) (@ _let_1 M))))))) (forall ((A_18 tptp.int) (B_11 tptp.int)) (= (@ (@ tptp.ord_less_int A_18) B_11) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A_18) B_11)) tptp.zero_zero_int))) (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N_5) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N_5)) M))))) (forall ((N_5 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N_5) M)) (@ (@ tptp.ord_less_nat M) N_5))) (forall ((M tptp.nat) (N_5 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N_5)) (@ tptp.suc M))) (forall ((N_5 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N_5) (@ (@ tptp.plus_plus_nat N_5) M)) tptp.zero_zero_nat)) (forall ((I tptp.nat) (J tptp.nat) (K_3 tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K_3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K_3)) J))) _let_21 (forall ((I tptp.nat) (J tptp.nat) (K_3 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K_3) (@ (@ tptp.minus_minus_nat (@ _let_1 K_3)) J)))) (forall ((X_14 tptp.int) (Y_2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X_14) Y_2)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X_14) Z)) (@ (@ tptp.minus_minus_int Y_2) Z)))) (forall ((A_17 tptp.int) (B_10 tptp.int) (C_7 tptp.int) (D_1 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_17) B_10) (@ (@ tptp.minus_minus_int C_7) D_1)) (= (= A_17 B_10) (= C_7 D_1)))) (forall ((A_16 tptp.int)) (= (@ (@ tptp.minus_minus_int A_16) tptp.zero_zero_int) A_16)) (forall ((A_15 tptp.int)) (= (@ (@ tptp.minus_minus_int A_15) A_15) tptp.zero_zero_int)) (forall ((A_14 tptp.int) (B_9 tptp.int)) (= (= A_14 B_9) (= (@ (@ tptp.minus_minus_int A_14) B_9) tptp.zero_zero_int))) (forall ((A_13 tptp.int) (B_8 tptp.int)) (= (= (@ (@ tptp.minus_minus_int A_13) B_8) tptp.zero_zero_int) (= A_13 B_8))) (forall ((M tptp.nat) (N_5 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N_5) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N_5) M) tptp.zero_zero_nat) (= M N_5)))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((N_5 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N_5) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N_5 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N_5)) (@ (@ tptp.minus_minus_nat M) N_5))) (forall ((M tptp.nat) (N_5 tptp.nat) (K_3 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N_5)) (@ tptp.suc K_3)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N_5)) K_3))) (forall ((N_5 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N_5) M)) M) (@ (@ tptp.ord_max_nat N_5) M))) (forall ((I tptp.nat) (N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N_5) (@ tptp.suc I))) N_5))) (forall ((N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N_5) (@ tptp.suc tptp.zero_zero_nat))) N_5))) (forall ((P (-> tptp.nat Bool)) (A_12 tptp.nat) (B_7 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A_12) B_7)) (and (=> (@ (@ tptp.ord_less_nat A_12) B_7) (@ P tptp.zero_zero_nat)) (forall ((D tptp.nat)) (=> (= A_12 (@ (@ tptp.plus_plus_nat B_7) D)) (@ P D)))))) (forall ((P (-> tptp.nat Bool)) (A_12 tptp.nat) (B_7 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A_12) B_7)) (not (or (and (@ (@ tptp.ord_less_nat A_12) B_7) (not (@ P tptp.zero_zero_nat))) (exists ((D tptp.nat)) (and (= A_12 (@ (@ tptp.plus_plus_nat B_7) D)) (not (@ P D)))))))) _let_20 (forall ((N_10 tptp.nat) (Xs_19 tptp.list_A2115238852le_alt) (Ys_2 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.drop_A1346709759le_alt N_10))) (= (@ _let_1 (@ (@ tptp.append179082452le_alt Xs_19) Ys_2)) (@ (@ tptp.append179082452le_alt (@ _let_1 Xs_19)) (@ (@ tptp.drop_A1346709759le_alt (@ (@ tptp.minus_minus_nat N_10) (@ tptp.size_s1858781230le_alt Xs_19))) Ys_2))))) (forall ((Ys_1 tptp.list_A2115238852le_alt) (N_9 tptp.nat) (Xs_18 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt Xs_18))) (let ((_let_2 (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.append179082452le_alt Xs_18) Ys_1)) N_9))) (let ((_let_3 (@ (@ tptp.ord_less_nat N_9) _let_1))) (and (=> _let_3 (= _let_2 (@ (@ tptp.nth_Ar125878976le_alt Xs_18) N_9))) (=> (not _let_3) (= _let_2 (@ (@ tptp.nth_Ar125878976le_alt Ys_1) (@ (@ tptp.minus_minus_nat N_9) _let_1))))))))) (forall ((Ys tptp.list_A2115238852le_alt) (X_13 tptp.arrow_475358991le_alt) (N_8 tptp.nat) (Xs_17 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt Xs_17))) (let ((_let_2 (@ tptp.append179082452le_alt Xs_17))) (let ((_let_3 (@ (@ (@ tptp.list_u62477863le_alt (@ _let_2 Ys)) N_8) X_13))) (let ((_let_4 (@ (@ tptp.ord_less_nat N_8) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.append179082452le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_17) N_8) X_13)) Ys))) (=> (not _let_4) (= _let_3 (@ _let_2 (@ (@ (@ tptp.list_u62477863le_alt Ys) (@ (@ tptp.minus_minus_nat N_8) _let_1)) X_13)))))))))) _let_19 (forall ((I_1 tptp.nat) (Xs_15 tptp.list_A2115238852le_alt)) (= (@ tptp.rev_Ar1106406943le_alt (@ (@ tptp.take_A614047655le_alt I_1) Xs_15)) (@ (@ tptp.drop_A1346709759le_alt (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_15)) I_1)) (@ tptp.rev_Ar1106406943le_alt Xs_15)))) (forall ((I tptp.nat) (P (-> tptp.nat Bool)) (K_3 tptp.nat)) (=> (@ P K_3) (=> (forall ((N_7 tptp.nat)) (=> (@ P (@ tptp.suc N_7)) (@ P N_7))) (@ P (@ (@ tptp.minus_minus_nat K_3) I))))) (forall ((X_12 tptp.arrow_475358991le_alt) (K_2 tptp.nat) (Xs_14 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.last_A1217315288le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_14) K_2) X_12)))) (let ((_let_2 (= K_2 (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_14)) tptp.one_one_nat)))) (=> (not (= Xs_14 tptp.nil_Ar1286194111le_alt)) (and (=> _let_2 (= _let_1 X_12)) (=> (not _let_2) (= _let_1 (@ tptp.last_A1217315288le_alt Xs_14)))))))) (forall ((A_11 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o tptp.bot_bot_nat_o) A_11) tptp.bot_bot_nat_o)) (forall ((A_10 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_10) tptp.bot_bot_nat_o) A_10)) (forall ((A_9 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_9) A_9) tptp.bot_bot_nat_o)) _let_18 (forall ((M tptp.nat) (N_5 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N_5)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N_5)))) (forall ((N_5 tptp.nat)) (= (@ tptp.suc N_5) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) N_5))) _let_17 _let_16 (forall ((X_10 tptp.nat)) (= (= tptp.one_one_nat X_10) (= X_10 tptp.one_one_nat))) _let_15 (forall ((A_8 tptp.nat)) (@ (@ tptp.ord_less_nat A_8) (@ (@ tptp.plus_plus_nat A_8) tptp.one_one_nat))) (forall ((A_8 tptp.int)) (@ (@ tptp.ord_less_int A_8) (@ (@ tptp.plus_plus_int A_8) tptp.one_one_int))) _let_14 _let_13 _let_12 (not (= tptp.zero_zero_nat tptp.one_one_nat)) _let_11 (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) _let_9 _let_8 (forall ((Xs_10 tptp.list_A2115238852le_alt)) (= (@ tptp.size_s1858781230le_alt (@ tptp.tl_Arr465451158le_alt Xs_10)) (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_10)) tptp.one_one_nat))) (forall ((N_6 tptp.nat) (Xs_9 tptp.list_A2115238852le_alt)) (= (@ tptp.tl_Arr465451158le_alt (@ (@ tptp.take_A614047655le_alt N_6) Xs_9)) (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat N_6) tptp.one_one_nat)) (@ tptp.tl_Arr465451158le_alt Xs_9)))) (forall ((N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (= N_5 (@ tptp.suc (@ (@ tptp.minus_minus_nat N_5) tptp.one_one_nat))))) (forall ((N_5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N_5) tptp.one_one_nat)) N_5))) (forall ((N_5 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N_5))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 N_5)) (=> (not _let_2) (= _let_1 (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N_5)))))))) (forall ((X_8 tptp.arrow_475358991le_alt) (Xs_8 tptp.list_A2115238852le_alt) (N_4 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_8) Xs_8)) N_4))) (let ((_let_2 (= N_4 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X_8)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_Ar125878976le_alt Xs_8) (@ (@ tptp.minus_minus_nat N_4) tptp.one_one_nat)))))))) _let_7 _let_6 (forall ((X_6 tptp.arrow_475358991le_alt) (K_1 tptp.nat) (Xs_5 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.butlas274947851le_alt Xs_5))) (let ((_let_2 (@ tptp.butlas274947851le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_5) K_1) X_6)))) (let ((_let_3 (= K_1 (@ (@ tptp.minus_minus_nat (@ tptp.size_s1858781230le_alt Xs_5)) tptp.one_one_nat)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ (@ tptp.list_u62477863le_alt _let_1) K_1) X_6)))))))) (forall ((X_5 tptp.arrow_475358991le_alt) (N_2 tptp.nat)) (=> (not (= N_2 tptp.zero_zero_nat)) (= (@ tptp.tl_Arr465451158le_alt (@ (@ tptp.replic1511538809le_alt N_2) X_5)) (@ (@ tptp.replic1511538809le_alt (@ (@ tptp.minus_minus_nat N_2) tptp.one_one_nat)) X_5)))) (forall ((X_4 tptp.arrow_475358991le_alt) (Xs_4 tptp.list_A2115238852le_alt) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_1) (= (@ (@ tptp.nth_Ar125878976le_alt (@ (@ tptp.cons_A228743023le_alt X_4) Xs_4)) N_1) (@ (@ tptp.nth_Ar125878976le_alt Xs_4) (@ (@ tptp.minus_minus_nat N_1) tptp.one_one_nat))))) _let_5 (forall ((Y_1 tptp.arrow_475358991le_alt) (K tptp.nat) (Xs_2 tptp.list_A2115238852le_alt)) (let ((_let_1 (@ tptp.size_s1858781230le_alt Xs_2))) (=> (@ (@ tptp.ord_less_nat K) _let_1) (= (@ tptp.rev_Ar1106406943le_alt (@ (@ (@ tptp.list_u62477863le_alt Xs_2) K) Y_1)) (@ (@ (@ tptp.list_u62477863le_alt (@ tptp.rev_Ar1106406943le_alt Xs_2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat _let_1) K)) tptp.one_one_nat)) Y_1))))) _let_4 (forall ((X_2 tptp.arrow_475358991le_alt) (Xs tptp.list_A2115238852le_alt) (V_2 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_2))) (let ((_let_2 (@ tptp.cons_A228743023le_alt X_2))) (let ((_let_3 (@ (@ tptp.take_A614047655le_alt _let_1) (@ _let_2 Xs)))) (let ((_let_4 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 tptp.nil_Ar1286194111le_alt)) (=> (not _let_4) (= _let_3 (@ _let_2 (@ (@ tptp.take_A614047655le_alt (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat)) Xs)))))))))) (forall ((A_7 tptp.int)) (=> (@ (@ tptp.member_int A_7) tptp.ring_1_Ints_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A_7)) A_7)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_7) tptp.zero_zero_int)))) (forall ((C_6 tptp.nat) (A_6 (-> tptp.nat Bool)) (B_6 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_6))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_6) B_6)) (not (=> (@ _let_1 A_6) (@ _let_1 B_6)))))) (forall ((B_5 (-> tptp.nat Bool)) (C_5 tptp.nat) (A_5 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_5))) (=> (@ _let_1 A_5) (=> (not (@ _let_1 B_5)) (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_5) B_5)))))) (forall ((B_4 tptp.int) (A_4 tptp.int)) (=> (@ (@ tptp.member_int A_4) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B_4) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int A_4) B_4)) tptp.ring_1_Ints_int)))) (forall ((V_1 tptp.int) (W_1 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.minus_minus_int V_1) W_1)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int V_1)) (@ tptp.number_number_of_int W_1)))) (forall ((V tptp.int) (W tptp.int) (C_4 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int W)) C_4)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V) W))) C_4))) (forall ((C_3 tptp.nat) (A_3 (-> tptp.nat Bool)) (B_3 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_3))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_3) B_3)) (not (@ _let_1 B_3))))) (forall ((C_2 tptp.nat) (A_2 (-> tptp.nat Bool)) (B_2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_2) B_2)) (@ _let_1 A_2)))) (forall ((C_1 tptp.nat) (A_1 (-> tptp.nat Bool)) (B_1 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_1))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_1) B_1)) (and (@ _let_1 A_1) (not (@ _let_1 B_1)))))) (forall ((A (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A) B) (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X_1))) (and (@ _let_1 A) (not (@ _let_1 B)))))))) (forall ((X tptp.list_A2115238852le_alt) (Y tptp.list_A2115238852le_alt)) (or (not (@ (@ tptp.fequal781288069le_alt X) Y)) (= X Y))) (forall ((X tptp.list_A2115238852le_alt) (Y tptp.list_A2115238852le_alt)) (or (not (= X Y)) (@ (@ tptp.fequal781288069le_alt X) Y))) _let_3 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 159.65/160.02 )
% 159.65/160.02 % SZS output end Proof for SCT169^2
% 159.65/160.02 % cvc5---1.0.5 exiting
% 159.65/160.02 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------