TSTP Solution File: ITP104^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP104^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 03:18:16 EDT 2023
% Result : Theorem 0.69s 0.88s
% Output : Proof 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP104^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.33 % Computer : n032.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sun Aug 27 11:37:45 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.19/0.46 %----Proving TH0
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : ITP104^1 : TPTP v8.1.2. Released v7.5.0.
% 0.19/0.46 % Domain : Interactive Theorem Proving
% 0.19/0.46 % Problem : Sledgehammer ListSlice problem prob_199__5618146_1
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Des21]
% 0.19/0.46 % Names : ListSlice/prob_199__5618146_1 [Des21]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.19/0.46 % Syntax : Number of formulae : 462 ( 122 unt; 112 typ; 0 def)
% 0.19/0.46 % Number of atoms : 1046 ( 371 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 12 ( 2 avg)
% 0.19/0.46 % Number of connectives : 3415 ( 124 ~; 18 |; 67 &;2673 @)
% 0.19/0.46 % ( 0 <=>; 533 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 18 ( 7 avg)
% 0.19/0.46 % Number of types : 18 ( 17 usr)
% 0.19/0.46 % Number of type conns : 235 ( 235 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 96 ( 95 usr; 4 con; 0-3 aty)
% 0.19/0.46 % Number of variables : 1096 ( 94 ^; 941 !; 61 ?;1096 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:28.219
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % Could-be-implicit typings (17)
% 0.19/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.19/0.46 list_l2071841302list_a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
% 0.19/0.46 list_list_list_nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.19/0.46 list_list_list_a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.19/0.46 set_list_list_a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 0.19/0.46 list_set_list_a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.19/0.46 list_list_nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.19/0.46 set_list_nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.19/0.46 list_set_nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 list_list_a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 set_list_a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 0.19/0.46 list_set_a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 list_nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.19/0.46 set_nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.19/0.46 list_a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.19/0.46 set_a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nat__Onat,type,
% 0.19/0.46 nat: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_tf__a,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 % Explicit typings (95)
% 0.19/0.46 thf(sy_c_List2_Of__image_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 f_image_list_list_a: list_list_list_a > set_nat > set_list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Of__image_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 f_image_list_nat: list_list_nat > set_nat > set_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Of__image_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 f_image_list_a: list_list_a > set_nat > set_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Of__image_001t__Nat__Onat,type,
% 0.19/0.46 f_image_nat: list_nat > set_nat > set_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Of__image_001tf__a,type,
% 0.19/0.46 f_image_a: list_a > set_nat > set_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Olist__asc_001t__Nat__Onat,type,
% 0.19/0.46 list_asc_nat: list_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Olist__asc_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 list_asc_set_list_a: list_set_list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Olist__asc_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.19/0.46 list_asc_set_nat: list_set_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Olist__asc_001t__Set__Oset_Itf__a_J,type,
% 0.19/0.46 list_asc_set_a: list_set_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Olist__desc_001t__Nat__Onat,type,
% 0.19/0.46 list_desc_nat: list_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Olist__desc_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 list_desc_set_list_a: list_set_list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Olist__desc_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.19/0.46 list_desc_set_nat: list_set_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Olist__desc_001t__Set__Oset_Itf__a_J,type,
% 0.19/0.46 list_desc_set_a: list_set_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Olist__strict__asc_001t__Nat__Onat,type,
% 0.19/0.46 list_strict_asc_nat: list_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List2_Olist__strict__desc_001t__Nat__Onat,type,
% 0.19/0.46 list_strict_desc_nat: list_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 listSl769338732list_a: list_list_list_a > nat > list_l2071841302list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 listSl2099749758st_nat: list_list_nat > nat > list_list_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 listSl703198822list_a: list_list_a > nat > list_list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001t__Nat__Onat,type,
% 0.19/0.46 listSl882585454e2_nat: list_nat > nat > list_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice2_001tf__a,type,
% 0.19/0.46 listSl1174287072ice2_a: list_a > nat > list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 listSl2102238196list_a: list_list_list_a > nat > list_l2071841302list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 listSl729562870st_nat: list_list_nat > nat > list_list_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 listSl162220270list_a: list_list_a > nat > list_list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__Nat__Onat,type,
% 0.19/0.46 listSl1630398182ce_nat: list_nat > nat > list_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001tf__a,type,
% 0.19/0.46 listSl97544552lice_a: list_a > nat > list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 listSl902632890list_a: list_list_list_a > nat > nat > list_l2071841302list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 listSl1506485424st_nat: list_list_nat > nat > nat > list_list_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__Nat__Onat,type,
% 0.19/0.46 listSl1794011552ux_nat: list_nat > nat > nat > list_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001tf__a,type,
% 0.19/0.46 listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Obutlast_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 butlast_list_list_a: list_list_list_a > list_list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Obutlast_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 butlast_list_nat: list_list_nat > list_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 butlast_list_a: list_list_a > list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 0.19/0.46 butlast_nat: list_nat > list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Obutlast_001tf__a,type,
% 0.19/0.46 butlast_a: list_a > list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Odistinct_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 distinct_list_list_a: list_list_list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Odistinct_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 distinct_list_nat: list_list_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Odistinct_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 distinct_list_a: list_list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 0.19/0.46 distinct_nat: list_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Odistinct_001tf__a,type,
% 0.19/0.46 distinct_a: list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 set_list_list_a2: list_list_list_a > set_list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 set_list_nat2: list_list_nat > set_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist_Oset_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 set_list_a2: list_list_a > set_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 0.19/0.46 set_nat2: list_nat > set_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist_Oset_001tf__a,type,
% 0.19/0.46 set_a2: list_a > set_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist__ex_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 list_ex_list_list_a: ( list_list_a > $o ) > list_list_list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist__ex_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 list_ex_list_nat: ( list_nat > $o ) > list_list_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist__ex_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 list_ex_list_a: ( list_a > $o ) > list_list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist__ex_001t__Nat__Onat,type,
% 0.19/0.46 list_ex_nat: ( nat > $o ) > list_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist__ex_001tf__a,type,
% 0.19/0.46 list_ex_a: ( a > $o ) > list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist__update_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 list_u1330012152list_a: list_list_list_a > nat > list_list_a > list_list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist__update_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 list_update_list_nat: list_list_nat > nat > list_nat > list_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist__update_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 list_update_list_a: list_list_a > nat > list_a > list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 0.19/0.46 list_update_nat: list_nat > nat > nat > list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Olist__update_001tf__a,type,
% 0.19/0.46 list_update_a: list_a > nat > a > list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Onth_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.19/0.46 nth_list_list_list_a: list_l2071841302list_a > nat > list_list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Onth_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.19/0.46 nth_list_list_nat: list_list_list_nat > nat > list_list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Onth_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 nth_list_list_a: list_list_list_a > nat > list_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Onth_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 nth_list_nat: list_list_nat > nat > list_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Onth_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 nth_list_a: list_list_a > nat > list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 0.19/0.46 nth_nat: list_nat > nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Onth_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 nth_set_list_a: list_set_list_a > nat > set_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.19/0.46 nth_set_nat: list_set_nat > nat > set_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Onth_001t__Set__Oset_Itf__a_J,type,
% 0.19/0.46 nth_set_a: list_set_a > nat > set_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_List_Onth_001tf__a,type,
% 0.19/0.46 nth_a: list_a > nat > a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.19/0.46 size_s1764310658list_a: list_l2071841302list_a > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_It__Nat__Onat_J_J_J,type,
% 0.19/0.46 size_s1321307156st_nat: list_list_list_nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.19/0.46 size_s575106428list_a: list_list_list_a > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.19/0.46 size_s1898481668st_nat: list_list_nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 size_s1427607542list_a: list_list_a > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 size_size_list_nat: list_nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 0.19/0.46 size_s1635937238list_a: list_set_list_a > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.19/0.46 size_s577819178et_nat: list_set_nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 0.19/0.46 size_size_list_set_a: list_set_a > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 size_size_list_a: list_a > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.19/0.46 ord_less_nat: nat > nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.19/0.46 ord_less_eq_nat: nat > nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.19/0.46 ord_le1756736906list_a: set_list_list_a > set_list_list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.19/0.46 ord_le1747345782st_nat: set_list_nat > set_list_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 ord_le1301786372list_a: set_list_a > set_list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.19/0.46 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.19/0.46 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.19/0.46 top_top_set_nat: set_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 0.19/0.46 divide_divide_nat: nat > nat > nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_OCollect_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 collect_list_a: ( list_a > $o ) > set_list_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.19/0.46 collect_nat: ( nat > $o ) > set_nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.19/0.46 collect_a: ( a > $o ) > set_a ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.19/0.46 member_list_list_a: list_list_a > set_list_list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.46 member_list_nat: list_nat > set_list_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__List__Olist_Itf__a_J,type,
% 0.19/0.46 member_list_a: list_a > set_list_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__Nat__Onat,type,
% 0.19/0.46 member_nat: nat > set_nat > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001tf__a,type,
% 0.19/0.46 member_a: a > set_a > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_k,type,
% 0.19/0.46 k: nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_m,type,
% 0.19/0.46 m: nat ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_xs,type,
% 0.19/0.46 xs: list_a ).
% 0.19/0.46
% 0.19/0.46 % Relevant facts (348)
% 0.19/0.46 thf(fact_0_nth__equalityI,axiom,
% 0.19/0.46 ! [Xs: list_list_nat,Ys: list_list_nat] :
% 0.19/0.46 ( ( ( size_s1898481668st_nat @ Xs )
% 0.19/0.46 = ( size_s1898481668st_nat @ Ys ) )
% 0.19/0.46 => ( ! [I: nat] :
% 0.19/0.46 ( ( ord_less_nat @ I @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.46 => ( ( nth_list_nat @ Xs @ I )
% 0.19/0.46 = ( nth_list_nat @ Ys @ I ) ) )
% 0.19/0.46 => ( Xs = Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nth_equalityI
% 0.19/0.46 thf(fact_1_nth__equalityI,axiom,
% 0.19/0.46 ! [Xs: list_list_list_a,Ys: list_list_list_a] :
% 0.19/0.46 ( ( ( size_s575106428list_a @ Xs )
% 0.19/0.46 = ( size_s575106428list_a @ Ys ) )
% 0.19/0.46 => ( ! [I: nat] :
% 0.19/0.46 ( ( ord_less_nat @ I @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.46 => ( ( nth_list_list_a @ Xs @ I )
% 0.19/0.46 = ( nth_list_list_a @ Ys @ I ) ) )
% 0.19/0.46 => ( Xs = Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nth_equalityI
% 0.19/0.46 thf(fact_2_nth__equalityI,axiom,
% 0.19/0.46 ! [Xs: list_nat,Ys: list_nat] :
% 0.19/0.46 ( ( ( size_size_list_nat @ Xs )
% 0.19/0.46 = ( size_size_list_nat @ Ys ) )
% 0.19/0.46 => ( ! [I: nat] :
% 0.19/0.46 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.19/0.46 => ( ( nth_nat @ Xs @ I )
% 0.19/0.46 = ( nth_nat @ Ys @ I ) ) )
% 0.19/0.46 => ( Xs = Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nth_equalityI
% 0.19/0.46 thf(fact_3_nth__equalityI,axiom,
% 0.19/0.46 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.19/0.46 ( ( ( size_s1427607542list_a @ Xs )
% 0.19/0.46 = ( size_s1427607542list_a @ Ys ) )
% 0.19/0.46 => ( ! [I: nat] :
% 0.19/0.46 ( ( ord_less_nat @ I @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.46 => ( ( nth_list_a @ Xs @ I )
% 0.19/0.46 = ( nth_list_a @ Ys @ I ) ) )
% 0.19/0.46 => ( Xs = Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nth_equalityI
% 0.19/0.46 thf(fact_4_nth__equalityI,axiom,
% 0.19/0.46 ! [Xs: list_a,Ys: list_a] :
% 0.19/0.46 ( ( ( size_size_list_a @ Xs )
% 0.19/0.46 = ( size_size_list_a @ Ys ) )
% 0.19/0.46 => ( ! [I: nat] :
% 0.19/0.46 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 0.19/0.46 => ( ( nth_a @ Xs @ I )
% 0.19/0.46 = ( nth_a @ Ys @ I ) ) )
% 0.19/0.46 => ( Xs = Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nth_equalityI
% 0.19/0.46 thf(fact_5_Skolem__list__nth,axiom,
% 0.19/0.46 ! [K: nat,P: nat > list_nat > $o] :
% 0.19/0.46 ( ( ! [I2: nat] :
% 0.19/0.46 ( ( ord_less_nat @ I2 @ K )
% 0.19/0.46 => ? [X: list_nat] : ( P @ I2 @ X ) ) )
% 0.19/0.46 = ( ? [Xs2: list_list_nat] :
% 0.19/0.46 ( ( ( size_s1898481668st_nat @ Xs2 )
% 0.19/0.46 = K )
% 0.19/0.47 & ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.19/0.47 => ( P @ I2 @ ( nth_list_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Skolem_list_nth
% 0.19/0.47 thf(fact_6_Skolem__list__nth,axiom,
% 0.19/0.47 ! [K: nat,P: nat > list_list_a > $o] :
% 0.19/0.47 ( ( ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.19/0.47 => ? [X: list_list_a] : ( P @ I2 @ X ) ) )
% 0.19/0.47 = ( ? [Xs2: list_list_list_a] :
% 0.19/0.47 ( ( ( size_s575106428list_a @ Xs2 )
% 0.19/0.47 = K )
% 0.19/0.47 & ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.19/0.47 => ( P @ I2 @ ( nth_list_list_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Skolem_list_nth
% 0.19/0.47 thf(fact_7_Skolem__list__nth,axiom,
% 0.19/0.47 ! [K: nat,P: nat > nat > $o] :
% 0.19/0.47 ( ( ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.19/0.47 => ? [X: nat] : ( P @ I2 @ X ) ) )
% 0.19/0.47 = ( ? [Xs2: list_nat] :
% 0.19/0.47 ( ( ( size_size_list_nat @ Xs2 )
% 0.19/0.47 = K )
% 0.19/0.47 & ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.19/0.47 => ( P @ I2 @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Skolem_list_nth
% 0.19/0.47 thf(fact_8_Skolem__list__nth,axiom,
% 0.19/0.47 ! [K: nat,P: nat > list_a > $o] :
% 0.19/0.47 ( ( ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.19/0.47 => ? [X: list_a] : ( P @ I2 @ X ) ) )
% 0.19/0.47 = ( ? [Xs2: list_list_a] :
% 0.19/0.47 ( ( ( size_s1427607542list_a @ Xs2 )
% 0.19/0.47 = K )
% 0.19/0.47 & ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.19/0.47 => ( P @ I2 @ ( nth_list_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Skolem_list_nth
% 0.19/0.47 thf(fact_9_Skolem__list__nth,axiom,
% 0.19/0.47 ! [K: nat,P: nat > a > $o] :
% 0.19/0.47 ( ( ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.19/0.47 => ? [X: a] : ( P @ I2 @ X ) ) )
% 0.19/0.47 = ( ? [Xs2: list_a] :
% 0.19/0.47 ( ( ( size_size_list_a @ Xs2 )
% 0.19/0.47 = K )
% 0.19/0.47 & ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ K )
% 0.19/0.47 => ( P @ I2 @ ( nth_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Skolem_list_nth
% 0.19/0.47 thf(fact_10_list__eq__iff__nth__eq,axiom,
% 0.19/0.47 ( ( ^ [Y: list_list_nat,Z: list_list_nat] : ( Y = Z ) )
% 0.19/0.47 = ( ^ [Xs2: list_list_nat,Ys2: list_list_nat] :
% 0.19/0.47 ( ( ( size_s1898481668st_nat @ Xs2 )
% 0.19/0.47 = ( size_s1898481668st_nat @ Ys2 ) )
% 0.19/0.47 & ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_s1898481668st_nat @ Xs2 ) )
% 0.19/0.47 => ( ( nth_list_nat @ Xs2 @ I2 )
% 0.19/0.47 = ( nth_list_nat @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_eq_iff_nth_eq
% 0.19/0.47 thf(fact_11_list__eq__iff__nth__eq,axiom,
% 0.19/0.47 ( ( ^ [Y: list_list_list_a,Z: list_list_list_a] : ( Y = Z ) )
% 0.19/0.47 = ( ^ [Xs2: list_list_list_a,Ys2: list_list_list_a] :
% 0.19/0.47 ( ( ( size_s575106428list_a @ Xs2 )
% 0.19/0.47 = ( size_s575106428list_a @ Ys2 ) )
% 0.19/0.47 & ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_s575106428list_a @ Xs2 ) )
% 0.19/0.47 => ( ( nth_list_list_a @ Xs2 @ I2 )
% 0.19/0.47 = ( nth_list_list_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_eq_iff_nth_eq
% 0.19/0.47 thf(fact_12_list__eq__iff__nth__eq,axiom,
% 0.19/0.47 ( ( ^ [Y: list_nat,Z: list_nat] : ( Y = Z ) )
% 0.19/0.47 = ( ^ [Xs2: list_nat,Ys2: list_nat] :
% 0.19/0.47 ( ( ( size_size_list_nat @ Xs2 )
% 0.19/0.47 = ( size_size_list_nat @ Ys2 ) )
% 0.19/0.47 & ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.19/0.47 => ( ( nth_nat @ Xs2 @ I2 )
% 0.19/0.47 = ( nth_nat @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_eq_iff_nth_eq
% 0.19/0.47 thf(fact_13_list__eq__iff__nth__eq,axiom,
% 0.19/0.47 ( ( ^ [Y: list_list_a,Z: list_list_a] : ( Y = Z ) )
% 0.19/0.47 = ( ^ [Xs2: list_list_a,Ys2: list_list_a] :
% 0.19/0.47 ( ( ( size_s1427607542list_a @ Xs2 )
% 0.19/0.47 = ( size_s1427607542list_a @ Ys2 ) )
% 0.19/0.47 & ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
% 0.19/0.47 => ( ( nth_list_a @ Xs2 @ I2 )
% 0.19/0.47 = ( nth_list_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_eq_iff_nth_eq
% 0.19/0.47 thf(fact_14_list__eq__iff__nth__eq,axiom,
% 0.19/0.47 ( ( ^ [Y: list_a,Z: list_a] : ( Y = Z ) )
% 0.19/0.47 = ( ^ [Xs2: list_a,Ys2: list_a] :
% 0.19/0.47 ( ( ( size_size_list_a @ Xs2 )
% 0.19/0.47 = ( size_size_list_a @ Ys2 ) )
% 0.19/0.47 & ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
% 0.19/0.47 => ( ( nth_a @ Xs2 @ I2 )
% 0.19/0.47 = ( nth_a @ Ys2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_eq_iff_nth_eq
% 0.19/0.47 thf(fact_15_list__slice2__list__slice__nth,axiom,
% 0.19/0.47 ! [M: nat,Xs: list_list_nat,K: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs ) @ K ) )
% 0.19/0.47 => ( ( nth_list_list_nat @ ( listSl2099749758st_nat @ Xs @ K ) @ M )
% 0.19/0.47 = ( nth_list_list_nat @ ( listSl729562870st_nat @ Xs @ K ) @ M ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice2_list_slice_nth
% 0.19/0.47 thf(fact_16_list__slice2__list__slice__nth,axiom,
% 0.19/0.47 ! [M: nat,Xs: list_list_list_a,K: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s575106428list_a @ Xs ) @ K ) )
% 0.19/0.47 => ( ( nth_list_list_list_a @ ( listSl769338732list_a @ Xs @ K ) @ M )
% 0.19/0.47 = ( nth_list_list_list_a @ ( listSl2102238196list_a @ Xs @ K ) @ M ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice2_list_slice_nth
% 0.19/0.47 thf(fact_17_list__slice2__list__slice__nth,axiom,
% 0.19/0.47 ! [M: nat,Xs: list_list_a,K: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1427607542list_a @ Xs ) @ K ) )
% 0.19/0.47 => ( ( nth_list_list_a @ ( listSl703198822list_a @ Xs @ K ) @ M )
% 0.19/0.47 = ( nth_list_list_a @ ( listSl162220270list_a @ Xs @ K ) @ M ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice2_list_slice_nth
% 0.19/0.47 thf(fact_18_list__slice2__list__slice__nth,axiom,
% 0.19/0.47 ! [M: nat,Xs: list_nat,K: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_nat @ Xs ) @ K ) )
% 0.19/0.47 => ( ( nth_list_nat @ ( listSl882585454e2_nat @ Xs @ K ) @ M )
% 0.19/0.47 = ( nth_list_nat @ ( listSl1630398182ce_nat @ Xs @ K ) @ M ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice2_list_slice_nth
% 0.19/0.47 thf(fact_19_list__slice2__list__slice__nth,axiom,
% 0.19/0.47 ! [M: nat,Xs: list_a,K: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
% 0.19/0.47 => ( ( nth_list_a @ ( listSl1174287072ice2_a @ Xs @ K ) @ M )
% 0.19/0.47 = ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice2_list_slice_nth
% 0.19/0.47 thf(fact_20_length__induct,axiom,
% 0.19/0.47 ! [P: list_list_nat > $o,Xs: list_list_nat] :
% 0.19/0.47 ( ! [Xs3: list_list_nat] :
% 0.19/0.47 ( ! [Ys3: list_list_nat] :
% 0.19/0.47 ( ( ord_less_nat @ ( size_s1898481668st_nat @ Ys3 ) @ ( size_s1898481668st_nat @ Xs3 ) )
% 0.19/0.47 => ( P @ Ys3 ) )
% 0.19/0.47 => ( P @ Xs3 ) )
% 0.19/0.47 => ( P @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % length_induct
% 0.19/0.47 thf(fact_21_length__induct,axiom,
% 0.19/0.47 ! [P: list_list_list_a > $o,Xs: list_list_list_a] :
% 0.19/0.47 ( ! [Xs3: list_list_list_a] :
% 0.19/0.47 ( ! [Ys3: list_list_list_a] :
% 0.19/0.47 ( ( ord_less_nat @ ( size_s575106428list_a @ Ys3 ) @ ( size_s575106428list_a @ Xs3 ) )
% 0.19/0.47 => ( P @ Ys3 ) )
% 0.19/0.47 => ( P @ Xs3 ) )
% 0.19/0.47 => ( P @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % length_induct
% 0.19/0.47 thf(fact_22_length__induct,axiom,
% 0.19/0.47 ! [P: list_list_a > $o,Xs: list_list_a] :
% 0.19/0.47 ( ! [Xs3: list_list_a] :
% 0.19/0.47 ( ! [Ys3: list_list_a] :
% 0.19/0.47 ( ( ord_less_nat @ ( size_s1427607542list_a @ Ys3 ) @ ( size_s1427607542list_a @ Xs3 ) )
% 0.19/0.47 => ( P @ Ys3 ) )
% 0.19/0.47 => ( P @ Xs3 ) )
% 0.19/0.47 => ( P @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % length_induct
% 0.19/0.47 thf(fact_23_length__induct,axiom,
% 0.19/0.47 ! [P: list_nat > $o,Xs: list_nat] :
% 0.19/0.47 ( ! [Xs3: list_nat] :
% 0.19/0.47 ( ! [Ys3: list_nat] :
% 0.19/0.47 ( ( ord_less_nat @ ( size_size_list_nat @ Ys3 ) @ ( size_size_list_nat @ Xs3 ) )
% 0.19/0.47 => ( P @ Ys3 ) )
% 0.19/0.47 => ( P @ Xs3 ) )
% 0.19/0.47 => ( P @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % length_induct
% 0.19/0.47 thf(fact_24_length__induct,axiom,
% 0.19/0.47 ! [P: list_a > $o,Xs: list_a] :
% 0.19/0.47 ( ! [Xs3: list_a] :
% 0.19/0.47 ( ! [Ys3: list_a] :
% 0.19/0.47 ( ( ord_less_nat @ ( size_size_list_a @ Ys3 ) @ ( size_size_list_a @ Xs3 ) )
% 0.19/0.47 => ( P @ Ys3 ) )
% 0.19/0.47 => ( P @ Xs3 ) )
% 0.19/0.47 => ( P @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % length_induct
% 0.19/0.47 thf(fact_25_list__strict__desc__trans,axiom,
% 0.19/0.47 ( list_strict_desc_nat
% 0.19/0.47 = ( ^ [Xs2: list_nat] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.19/0.47 => ( ord_less_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_strict_desc_trans
% 0.19/0.47 thf(fact_26_list__slice__nth__length,axiom,
% 0.19/0.47 ! [M: nat,Xs: list_list_nat,K: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs ) @ K ) )
% 0.19/0.47 => ( ( size_s1898481668st_nat @ ( nth_list_list_nat @ ( listSl729562870st_nat @ Xs @ K ) @ M ) )
% 0.19/0.47 = K ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_nth_length
% 0.19/0.47 thf(fact_27_list__slice__nth__length,axiom,
% 0.19/0.47 ! [M: nat,Xs: list_list_list_a,K: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s575106428list_a @ Xs ) @ K ) )
% 0.19/0.47 => ( ( size_s575106428list_a @ ( nth_list_list_list_a @ ( listSl2102238196list_a @ Xs @ K ) @ M ) )
% 0.19/0.47 = K ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_nth_length
% 0.19/0.47 thf(fact_28_list__slice__nth__length,axiom,
% 0.19/0.47 ! [M: nat,Xs: list_list_a,K: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_s1427607542list_a @ Xs ) @ K ) )
% 0.19/0.47 => ( ( size_s1427607542list_a @ ( nth_list_list_a @ ( listSl162220270list_a @ Xs @ K ) @ M ) )
% 0.19/0.47 = K ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_nth_length
% 0.19/0.47 thf(fact_29_list__slice__nth__length,axiom,
% 0.19/0.47 ! [M: nat,Xs: list_nat,K: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_nat @ Xs ) @ K ) )
% 0.19/0.47 => ( ( size_size_list_nat @ ( nth_list_nat @ ( listSl1630398182ce_nat @ Xs @ K ) @ M ) )
% 0.19/0.47 = K ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_nth_length
% 0.19/0.47 thf(fact_30_list__slice__nth__length,axiom,
% 0.19/0.47 ! [M: nat,Xs: list_a,K: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
% 0.19/0.47 => ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) )
% 0.19/0.47 = K ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_nth_length
% 0.19/0.47 thf(fact_31_list__strict__asc__trans,axiom,
% 0.19/0.47 ( list_strict_asc_nat
% 0.19/0.47 = ( ^ [Xs2: list_nat] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.19/0.47 => ( ord_less_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_strict_asc_trans
% 0.19/0.47 thf(fact_32_Ex__list__of__length,axiom,
% 0.19/0.47 ! [N: nat] :
% 0.19/0.47 ? [Xs3: list_list_nat] :
% 0.19/0.47 ( ( size_s1898481668st_nat @ Xs3 )
% 0.19/0.47 = N ) ).
% 0.19/0.47
% 0.19/0.47 % Ex_list_of_length
% 0.19/0.47 thf(fact_33_Ex__list__of__length,axiom,
% 0.19/0.47 ! [N: nat] :
% 0.19/0.47 ? [Xs3: list_list_list_a] :
% 0.19/0.47 ( ( size_s575106428list_a @ Xs3 )
% 0.19/0.47 = N ) ).
% 0.19/0.47
% 0.19/0.47 % Ex_list_of_length
% 0.19/0.47 thf(fact_34_Ex__list__of__length,axiom,
% 0.19/0.47 ! [N: nat] :
% 0.19/0.47 ? [Xs3: list_list_a] :
% 0.19/0.47 ( ( size_s1427607542list_a @ Xs3 )
% 0.19/0.47 = N ) ).
% 0.19/0.47
% 0.19/0.47 % Ex_list_of_length
% 0.19/0.47 thf(fact_35_Ex__list__of__length,axiom,
% 0.19/0.47 ! [N: nat] :
% 0.19/0.47 ? [Xs3: list_nat] :
% 0.19/0.47 ( ( size_size_list_nat @ Xs3 )
% 0.19/0.47 = N ) ).
% 0.19/0.47
% 0.19/0.47 % Ex_list_of_length
% 0.19/0.47 thf(fact_36_Ex__list__of__length,axiom,
% 0.19/0.47 ! [N: nat] :
% 0.19/0.47 ? [Xs3: list_a] :
% 0.19/0.47 ( ( size_size_list_a @ Xs3 )
% 0.19/0.47 = N ) ).
% 0.19/0.47
% 0.19/0.47 % Ex_list_of_length
% 0.19/0.47 thf(fact_37_neq__if__length__neq,axiom,
% 0.19/0.47 ! [Xs: list_list_nat,Ys: list_list_nat] :
% 0.19/0.47 ( ( ( size_s1898481668st_nat @ Xs )
% 0.19/0.47 != ( size_s1898481668st_nat @ Ys ) )
% 0.19/0.47 => ( Xs != Ys ) ) ).
% 0.19/0.47
% 0.19/0.47 % neq_if_length_neq
% 0.19/0.47 thf(fact_38_neq__if__length__neq,axiom,
% 0.19/0.47 ! [Xs: list_list_list_a,Ys: list_list_list_a] :
% 0.19/0.47 ( ( ( size_s575106428list_a @ Xs )
% 0.19/0.47 != ( size_s575106428list_a @ Ys ) )
% 0.19/0.47 => ( Xs != Ys ) ) ).
% 0.19/0.47
% 0.19/0.47 % neq_if_length_neq
% 0.19/0.47 thf(fact_39_neq__if__length__neq,axiom,
% 0.19/0.47 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.19/0.47 ( ( ( size_s1427607542list_a @ Xs )
% 0.19/0.47 != ( size_s1427607542list_a @ Ys ) )
% 0.19/0.47 => ( Xs != Ys ) ) ).
% 0.19/0.47
% 0.19/0.47 % neq_if_length_neq
% 0.19/0.47 thf(fact_40_neq__if__length__neq,axiom,
% 0.19/0.47 ! [Xs: list_nat,Ys: list_nat] :
% 0.19/0.47 ( ( ( size_size_list_nat @ Xs )
% 0.19/0.47 != ( size_size_list_nat @ Ys ) )
% 0.19/0.47 => ( Xs != Ys ) ) ).
% 0.19/0.47
% 0.19/0.47 % neq_if_length_neq
% 0.19/0.47 thf(fact_41_neq__if__length__neq,axiom,
% 0.19/0.47 ! [Xs: list_a,Ys: list_a] :
% 0.19/0.47 ( ( ( size_size_list_a @ Xs )
% 0.19/0.47 != ( size_size_list_a @ Ys ) )
% 0.19/0.47 => ( Xs != Ys ) ) ).
% 0.19/0.47
% 0.19/0.47 % neq_if_length_neq
% 0.19/0.47 thf(fact_42_size__neq__size__imp__neq,axiom,
% 0.19/0.47 ! [X2: list_list_nat,Y2: list_list_nat] :
% 0.19/0.47 ( ( ( size_s1898481668st_nat @ X2 )
% 0.19/0.47 != ( size_s1898481668st_nat @ Y2 ) )
% 0.19/0.47 => ( X2 != Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % size_neq_size_imp_neq
% 0.19/0.47 thf(fact_43_size__neq__size__imp__neq,axiom,
% 0.19/0.47 ! [X2: list_list_list_a,Y2: list_list_list_a] :
% 0.19/0.47 ( ( ( size_s575106428list_a @ X2 )
% 0.19/0.47 != ( size_s575106428list_a @ Y2 ) )
% 0.19/0.47 => ( X2 != Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % size_neq_size_imp_neq
% 0.19/0.47 thf(fact_44_size__neq__size__imp__neq,axiom,
% 0.19/0.47 ! [X2: list_a,Y2: list_a] :
% 0.19/0.47 ( ( ( size_size_list_a @ X2 )
% 0.19/0.47 != ( size_size_list_a @ Y2 ) )
% 0.19/0.47 => ( X2 != Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % size_neq_size_imp_neq
% 0.19/0.47 thf(fact_45_size__neq__size__imp__neq,axiom,
% 0.19/0.47 ! [X2: list_list_a,Y2: list_list_a] :
% 0.19/0.47 ( ( ( size_s1427607542list_a @ X2 )
% 0.19/0.47 != ( size_s1427607542list_a @ Y2 ) )
% 0.19/0.47 => ( X2 != Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % size_neq_size_imp_neq
% 0.19/0.47 thf(fact_46_size__neq__size__imp__neq,axiom,
% 0.19/0.47 ! [X2: list_nat,Y2: list_nat] :
% 0.19/0.47 ( ( ( size_size_list_nat @ X2 )
% 0.19/0.47 != ( size_size_list_nat @ Y2 ) )
% 0.19/0.47 => ( X2 != Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % size_neq_size_imp_neq
% 0.19/0.47 thf(fact_47_nat__neq__iff,axiom,
% 0.19/0.47 ! [M: nat,N: nat] :
% 0.19/0.47 ( ( M != N )
% 0.19/0.47 = ( ( ord_less_nat @ M @ N )
% 0.19/0.47 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nat_neq_iff
% 0.19/0.47 thf(fact_48_list__slice__length,axiom,
% 0.19/0.47 ! [Xs: list_list_nat,K: nat] :
% 0.19/0.47 ( ( size_s1321307156st_nat @ ( listSl729562870st_nat @ Xs @ K ) )
% 0.19/0.47 = ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs ) @ K ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_length
% 0.19/0.47 thf(fact_49_list__slice__length,axiom,
% 0.19/0.47 ! [Xs: list_list_list_a,K: nat] :
% 0.19/0.47 ( ( size_s1764310658list_a @ ( listSl2102238196list_a @ Xs @ K ) )
% 0.19/0.47 = ( divide_divide_nat @ ( size_s575106428list_a @ Xs ) @ K ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_length
% 0.19/0.47 thf(fact_50_list__slice__length,axiom,
% 0.19/0.47 ! [Xs: list_list_a,K: nat] :
% 0.19/0.47 ( ( size_s575106428list_a @ ( listSl162220270list_a @ Xs @ K ) )
% 0.19/0.47 = ( divide_divide_nat @ ( size_s1427607542list_a @ Xs ) @ K ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_length
% 0.19/0.47 thf(fact_51_list__slice__length,axiom,
% 0.19/0.47 ! [Xs: list_nat,K: nat] :
% 0.19/0.47 ( ( size_s1898481668st_nat @ ( listSl1630398182ce_nat @ Xs @ K ) )
% 0.19/0.47 = ( divide_divide_nat @ ( size_size_list_nat @ Xs ) @ K ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_length
% 0.19/0.47 thf(fact_52_list__slice__length,axiom,
% 0.19/0.47 ! [Xs: list_a,K: nat] :
% 0.19/0.47 ( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
% 0.19/0.47 = ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_length
% 0.19/0.47 thf(fact_53_linorder__neqE__nat,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( X2 != Y2 )
% 0.19/0.47 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % linorder_neqE_nat
% 0.19/0.47 thf(fact_54_infinite__descent,axiom,
% 0.19/0.47 ! [P: nat > $o,N: nat] :
% 0.19/0.47 ( ! [N2: nat] :
% 0.19/0.47 ( ~ ( P @ N2 )
% 0.19/0.47 => ? [M2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.19/0.47 & ~ ( P @ M2 ) ) )
% 0.19/0.47 => ( P @ N ) ) ).
% 0.19/0.47
% 0.19/0.47 % infinite_descent
% 0.19/0.47 thf(fact_55_nat__less__induct,axiom,
% 0.19/0.47 ! [P: nat > $o,N: nat] :
% 0.19/0.47 ( ! [N2: nat] :
% 0.19/0.47 ( ! [M2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.19/0.47 => ( P @ M2 ) )
% 0.19/0.47 => ( P @ N2 ) )
% 0.19/0.47 => ( P @ N ) ) ).
% 0.19/0.47
% 0.19/0.47 % nat_less_induct
% 0.19/0.47 thf(fact_56_less__irrefl__nat,axiom,
% 0.19/0.47 ! [N: nat] :
% 0.19/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.19/0.47
% 0.19/0.47 % less_irrefl_nat
% 0.19/0.47 thf(fact_57_less__not__refl3,axiom,
% 0.19/0.47 ! [S: nat,T: nat] :
% 0.19/0.47 ( ( ord_less_nat @ S @ T )
% 0.19/0.47 => ( S != T ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_not_refl3
% 0.19/0.47 thf(fact_58_less__not__refl2,axiom,
% 0.19/0.47 ! [N: nat,M: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N @ M )
% 0.19/0.47 => ( M != N ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_not_refl2
% 0.19/0.47 thf(fact_59_less__not__refl,axiom,
% 0.19/0.47 ! [N: nat] :
% 0.19/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.19/0.47
% 0.19/0.47 % less_not_refl
% 0.19/0.47 thf(fact_60_list__slice__def,axiom,
% 0.19/0.47 ( listSl729562870st_nat
% 0.19/0.47 = ( ^ [Xs2: list_list_nat,K2: nat] : ( listSl1506485424st_nat @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_s1898481668st_nat @ Xs2 ) @ K2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_def
% 0.19/0.47 thf(fact_61_list__slice__def,axiom,
% 0.19/0.47 ( listSl2102238196list_a
% 0.19/0.47 = ( ^ [Xs2: list_list_list_a,K2: nat] : ( listSl902632890list_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_s575106428list_a @ Xs2 ) @ K2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_def
% 0.19/0.47 thf(fact_62_list__slice__def,axiom,
% 0.19/0.47 ( listSl162220270list_a
% 0.19/0.47 = ( ^ [Xs2: list_list_a,K2: nat] : ( listSl856612276list_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_s1427607542list_a @ Xs2 ) @ K2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_def
% 0.19/0.47 thf(fact_63_list__slice__def,axiom,
% 0.19/0.47 ( listSl1630398182ce_nat
% 0.19/0.47 = ( ^ [Xs2: list_nat,K2: nat] : ( listSl1794011552ux_nat @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_size_list_nat @ Xs2 ) @ K2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_def
% 0.19/0.47 thf(fact_64_list__slice__def,axiom,
% 0.19/0.47 ( listSl97544552lice_a
% 0.19/0.47 = ( ^ [Xs2: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs2 ) @ K2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_def
% 0.19/0.47 thf(fact_65_list__strict__desc__imp__list__desc,axiom,
% 0.19/0.47 ! [Xs: list_nat] :
% 0.19/0.47 ( ( list_strict_desc_nat @ Xs )
% 0.19/0.47 => ( list_desc_nat @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_strict_desc_imp_list_desc
% 0.19/0.47 thf(fact_66_list__ex__length,axiom,
% 0.19/0.47 ( list_ex_list_nat
% 0.19/0.47 = ( ^ [P2: list_nat > $o,Xs2: list_list_nat] :
% 0.19/0.47 ? [N3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N3 @ ( size_s1898481668st_nat @ Xs2 ) )
% 0.19/0.47 & ( P2 @ ( nth_list_nat @ Xs2 @ N3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_ex_length
% 0.19/0.47 thf(fact_67_list__ex__length,axiom,
% 0.19/0.47 ( list_ex_list_list_a
% 0.19/0.47 = ( ^ [P2: list_list_a > $o,Xs2: list_list_list_a] :
% 0.19/0.47 ? [N3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N3 @ ( size_s575106428list_a @ Xs2 ) )
% 0.19/0.47 & ( P2 @ ( nth_list_list_a @ Xs2 @ N3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_ex_length
% 0.19/0.47 thf(fact_68_list__ex__length,axiom,
% 0.19/0.47 ( list_ex_a
% 0.19/0.47 = ( ^ [P2: a > $o,Xs2: list_a] :
% 0.19/0.47 ? [N3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N3 @ ( size_size_list_a @ Xs2 ) )
% 0.19/0.47 & ( P2 @ ( nth_a @ Xs2 @ N3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_ex_length
% 0.19/0.47 thf(fact_69_list__ex__length,axiom,
% 0.19/0.47 ( list_ex_list_a
% 0.19/0.47 = ( ^ [P2: list_a > $o,Xs2: list_list_a] :
% 0.19/0.47 ? [N3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N3 @ ( size_s1427607542list_a @ Xs2 ) )
% 0.19/0.47 & ( P2 @ ( nth_list_a @ Xs2 @ N3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_ex_length
% 0.19/0.47 thf(fact_70_list__ex__length,axiom,
% 0.19/0.47 ( list_ex_nat
% 0.19/0.47 = ( ^ [P2: nat > $o,Xs2: list_nat] :
% 0.19/0.47 ? [N3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N3 @ ( size_size_list_nat @ Xs2 ) )
% 0.19/0.47 & ( P2 @ ( nth_nat @ Xs2 @ N3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_ex_length
% 0.19/0.47 thf(fact_71_f__image__eqI,axiom,
% 0.19/0.47 ! [X2: list_nat,Xs: list_list_nat,N: nat,A: set_nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_list_nat @ Xs @ N ) )
% 0.19/0.47 => ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_eqI
% 0.19/0.47 thf(fact_72_f__image__eqI,axiom,
% 0.19/0.47 ! [X2: list_list_a,Xs: list_list_list_a,N: nat,A: set_nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_list_list_a @ Xs @ N ) )
% 0.19/0.47 => ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_eqI
% 0.19/0.47 thf(fact_73_f__image__eqI,axiom,
% 0.19/0.47 ! [X2: a,Xs: list_a,N: nat,A: set_nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_a @ Xs @ N ) )
% 0.19/0.47 => ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( member_a @ X2 @ ( f_image_a @ Xs @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_eqI
% 0.19/0.47 thf(fact_74_f__image__eqI,axiom,
% 0.19/0.47 ! [X2: list_a,Xs: list_list_a,N: nat,A: set_nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_list_a @ Xs @ N ) )
% 0.19/0.47 => ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_eqI
% 0.19/0.47 thf(fact_75_f__image__eqI,axiom,
% 0.19/0.47 ! [X2: nat,Xs: list_nat,N: nat,A: set_nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_nat @ Xs @ N ) )
% 0.19/0.47 => ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_eqI
% 0.19/0.47 thf(fact_76_list__strict__asc__imp__list__asc,axiom,
% 0.19/0.47 ! [Xs: list_nat] :
% 0.19/0.47 ( ( list_strict_asc_nat @ Xs )
% 0.19/0.47 => ( list_asc_nat @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_strict_asc_imp_list_asc
% 0.19/0.47 thf(fact_77_nth__list__update__eq,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_nat,X2: list_nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ I3 )
% 0.19/0.47 = X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update_eq
% 0.19/0.47 thf(fact_78_nth__list__update__eq,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_list_a,X2: list_list_a] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ I3 )
% 0.19/0.47 = X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update_eq
% 0.19/0.47 thf(fact_79_nth__list__update__eq,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_a,X2: a] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I3 )
% 0.19/0.47 = X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update_eq
% 0.19/0.47 thf(fact_80_nth__list__update__eq,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_a,X2: list_a] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I3 )
% 0.19/0.47 = X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update_eq
% 0.19/0.47 thf(fact_81_nth__list__update__eq,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_nat,X2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ I3 )
% 0.19/0.47 = X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update_eq
% 0.19/0.47 thf(fact_82_rev__f__imageI,axiom,
% 0.19/0.47 ! [N: nat,A: set_nat,Xs: list_list_nat,X2: list_nat] :
% 0.19/0.47 ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( ( X2
% 0.19/0.47 = ( nth_list_nat @ Xs @ N ) )
% 0.19/0.47 => ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rev_f_imageI
% 0.19/0.47 thf(fact_83_rev__f__imageI,axiom,
% 0.19/0.47 ! [N: nat,A: set_nat,Xs: list_list_list_a,X2: list_list_a] :
% 0.19/0.47 ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( ( X2
% 0.19/0.47 = ( nth_list_list_a @ Xs @ N ) )
% 0.19/0.47 => ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rev_f_imageI
% 0.19/0.47 thf(fact_84_rev__f__imageI,axiom,
% 0.19/0.47 ! [N: nat,A: set_nat,Xs: list_a,X2: a] :
% 0.19/0.47 ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ( X2
% 0.19/0.47 = ( nth_a @ Xs @ N ) )
% 0.19/0.47 => ( member_a @ X2 @ ( f_image_a @ Xs @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rev_f_imageI
% 0.19/0.47 thf(fact_85_rev__f__imageI,axiom,
% 0.19/0.47 ! [N: nat,A: set_nat,Xs: list_list_a,X2: list_a] :
% 0.19/0.47 ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ( X2
% 0.19/0.47 = ( nth_list_a @ Xs @ N ) )
% 0.19/0.47 => ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rev_f_imageI
% 0.19/0.47 thf(fact_86_rev__f__imageI,axiom,
% 0.19/0.47 ! [N: nat,A: set_nat,Xs: list_nat,X2: nat] :
% 0.19/0.47 ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ( X2
% 0.19/0.47 = ( nth_nat @ Xs @ N ) )
% 0.19/0.47 => ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rev_f_imageI
% 0.19/0.47 thf(fact_87_f__image__iff,axiom,
% 0.19/0.47 ! [X2: list_nat,Xs: list_list_nat,A: set_nat] :
% 0.19/0.47 ( ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) )
% 0.19/0.47 = ( ? [X3: nat] :
% 0.19/0.47 ( ( member_nat @ X3 @ A )
% 0.19/0.47 & ( ord_less_nat @ X3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 & ( X2
% 0.19/0.47 = ( nth_list_nat @ Xs @ X3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_iff
% 0.19/0.47 thf(fact_88_f__image__iff,axiom,
% 0.19/0.47 ! [X2: list_list_a,Xs: list_list_list_a,A: set_nat] :
% 0.19/0.47 ( ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) )
% 0.19/0.47 = ( ? [X3: nat] :
% 0.19/0.47 ( ( member_nat @ X3 @ A )
% 0.19/0.47 & ( ord_less_nat @ X3 @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 & ( X2
% 0.19/0.47 = ( nth_list_list_a @ Xs @ X3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_iff
% 0.19/0.47 thf(fact_89_f__image__iff,axiom,
% 0.19/0.47 ! [X2: a,Xs: list_a,A: set_nat] :
% 0.19/0.47 ( ( member_a @ X2 @ ( f_image_a @ Xs @ A ) )
% 0.19/0.47 = ( ? [X3: nat] :
% 0.19/0.47 ( ( member_nat @ X3 @ A )
% 0.19/0.47 & ( ord_less_nat @ X3 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 & ( X2
% 0.19/0.47 = ( nth_a @ Xs @ X3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_iff
% 0.19/0.47 thf(fact_90_f__image__iff,axiom,
% 0.19/0.47 ! [X2: list_a,Xs: list_list_a,A: set_nat] :
% 0.19/0.47 ( ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) )
% 0.19/0.47 = ( ? [X3: nat] :
% 0.19/0.47 ( ( member_nat @ X3 @ A )
% 0.19/0.47 & ( ord_less_nat @ X3 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 & ( X2
% 0.19/0.47 = ( nth_list_a @ Xs @ X3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_iff
% 0.19/0.47 thf(fact_91_f__image__iff,axiom,
% 0.19/0.47 ! [X2: nat,Xs: list_nat,A: set_nat] :
% 0.19/0.47 ( ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) )
% 0.19/0.47 = ( ? [X3: nat] :
% 0.19/0.47 ( ( member_nat @ X3 @ A )
% 0.19/0.47 & ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 & ( X2
% 0.19/0.47 = ( nth_nat @ Xs @ X3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_iff
% 0.19/0.47 thf(fact_92_nth__butlast,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_list_nat] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ ( butlast_list_nat @ Xs ) ) )
% 0.19/0.47 => ( ( nth_list_nat @ ( butlast_list_nat @ Xs ) @ N )
% 0.19/0.47 = ( nth_list_nat @ Xs @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_butlast
% 0.19/0.47 thf(fact_93_nth__butlast,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_list_list_a] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_s575106428list_a @ ( butlast_list_list_a @ Xs ) ) )
% 0.19/0.47 => ( ( nth_list_list_a @ ( butlast_list_list_a @ Xs ) @ N )
% 0.19/0.47 = ( nth_list_list_a @ Xs @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_butlast
% 0.19/0.47 thf(fact_94_nth__butlast,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_a] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ ( butlast_a @ Xs ) ) )
% 0.19/0.47 => ( ( nth_a @ ( butlast_a @ Xs ) @ N )
% 0.19/0.47 = ( nth_a @ Xs @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_butlast
% 0.19/0.47 thf(fact_95_nth__butlast,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_list_a] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ ( butlast_list_a @ Xs ) ) )
% 0.19/0.47 => ( ( nth_list_a @ ( butlast_list_a @ Xs ) @ N )
% 0.19/0.47 = ( nth_list_a @ Xs @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_butlast
% 0.19/0.47 thf(fact_96_nth__butlast,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_nat] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ ( butlast_nat @ Xs ) ) )
% 0.19/0.47 => ( ( nth_nat @ ( butlast_nat @ Xs ) @ N )
% 0.19/0.47 = ( nth_nat @ Xs @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_butlast
% 0.19/0.47 thf(fact_97_f__imageI,axiom,
% 0.19/0.47 ! [N: nat,A: set_nat,Xs: list_list_nat] :
% 0.19/0.47 ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( member_list_nat @ ( nth_list_nat @ Xs @ N ) @ ( f_image_list_nat @ Xs @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_imageI
% 0.19/0.47 thf(fact_98_f__imageI,axiom,
% 0.19/0.47 ! [N: nat,A: set_nat,Xs: list_list_list_a] :
% 0.19/0.47 ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( member_list_list_a @ ( nth_list_list_a @ Xs @ N ) @ ( f_image_list_list_a @ Xs @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_imageI
% 0.19/0.47 thf(fact_99_f__imageI,axiom,
% 0.19/0.47 ! [N: nat,A: set_nat,Xs: list_a] :
% 0.19/0.47 ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( member_a @ ( nth_a @ Xs @ N ) @ ( f_image_a @ Xs @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_imageI
% 0.19/0.47 thf(fact_100_f__imageI,axiom,
% 0.19/0.47 ! [N: nat,A: set_nat,Xs: list_list_a] :
% 0.19/0.47 ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( member_list_a @ ( nth_list_a @ Xs @ N ) @ ( f_image_list_a @ Xs @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_imageI
% 0.19/0.47 thf(fact_101_f__imageI,axiom,
% 0.19/0.47 ! [N: nat,A: set_nat,Xs: list_nat] :
% 0.19/0.47 ( ( member_nat @ N @ A )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( f_image_nat @ Xs @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_imageI
% 0.19/0.47 thf(fact_102_f__imageE,axiom,
% 0.19/0.47 ! [X2: list_nat,Xs: list_list_nat,A: set_nat] :
% 0.19/0.47 ( ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ A ) )
% 0.19/0.47 => ~ ! [N2: nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_list_nat @ Xs @ N2 ) )
% 0.19/0.47 => ( ( member_nat @ N2 @ A )
% 0.19/0.47 => ~ ( ord_less_nat @ N2 @ ( size_s1898481668st_nat @ Xs ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_imageE
% 0.19/0.47 thf(fact_103_f__imageE,axiom,
% 0.19/0.47 ! [X2: list_list_a,Xs: list_list_list_a,A: set_nat] :
% 0.19/0.47 ( ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ A ) )
% 0.19/0.47 => ~ ! [N2: nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_list_list_a @ Xs @ N2 ) )
% 0.19/0.47 => ( ( member_nat @ N2 @ A )
% 0.19/0.47 => ~ ( ord_less_nat @ N2 @ ( size_s575106428list_a @ Xs ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_imageE
% 0.19/0.47 thf(fact_104_f__imageE,axiom,
% 0.19/0.47 ! [X2: a,Xs: list_a,A: set_nat] :
% 0.19/0.47 ( ( member_a @ X2 @ ( f_image_a @ Xs @ A ) )
% 0.19/0.47 => ~ ! [N2: nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_a @ Xs @ N2 ) )
% 0.19/0.47 => ( ( member_nat @ N2 @ A )
% 0.19/0.47 => ~ ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_imageE
% 0.19/0.47 thf(fact_105_f__imageE,axiom,
% 0.19/0.47 ! [X2: list_a,Xs: list_list_a,A: set_nat] :
% 0.19/0.47 ( ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ A ) )
% 0.19/0.47 => ~ ! [N2: nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_list_a @ Xs @ N2 ) )
% 0.19/0.47 => ( ( member_nat @ N2 @ A )
% 0.19/0.47 => ~ ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_imageE
% 0.19/0.47 thf(fact_106_f__imageE,axiom,
% 0.19/0.47 ! [X2: nat,Xs: list_nat,A: set_nat] :
% 0.19/0.47 ( ( member_nat @ X2 @ ( f_image_nat @ Xs @ A ) )
% 0.19/0.47 => ~ ! [N2: nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_nat @ Xs @ N2 ) )
% 0.19/0.47 => ( ( member_nat @ N2 @ A )
% 0.19/0.47 => ~ ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_imageE
% 0.19/0.47 thf(fact_107_list__update__overwrite,axiom,
% 0.19/0.47 ! [Xs: list_nat,I3: nat,X2: nat,Y2: nat] :
% 0.19/0.47 ( ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ I3 @ Y2 )
% 0.19/0.47 = ( list_update_nat @ Xs @ I3 @ Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_overwrite
% 0.19/0.47 thf(fact_108_list__update__overwrite,axiom,
% 0.19/0.47 ! [Xs: list_list_a,I3: nat,X2: list_a,Y2: list_a] :
% 0.19/0.47 ( ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I3 @ Y2 )
% 0.19/0.47 = ( list_update_list_a @ Xs @ I3 @ Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_overwrite
% 0.19/0.47 thf(fact_109_list__update__overwrite,axiom,
% 0.19/0.47 ! [Xs: list_a,I3: nat,X2: a,Y2: a] :
% 0.19/0.47 ( ( list_update_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I3 @ Y2 )
% 0.19/0.47 = ( list_update_a @ Xs @ I3 @ Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_overwrite
% 0.19/0.47 thf(fact_110_length__list__update,axiom,
% 0.19/0.47 ! [Xs: list_list_nat,I3: nat,X2: list_nat] :
% 0.19/0.47 ( ( size_s1898481668st_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) )
% 0.19/0.47 = ( size_s1898481668st_nat @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % length_list_update
% 0.19/0.47 thf(fact_111_length__list__update,axiom,
% 0.19/0.47 ! [Xs: list_list_list_a,I3: nat,X2: list_list_a] :
% 0.19/0.47 ( ( size_s575106428list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) )
% 0.19/0.47 = ( size_s575106428list_a @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % length_list_update
% 0.19/0.47 thf(fact_112_length__list__update,axiom,
% 0.19/0.47 ! [Xs: list_a,I3: nat,X2: a] :
% 0.19/0.47 ( ( size_size_list_a @ ( list_update_a @ Xs @ I3 @ X2 ) )
% 0.19/0.47 = ( size_size_list_a @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % length_list_update
% 0.19/0.47 thf(fact_113_length__list__update,axiom,
% 0.19/0.47 ! [Xs: list_list_a,I3: nat,X2: list_a] :
% 0.19/0.47 ( ( size_s1427607542list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) )
% 0.19/0.47 = ( size_s1427607542list_a @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % length_list_update
% 0.19/0.47 thf(fact_114_length__list__update,axiom,
% 0.19/0.47 ! [Xs: list_nat,I3: nat,X2: nat] :
% 0.19/0.47 ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) )
% 0.19/0.47 = ( size_size_list_nat @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % length_list_update
% 0.19/0.47 thf(fact_115_list__update__id,axiom,
% 0.19/0.47 ! [Xs: list_list_nat,I3: nat] :
% 0.19/0.47 ( ( list_update_list_nat @ Xs @ I3 @ ( nth_list_nat @ Xs @ I3 ) )
% 0.19/0.47 = Xs ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_id
% 0.19/0.47 thf(fact_116_list__update__id,axiom,
% 0.19/0.47 ! [Xs: list_list_list_a,I3: nat] :
% 0.19/0.47 ( ( list_u1330012152list_a @ Xs @ I3 @ ( nth_list_list_a @ Xs @ I3 ) )
% 0.19/0.47 = Xs ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_id
% 0.19/0.47 thf(fact_117_list__update__id,axiom,
% 0.19/0.47 ! [Xs: list_list_a,I3: nat] :
% 0.19/0.47 ( ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ I3 ) )
% 0.19/0.47 = Xs ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_id
% 0.19/0.47 thf(fact_118_list__update__id,axiom,
% 0.19/0.47 ! [Xs: list_a,I3: nat] :
% 0.19/0.47 ( ( list_update_a @ Xs @ I3 @ ( nth_a @ Xs @ I3 ) )
% 0.19/0.47 = Xs ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_id
% 0.19/0.47 thf(fact_119_list__update__id,axiom,
% 0.19/0.47 ! [Xs: list_nat,I3: nat] :
% 0.19/0.47 ( ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ I3 ) )
% 0.19/0.47 = Xs ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_id
% 0.19/0.47 thf(fact_120_nth__list__update__neq,axiom,
% 0.19/0.47 ! [I3: nat,J2: nat,Xs: list_list_nat,X2: list_nat] :
% 0.19/0.47 ( ( I3 != J2 )
% 0.19/0.47 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = ( nth_list_nat @ Xs @ J2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update_neq
% 0.19/0.47 thf(fact_121_nth__list__update__neq,axiom,
% 0.19/0.47 ! [I3: nat,J2: nat,Xs: list_list_list_a,X2: list_list_a] :
% 0.19/0.47 ( ( I3 != J2 )
% 0.19/0.47 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = ( nth_list_list_a @ Xs @ J2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update_neq
% 0.19/0.47 thf(fact_122_nth__list__update__neq,axiom,
% 0.19/0.47 ! [I3: nat,J2: nat,Xs: list_list_a,X2: list_a] :
% 0.19/0.47 ( ( I3 != J2 )
% 0.19/0.47 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = ( nth_list_a @ Xs @ J2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update_neq
% 0.19/0.47 thf(fact_123_nth__list__update__neq,axiom,
% 0.19/0.47 ! [I3: nat,J2: nat,Xs: list_a,X2: a] :
% 0.19/0.47 ( ( I3 != J2 )
% 0.19/0.47 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = ( nth_a @ Xs @ J2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update_neq
% 0.19/0.47 thf(fact_124_nth__list__update__neq,axiom,
% 0.19/0.47 ! [I3: nat,J2: nat,Xs: list_nat,X2: nat] :
% 0.19/0.47 ( ( I3 != J2 )
% 0.19/0.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = ( nth_nat @ Xs @ J2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update_neq
% 0.19/0.47 thf(fact_125_list__update__swap,axiom,
% 0.19/0.47 ! [I3: nat,I4: nat,Xs: list_nat,X2: nat,X4: nat] :
% 0.19/0.47 ( ( I3 != I4 )
% 0.19/0.47 => ( ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ I4 @ X4 )
% 0.19/0.47 = ( list_update_nat @ ( list_update_nat @ Xs @ I4 @ X4 ) @ I3 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_swap
% 0.19/0.47 thf(fact_126_list__update__swap,axiom,
% 0.19/0.47 ! [I3: nat,I4: nat,Xs: list_list_a,X2: list_a,X4: list_a] :
% 0.19/0.47 ( ( I3 != I4 )
% 0.19/0.47 => ( ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I4 @ X4 )
% 0.19/0.47 = ( list_update_list_a @ ( list_update_list_a @ Xs @ I4 @ X4 ) @ I3 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_swap
% 0.19/0.47 thf(fact_127_list__update__swap,axiom,
% 0.19/0.47 ! [I3: nat,I4: nat,Xs: list_a,X2: a,X4: a] :
% 0.19/0.47 ( ( I3 != I4 )
% 0.19/0.47 => ( ( list_update_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I4 @ X4 )
% 0.19/0.47 = ( list_update_a @ ( list_update_a @ Xs @ I4 @ X4 ) @ I3 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_swap
% 0.19/0.47 thf(fact_128_list__slice__aux__length,axiom,
% 0.19/0.47 ! [Xs: list_nat,K: nat,N: nat] :
% 0.19/0.47 ( ( size_s1898481668st_nat @ ( listSl1794011552ux_nat @ Xs @ K @ N ) )
% 0.19/0.47 = N ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_aux_length
% 0.19/0.47 thf(fact_129_list__slice__aux__length,axiom,
% 0.19/0.47 ! [Xs: list_list_a,K: nat,N: nat] :
% 0.19/0.47 ( ( size_s575106428list_a @ ( listSl856612276list_a @ Xs @ K @ N ) )
% 0.19/0.47 = N ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_aux_length
% 0.19/0.47 thf(fact_130_list__slice__aux__length,axiom,
% 0.19/0.47 ! [Xs: list_a,K: nat,N: nat] :
% 0.19/0.47 ( ( size_s1427607542list_a @ ( listSl1495374126_aux_a @ Xs @ K @ N ) )
% 0.19/0.47 = N ) ).
% 0.19/0.47
% 0.19/0.47 % list_slice_aux_length
% 0.19/0.47 thf(fact_131_nth__list__update,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_nat,J2: nat,X2: list_nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( ( ( I3 = J2 )
% 0.19/0.47 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = X2 ) )
% 0.19/0.47 & ( ( I3 != J2 )
% 0.19/0.47 => ( ( nth_list_nat @ ( list_update_list_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = ( nth_list_nat @ Xs @ J2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update
% 0.19/0.47 thf(fact_132_nth__list__update,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_list_a,J2: nat,X2: list_list_a] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( ( ( I3 = J2 )
% 0.19/0.47 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = X2 ) )
% 0.19/0.47 & ( ( I3 != J2 )
% 0.19/0.47 => ( ( nth_list_list_a @ ( list_u1330012152list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = ( nth_list_list_a @ Xs @ J2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update
% 0.19/0.47 thf(fact_133_nth__list__update,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_a,J2: nat,X2: a] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ( ( I3 = J2 )
% 0.19/0.47 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = X2 ) )
% 0.19/0.47 & ( ( I3 != J2 )
% 0.19/0.47 => ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = ( nth_a @ Xs @ J2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update
% 0.19/0.47 thf(fact_134_nth__list__update,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_a,J2: nat,X2: list_a] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ( ( I3 = J2 )
% 0.19/0.47 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = X2 ) )
% 0.19/0.47 & ( ( I3 != J2 )
% 0.19/0.47 => ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = ( nth_list_a @ Xs @ J2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update
% 0.19/0.47 thf(fact_135_nth__list__update,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_nat,J2: nat,X2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ( ( I3 = J2 )
% 0.19/0.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = X2 ) )
% 0.19/0.47 & ( ( I3 != J2 )
% 0.19/0.47 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J2 )
% 0.19/0.47 = ( nth_nat @ Xs @ J2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_list_update
% 0.19/0.47 thf(fact_136_list__update__same__conv,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_nat,X2: list_nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( ( ( list_update_list_nat @ Xs @ I3 @ X2 )
% 0.19/0.47 = Xs )
% 0.19/0.47 = ( ( nth_list_nat @ Xs @ I3 )
% 0.19/0.47 = X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_same_conv
% 0.19/0.47 thf(fact_137_list__update__same__conv,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_list_a,X2: list_list_a] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( ( ( list_u1330012152list_a @ Xs @ I3 @ X2 )
% 0.19/0.47 = Xs )
% 0.19/0.47 = ( ( nth_list_list_a @ Xs @ I3 )
% 0.19/0.47 = X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_same_conv
% 0.19/0.47 thf(fact_138_list__update__same__conv,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_a,X2: a] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ( ( list_update_a @ Xs @ I3 @ X2 )
% 0.19/0.47 = Xs )
% 0.19/0.47 = ( ( nth_a @ Xs @ I3 )
% 0.19/0.47 = X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_same_conv
% 0.19/0.47 thf(fact_139_list__update__same__conv,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_a,X2: list_a] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ( ( list_update_list_a @ Xs @ I3 @ X2 )
% 0.19/0.47 = Xs )
% 0.19/0.47 = ( ( nth_list_a @ Xs @ I3 )
% 0.19/0.47 = X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_same_conv
% 0.19/0.47 thf(fact_140_list__update__same__conv,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_nat,X2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ( ( list_update_nat @ Xs @ I3 @ X2 )
% 0.19/0.47 = Xs )
% 0.19/0.47 = ( ( nth_nat @ Xs @ I3 )
% 0.19/0.47 = X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_same_conv
% 0.19/0.47 thf(fact_141_set__swap,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_nat,J2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( ( set_list_nat2 @ ( list_update_list_nat @ ( list_update_list_nat @ Xs @ I3 @ ( nth_list_nat @ Xs @ J2 ) ) @ J2 @ ( nth_list_nat @ Xs @ I3 ) ) )
% 0.19/0.47 = ( set_list_nat2 @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % set_swap
% 0.19/0.47 thf(fact_142_set__swap,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_list_a,J2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( ( set_list_list_a2 @ ( list_u1330012152list_a @ ( list_u1330012152list_a @ Xs @ I3 @ ( nth_list_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_list_a @ Xs @ I3 ) ) )
% 0.19/0.47 = ( set_list_list_a2 @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % set_swap
% 0.19/0.47 thf(fact_143_set__swap,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_a,J2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ( set_a2 @ ( list_update_a @ ( list_update_a @ Xs @ I3 @ ( nth_a @ Xs @ J2 ) ) @ J2 @ ( nth_a @ Xs @ I3 ) ) )
% 0.19/0.47 = ( set_a2 @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % set_swap
% 0.19/0.47 thf(fact_144_set__swap,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_a,J2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ( set_list_a2 @ ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_a @ Xs @ I3 ) ) )
% 0.19/0.47 = ( set_list_a2 @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % set_swap
% 0.19/0.47 thf(fact_145_set__swap,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_nat,J2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ J2 ) ) @ J2 @ ( nth_nat @ Xs @ I3 ) ) )
% 0.19/0.47 = ( set_nat2 @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % set_swap
% 0.19/0.47 thf(fact_146_list__desc__trans,axiom,
% 0.19/0.47 ( list_desc_set_nat
% 0.19/0.47 = ( ^ [Xs2: list_set_nat] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_s577819178et_nat @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.19/0.47 => ( ord_less_eq_set_nat @ ( nth_set_nat @ Xs2 @ J ) @ ( nth_set_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_desc_trans
% 0.19/0.47 thf(fact_147_list__desc__trans,axiom,
% 0.19/0.47 ( list_desc_set_list_a
% 0.19/0.47 = ( ^ [Xs2: list_set_list_a] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_s1635937238list_a @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.19/0.47 => ( ord_le1301786372list_a @ ( nth_set_list_a @ Xs2 @ J ) @ ( nth_set_list_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_desc_trans
% 0.19/0.47 thf(fact_148_list__desc__trans,axiom,
% 0.19/0.47 ( list_desc_set_a
% 0.19/0.47 = ( ^ [Xs2: list_set_a] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_size_list_set_a @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.19/0.47 => ( ord_less_eq_set_a @ ( nth_set_a @ Xs2 @ J ) @ ( nth_set_a @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_desc_trans
% 0.19/0.47 thf(fact_149_list__desc__trans,axiom,
% 0.19/0.47 ( list_desc_nat
% 0.19/0.47 = ( ^ [Xs2: list_nat] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.19/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_desc_trans
% 0.19/0.47 thf(fact_150_list__asc__trans,axiom,
% 0.19/0.47 ( list_asc_set_nat
% 0.19/0.47 = ( ^ [Xs2: list_set_nat] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_s577819178et_nat @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.19/0.47 => ( ord_less_eq_set_nat @ ( nth_set_nat @ Xs2 @ I2 ) @ ( nth_set_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_asc_trans
% 0.19/0.47 thf(fact_151_list__asc__trans,axiom,
% 0.19/0.47 ( list_asc_set_list_a
% 0.19/0.47 = ( ^ [Xs2: list_set_list_a] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_s1635937238list_a @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.19/0.47 => ( ord_le1301786372list_a @ ( nth_set_list_a @ Xs2 @ I2 ) @ ( nth_set_list_a @ Xs2 @ J ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_asc_trans
% 0.19/0.47 thf(fact_152_list__asc__trans,axiom,
% 0.19/0.47 ( list_asc_set_a
% 0.19/0.47 = ( ^ [Xs2: list_set_a] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_size_list_set_a @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.19/0.47 => ( ord_less_eq_set_a @ ( nth_set_a @ Xs2 @ I2 ) @ ( nth_set_a @ Xs2 @ J ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_asc_trans
% 0.19/0.47 thf(fact_153_list__asc__trans,axiom,
% 0.19/0.47 ( list_asc_nat
% 0.19/0.47 = ( ^ [Xs2: list_nat] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.19/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_asc_trans
% 0.19/0.47 thf(fact_154_mem__Collect__eq,axiom,
% 0.19/0.47 ! [A2: nat,P: nat > $o] :
% 0.19/0.47 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 0.19/0.47 = ( P @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % mem_Collect_eq
% 0.19/0.47 thf(fact_155_mem__Collect__eq,axiom,
% 0.19/0.47 ! [A2: list_a,P: list_a > $o] :
% 0.19/0.47 ( ( member_list_a @ A2 @ ( collect_list_a @ P ) )
% 0.19/0.47 = ( P @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % mem_Collect_eq
% 0.19/0.47 thf(fact_156_mem__Collect__eq,axiom,
% 0.19/0.47 ! [A2: a,P: a > $o] :
% 0.19/0.47 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.19/0.47 = ( P @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % mem_Collect_eq
% 0.19/0.47 thf(fact_157_Collect__mem__eq,axiom,
% 0.19/0.47 ! [A: set_nat] :
% 0.19/0.47 ( ( collect_nat
% 0.19/0.47 @ ^ [X3: nat] : ( member_nat @ X3 @ A ) )
% 0.19/0.47 = A ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_mem_eq
% 0.19/0.47 thf(fact_158_Collect__mem__eq,axiom,
% 0.19/0.47 ! [A: set_list_a] :
% 0.19/0.47 ( ( collect_list_a
% 0.19/0.47 @ ^ [X3: list_a] : ( member_list_a @ X3 @ A ) )
% 0.19/0.47 = A ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_mem_eq
% 0.19/0.47 thf(fact_159_Collect__mem__eq,axiom,
% 0.19/0.47 ! [A: set_a] :
% 0.19/0.47 ( ( collect_a
% 0.19/0.47 @ ^ [X3: a] : ( member_a @ X3 @ A ) )
% 0.19/0.47 = A ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_mem_eq
% 0.19/0.47 thf(fact_160_distinct__swap,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_nat,J2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( ( distinct_list_nat @ ( list_update_list_nat @ ( list_update_list_nat @ Xs @ I3 @ ( nth_list_nat @ Xs @ J2 ) ) @ J2 @ ( nth_list_nat @ Xs @ I3 ) ) )
% 0.19/0.47 = ( distinct_list_nat @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_swap
% 0.19/0.47 thf(fact_161_distinct__swap,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_list_a,J2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( ( distinct_list_list_a @ ( list_u1330012152list_a @ ( list_u1330012152list_a @ Xs @ I3 @ ( nth_list_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_list_a @ Xs @ I3 ) ) )
% 0.19/0.47 = ( distinct_list_list_a @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_swap
% 0.19/0.47 thf(fact_162_distinct__swap,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_a,J2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ( distinct_a @ ( list_update_a @ ( list_update_a @ Xs @ I3 @ ( nth_a @ Xs @ J2 ) ) @ J2 @ ( nth_a @ Xs @ I3 ) ) )
% 0.19/0.47 = ( distinct_a @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_swap
% 0.19/0.47 thf(fact_163_distinct__swap,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_list_a,J2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ( distinct_list_a @ ( list_update_list_a @ ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ J2 ) ) @ J2 @ ( nth_list_a @ Xs @ I3 ) ) )
% 0.19/0.47 = ( distinct_list_a @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_swap
% 0.19/0.47 thf(fact_164_distinct__swap,axiom,
% 0.19/0.47 ! [I3: nat,Xs: list_nat,J2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ( distinct_nat @ ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ J2 ) ) @ J2 @ ( nth_nat @ Xs @ I3 ) ) )
% 0.19/0.47 = ( distinct_nat @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_swap
% 0.19/0.47 thf(fact_165_f__rangeE,axiom,
% 0.19/0.47 ! [X2: list_nat,Xs: list_list_nat] :
% 0.19/0.47 ( ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ top_top_set_nat ) )
% 0.19/0.47 => ~ ! [N2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N2 @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( X2
% 0.19/0.47 != ( nth_list_nat @ Xs @ N2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_rangeE
% 0.19/0.47 thf(fact_166_f__rangeE,axiom,
% 0.19/0.47 ! [X2: list_list_a,Xs: list_list_list_a] :
% 0.19/0.47 ( ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ top_top_set_nat ) )
% 0.19/0.47 => ~ ! [N2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N2 @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( X2
% 0.19/0.47 != ( nth_list_list_a @ Xs @ N2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_rangeE
% 0.19/0.47 thf(fact_167_f__rangeE,axiom,
% 0.19/0.47 ! [X2: a,Xs: list_a] :
% 0.19/0.47 ( ( member_a @ X2 @ ( f_image_a @ Xs @ top_top_set_nat ) )
% 0.19/0.47 => ~ ! [N2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( X2
% 0.19/0.47 != ( nth_a @ Xs @ N2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_rangeE
% 0.19/0.47 thf(fact_168_f__rangeE,axiom,
% 0.19/0.47 ! [X2: list_a,Xs: list_list_a] :
% 0.19/0.47 ( ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ top_top_set_nat ) )
% 0.19/0.47 => ~ ! [N2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( X2
% 0.19/0.47 != ( nth_list_a @ Xs @ N2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_rangeE
% 0.19/0.47 thf(fact_169_f__rangeE,axiom,
% 0.19/0.47 ! [X2: nat,Xs: list_nat] :
% 0.19/0.47 ( ( member_nat @ X2 @ ( f_image_nat @ Xs @ top_top_set_nat ) )
% 0.19/0.47 => ~ ! [N2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( X2
% 0.19/0.47 != ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_rangeE
% 0.19/0.47 thf(fact_170_f__rangeI,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_list_nat] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( member_list_nat @ ( nth_list_nat @ Xs @ N ) @ ( f_image_list_nat @ Xs @ top_top_set_nat ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_rangeI
% 0.19/0.47 thf(fact_171_f__rangeI,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_list_list_a] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( member_list_list_a @ ( nth_list_list_a @ Xs @ N ) @ ( f_image_list_list_a @ Xs @ top_top_set_nat ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_rangeI
% 0.19/0.47 thf(fact_172_f__rangeI,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_a] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( member_a @ ( nth_a @ Xs @ N ) @ ( f_image_a @ Xs @ top_top_set_nat ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_rangeI
% 0.19/0.47 thf(fact_173_f__rangeI,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_list_a] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( member_list_a @ ( nth_list_a @ Xs @ N ) @ ( f_image_list_a @ Xs @ top_top_set_nat ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_rangeI
% 0.19/0.47 thf(fact_174_f__rangeI,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_nat] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( f_image_nat @ Xs @ top_top_set_nat ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_rangeI
% 0.19/0.47 thf(fact_175_f__range__eqI,axiom,
% 0.19/0.47 ! [X2: list_nat,Xs: list_list_nat,N: nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_list_nat @ Xs @ N ) )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s1898481668st_nat @ Xs ) )
% 0.19/0.47 => ( member_list_nat @ X2 @ ( f_image_list_nat @ Xs @ top_top_set_nat ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_range_eqI
% 0.19/0.47 thf(fact_176_f__range__eqI,axiom,
% 0.19/0.47 ! [X2: list_list_a,Xs: list_list_list_a,N: nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_list_list_a @ Xs @ N ) )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.19/0.47 => ( member_list_list_a @ X2 @ ( f_image_list_list_a @ Xs @ top_top_set_nat ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_range_eqI
% 0.19/0.47 thf(fact_177_f__range__eqI,axiom,
% 0.19/0.47 ! [X2: a,Xs: list_a,N: nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_a @ Xs @ N ) )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( member_a @ X2 @ ( f_image_a @ Xs @ top_top_set_nat ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_range_eqI
% 0.19/0.47 thf(fact_178_f__range__eqI,axiom,
% 0.19/0.47 ! [X2: list_a,Xs: list_list_a,N: nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_list_a @ Xs @ N ) )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( member_list_a @ X2 @ ( f_image_list_a @ Xs @ top_top_set_nat ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_range_eqI
% 0.19/0.47 thf(fact_179_f__range__eqI,axiom,
% 0.19/0.47 ! [X2: nat,Xs: list_nat,N: nat] :
% 0.19/0.47 ( ( X2
% 0.19/0.47 = ( nth_nat @ Xs @ N ) )
% 0.19/0.47 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( member_nat @ X2 @ ( f_image_nat @ Xs @ top_top_set_nat ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_range_eqI
% 0.19/0.47 thf(fact_180_f__image__subsetI,axiom,
% 0.19/0.47 ! [A: set_nat,Xs: list_list_nat,B: set_list_nat] :
% 0.19/0.47 ( ! [N2: nat] :
% 0.19/0.47 ( ( ( member_nat @ N2 @ A )
% 0.19/0.47 & ( ord_less_nat @ N2 @ ( size_s1898481668st_nat @ Xs ) ) )
% 0.19/0.47 => ( member_list_nat @ ( nth_list_nat @ Xs @ N2 ) @ B ) )
% 0.19/0.47 => ( ord_le1747345782st_nat @ ( f_image_list_nat @ Xs @ A ) @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_subsetI
% 0.19/0.47 thf(fact_181_f__image__subsetI,axiom,
% 0.19/0.47 ! [A: set_nat,Xs: list_list_list_a,B: set_list_list_a] :
% 0.19/0.47 ( ! [N2: nat] :
% 0.19/0.47 ( ( ( member_nat @ N2 @ A )
% 0.19/0.47 & ( ord_less_nat @ N2 @ ( size_s575106428list_a @ Xs ) ) )
% 0.19/0.47 => ( member_list_list_a @ ( nth_list_list_a @ Xs @ N2 ) @ B ) )
% 0.19/0.47 => ( ord_le1756736906list_a @ ( f_image_list_list_a @ Xs @ A ) @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_subsetI
% 0.19/0.47 thf(fact_182_f__image__subsetI,axiom,
% 0.19/0.47 ! [A: set_nat,Xs: list_a,B: set_a] :
% 0.19/0.47 ( ! [N2: nat] :
% 0.19/0.47 ( ( ( member_nat @ N2 @ A )
% 0.19/0.47 & ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) ) )
% 0.19/0.47 => ( member_a @ ( nth_a @ Xs @ N2 ) @ B ) )
% 0.19/0.47 => ( ord_less_eq_set_a @ ( f_image_a @ Xs @ A ) @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_subsetI
% 0.19/0.47 thf(fact_183_f__image__subsetI,axiom,
% 0.19/0.47 ! [A: set_nat,Xs: list_list_a,B: set_list_a] :
% 0.19/0.47 ( ! [N2: nat] :
% 0.19/0.47 ( ( ( member_nat @ N2 @ A )
% 0.19/0.47 & ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) ) )
% 0.19/0.47 => ( member_list_a @ ( nth_list_a @ Xs @ N2 ) @ B ) )
% 0.19/0.47 => ( ord_le1301786372list_a @ ( f_image_list_a @ Xs @ A ) @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_subsetI
% 0.19/0.47 thf(fact_184_f__image__subsetI,axiom,
% 0.19/0.47 ! [A: set_nat,Xs: list_nat,B: set_nat] :
% 0.19/0.47 ( ! [N2: nat] :
% 0.19/0.47 ( ( ( member_nat @ N2 @ A )
% 0.19/0.47 & ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) ) )
% 0.19/0.47 => ( member_nat @ ( nth_nat @ Xs @ N2 ) @ B ) )
% 0.19/0.47 => ( ord_less_eq_set_nat @ ( f_image_nat @ Xs @ A ) @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_subsetI
% 0.19/0.47 thf(fact_185_f__image__subset__iff,axiom,
% 0.19/0.47 ! [Xs: list_a,A: set_nat,B: set_a] :
% 0.19/0.47 ( ( ord_less_eq_set_a @ ( f_image_a @ Xs @ A ) @ B )
% 0.19/0.47 = ( ! [X3: nat] :
% 0.19/0.47 ( ( member_nat @ X3 @ A )
% 0.19/0.47 => ( ( ord_less_nat @ X3 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( member_a @ ( nth_a @ Xs @ X3 ) @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_subset_iff
% 0.19/0.47 thf(fact_186_f__image__subset__iff,axiom,
% 0.19/0.47 ! [Xs: list_list_a,A: set_nat,B: set_list_a] :
% 0.19/0.47 ( ( ord_le1301786372list_a @ ( f_image_list_a @ Xs @ A ) @ B )
% 0.19/0.47 = ( ! [X3: nat] :
% 0.19/0.47 ( ( member_nat @ X3 @ A )
% 0.19/0.47 => ( ( ord_less_nat @ X3 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( member_list_a @ ( nth_list_a @ Xs @ X3 ) @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_subset_iff
% 0.19/0.47 thf(fact_187_f__image__subset__iff,axiom,
% 0.19/0.47 ! [Xs: list_nat,A: set_nat,B: set_nat] :
% 0.19/0.47 ( ( ord_less_eq_set_nat @ ( f_image_nat @ Xs @ A ) @ B )
% 0.19/0.47 = ( ! [X3: nat] :
% 0.19/0.47 ( ( member_nat @ X3 @ A )
% 0.19/0.47 => ( ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( member_nat @ ( nth_nat @ Xs @ X3 ) @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_subset_iff
% 0.19/0.47 thf(fact_188_list__update__beyond,axiom,
% 0.19/0.47 ! [Xs: list_a,I3: nat,X2: a] :
% 0.19/0.47 ( ( ord_less_eq_nat @ ( size_size_list_a @ Xs ) @ I3 )
% 0.19/0.47 => ( ( list_update_a @ Xs @ I3 @ X2 )
% 0.19/0.47 = Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_beyond
% 0.19/0.47 thf(fact_189_list__update__beyond,axiom,
% 0.19/0.47 ! [Xs: list_list_a,I3: nat,X2: list_a] :
% 0.19/0.47 ( ( ord_less_eq_nat @ ( size_s1427607542list_a @ Xs ) @ I3 )
% 0.19/0.47 => ( ( list_update_list_a @ Xs @ I3 @ X2 )
% 0.19/0.47 = Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_beyond
% 0.19/0.47 thf(fact_190_list__update__beyond,axiom,
% 0.19/0.47 ! [Xs: list_nat,I3: nat,X2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I3 )
% 0.19/0.47 => ( ( list_update_nat @ Xs @ I3 @ X2 )
% 0.19/0.47 = Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_update_beyond
% 0.19/0.47 thf(fact_191_less__mono__imp__le__mono,axiom,
% 0.19/0.47 ! [F: nat > nat,I3: nat,J2: nat] :
% 0.19/0.47 ( ! [I: nat,J3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I @ J3 )
% 0.19/0.47 => ( ord_less_nat @ ( F @ I ) @ ( F @ J3 ) ) )
% 0.19/0.47 => ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.19/0.47 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( F @ J2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_mono_imp_le_mono
% 0.19/0.47 thf(fact_192_le__neq__implies__less,axiom,
% 0.19/0.47 ! [M: nat,N: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.19/0.47 => ( ( M != N )
% 0.19/0.47 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_neq_implies_less
% 0.19/0.47 thf(fact_193_less__or__eq__imp__le,axiom,
% 0.19/0.47 ! [M: nat,N: nat] :
% 0.19/0.47 ( ( ( ord_less_nat @ M @ N )
% 0.19/0.47 | ( M = N ) )
% 0.19/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_or_eq_imp_le
% 0.19/0.47 thf(fact_194_le__eq__less__or__eq,axiom,
% 0.19/0.47 ( ord_less_eq_nat
% 0.19/0.47 = ( ^ [M3: nat,N3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M3 @ N3 )
% 0.19/0.47 | ( M3 = N3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_eq_less_or_eq
% 0.19/0.47 thf(fact_195_less__imp__le__nat,axiom,
% 0.19/0.47 ! [M: nat,N: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M @ N )
% 0.19/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_le_nat
% 0.19/0.47 thf(fact_196_nat__less__le,axiom,
% 0.19/0.47 ( ord_less_nat
% 0.19/0.47 = ( ^ [M3: nat,N3: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ M3 @ N3 )
% 0.19/0.47 & ( M3 != N3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nat_less_le
% 0.19/0.47 thf(fact_197_distinct__Ex1,axiom,
% 0.19/0.47 ! [Xs: list_a,X2: a] :
% 0.19/0.47 ( ( distinct_a @ Xs )
% 0.19/0.47 => ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
% 0.19/0.47 => ? [X5: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 & ( ( nth_a @ Xs @ X5 )
% 0.19/0.47 = X2 )
% 0.19/0.47 & ! [Y3: nat] :
% 0.19/0.47 ( ( ( ord_less_nat @ Y3 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 & ( ( nth_a @ Xs @ Y3 )
% 0.19/0.47 = X2 ) )
% 0.19/0.47 => ( Y3 = X5 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_Ex1
% 0.19/0.47 thf(fact_198_distinct__Ex1,axiom,
% 0.19/0.47 ! [Xs: list_list_a,X2: list_a] :
% 0.19/0.47 ( ( distinct_list_a @ Xs )
% 0.19/0.47 => ( ( member_list_a @ X2 @ ( set_list_a2 @ Xs ) )
% 0.19/0.47 => ? [X5: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 & ( ( nth_list_a @ Xs @ X5 )
% 0.19/0.47 = X2 )
% 0.19/0.47 & ! [Y3: nat] :
% 0.19/0.47 ( ( ( ord_less_nat @ Y3 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 & ( ( nth_list_a @ Xs @ Y3 )
% 0.19/0.47 = X2 ) )
% 0.19/0.47 => ( Y3 = X5 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_Ex1
% 0.19/0.47 thf(fact_199_distinct__Ex1,axiom,
% 0.19/0.47 ! [Xs: list_nat,X2: nat] :
% 0.19/0.47 ( ( distinct_nat @ Xs )
% 0.19/0.47 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.19/0.47 => ? [X5: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 & ( ( nth_nat @ Xs @ X5 )
% 0.19/0.47 = X2 )
% 0.19/0.47 & ! [Y3: nat] :
% 0.19/0.47 ( ( ( ord_less_nat @ Y3 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 & ( ( nth_nat @ Xs @ Y3 )
% 0.19/0.47 = X2 ) )
% 0.19/0.47 => ( Y3 = X5 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_Ex1
% 0.19/0.47 thf(fact_200_list__strict__asc__distinct,axiom,
% 0.19/0.47 ! [Xs: list_nat] :
% 0.19/0.47 ( ( list_strict_asc_nat @ Xs )
% 0.19/0.47 => ( distinct_nat @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_strict_asc_distinct
% 0.19/0.47 thf(fact_201_list__strict__desc__distinct,axiom,
% 0.19/0.47 ! [Xs: list_nat] :
% 0.19/0.47 ( ( list_strict_desc_nat @ Xs )
% 0.19/0.47 => ( distinct_nat @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_strict_desc_distinct
% 0.19/0.47 thf(fact_202_list__strict__asc__trans__le,axiom,
% 0.19/0.47 ! [Xs: list_nat] :
% 0.19/0.47 ( ( list_strict_asc_nat @ Xs )
% 0.19/0.47 => ! [J4: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J4 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ! [I5: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ I5 @ J4 )
% 0.19/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I5 ) @ ( nth_nat @ Xs @ J4 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_strict_asc_trans_le
% 0.19/0.47 thf(fact_203_list__asc__trans__le,axiom,
% 0.19/0.47 ( list_asc_nat
% 0.19/0.47 = ( ^ [Xs2: list_nat] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ I2 @ J )
% 0.19/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_asc_trans_le
% 0.19/0.47 thf(fact_204_list__desc__trans__le,axiom,
% 0.19/0.47 ( list_desc_nat
% 0.19/0.47 = ( ^ [Xs2: list_nat] :
% 0.19/0.47 ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.19/0.47 => ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ I2 @ J )
% 0.19/0.47 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_desc_trans_le
% 0.19/0.47 thf(fact_205_nth__eq__iff__index__eq,axiom,
% 0.19/0.47 ! [Xs: list_a,I3: nat,J2: nat] :
% 0.19/0.47 ( ( distinct_a @ Xs )
% 0.19/0.47 => ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ( ( nth_a @ Xs @ I3 )
% 0.19/0.47 = ( nth_a @ Xs @ J2 ) )
% 0.19/0.47 = ( I3 = J2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_eq_iff_index_eq
% 0.19/0.47 thf(fact_206_nth__eq__iff__index__eq,axiom,
% 0.19/0.47 ! [Xs: list_list_a,I3: nat,J2: nat] :
% 0.19/0.47 ( ( distinct_list_a @ Xs )
% 0.19/0.47 => ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ( ( nth_list_a @ Xs @ I3 )
% 0.19/0.47 = ( nth_list_a @ Xs @ J2 ) )
% 0.19/0.47 = ( I3 = J2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_eq_iff_index_eq
% 0.19/0.47 thf(fact_207_nth__eq__iff__index__eq,axiom,
% 0.19/0.47 ! [Xs: list_nat,I3: nat,J2: nat] :
% 0.19/0.47 ( ( distinct_nat @ Xs )
% 0.19/0.47 => ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ( ( nth_nat @ Xs @ I3 )
% 0.19/0.47 = ( nth_nat @ Xs @ J2 ) )
% 0.19/0.47 = ( I3 = J2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_eq_iff_index_eq
% 0.19/0.47 thf(fact_208_distinct__conv__nth,axiom,
% 0.19/0.47 ( distinct_a
% 0.19/0.47 = ( ^ [Xs2: list_a] :
% 0.19/0.47 ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
% 0.19/0.47 => ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_size_list_a @ Xs2 ) )
% 0.19/0.47 => ( ( I2 != J )
% 0.19/0.47 => ( ( nth_a @ Xs2 @ I2 )
% 0.19/0.47 != ( nth_a @ Xs2 @ J ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_conv_nth
% 0.19/0.47 thf(fact_209_distinct__conv__nth,axiom,
% 0.19/0.47 ( distinct_list_a
% 0.19/0.47 = ( ^ [Xs2: list_list_a] :
% 0.19/0.47 ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
% 0.19/0.47 => ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_s1427607542list_a @ Xs2 ) )
% 0.19/0.47 => ( ( I2 != J )
% 0.19/0.47 => ( ( nth_list_a @ Xs2 @ I2 )
% 0.19/0.47 != ( nth_list_a @ Xs2 @ J ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_conv_nth
% 0.19/0.47 thf(fact_210_distinct__conv__nth,axiom,
% 0.19/0.47 ( distinct_nat
% 0.19/0.47 = ( ^ [Xs2: list_nat] :
% 0.19/0.47 ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.19/0.47 => ! [J: nat] :
% 0.19/0.47 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 0.19/0.47 => ( ( I2 != J )
% 0.19/0.47 => ( ( nth_nat @ Xs2 @ I2 )
% 0.19/0.47 != ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % distinct_conv_nth
% 0.19/0.47 thf(fact_211_all__set__conv__all__nth,axiom,
% 0.19/0.47 ! [Xs: list_a,P: a > $o] :
% 0.19/0.47 ( ( ! [X3: a] :
% 0.19/0.47 ( ( member_a @ X3 @ ( set_a2 @ Xs ) )
% 0.19/0.47 => ( P @ X3 ) ) )
% 0.19/0.47 = ( ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( P @ ( nth_a @ Xs @ I2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % all_set_conv_all_nth
% 0.19/0.47 thf(fact_212_all__set__conv__all__nth,axiom,
% 0.19/0.47 ! [Xs: list_list_a,P: list_a > $o] :
% 0.19/0.47 ( ( ! [X3: list_a] :
% 0.19/0.47 ( ( member_list_a @ X3 @ ( set_list_a2 @ Xs ) )
% 0.19/0.47 => ( P @ X3 ) ) )
% 0.19/0.47 = ( ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( P @ ( nth_list_a @ Xs @ I2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % all_set_conv_all_nth
% 0.19/0.47 thf(fact_213_all__set__conv__all__nth,axiom,
% 0.19/0.47 ! [Xs: list_nat,P: nat > $o] :
% 0.19/0.47 ( ( ! [X3: nat] :
% 0.19/0.47 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.19/0.47 => ( P @ X3 ) ) )
% 0.19/0.47 = ( ! [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( P @ ( nth_nat @ Xs @ I2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % all_set_conv_all_nth
% 0.19/0.47 thf(fact_214_all__nth__imp__all__set,axiom,
% 0.19/0.47 ! [Xs: list_a,P: a > $o,X2: a] :
% 0.19/0.47 ( ! [I: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( P @ ( nth_a @ Xs @ I ) ) )
% 0.19/0.47 => ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
% 0.19/0.47 => ( P @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % all_nth_imp_all_set
% 0.19/0.47 thf(fact_215_all__nth__imp__all__set,axiom,
% 0.19/0.47 ! [Xs: list_list_a,P: list_a > $o,X2: list_a] :
% 0.19/0.47 ( ! [I: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( P @ ( nth_list_a @ Xs @ I ) ) )
% 0.19/0.47 => ( ( member_list_a @ X2 @ ( set_list_a2 @ Xs ) )
% 0.19/0.47 => ( P @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % all_nth_imp_all_set
% 0.19/0.47 thf(fact_216_all__nth__imp__all__set,axiom,
% 0.19/0.47 ! [Xs: list_nat,P: nat > $o,X2: nat] :
% 0.19/0.47 ( ! [I: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( P @ ( nth_nat @ Xs @ I ) ) )
% 0.19/0.47 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.19/0.47 => ( P @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % all_nth_imp_all_set
% 0.19/0.47 thf(fact_217_in__set__conv__nth,axiom,
% 0.19/0.47 ! [X2: a,Xs: list_a] :
% 0.19/0.47 ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
% 0.19/0.47 = ( ? [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 & ( ( nth_a @ Xs @ I2 )
% 0.19/0.47 = X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % in_set_conv_nth
% 0.19/0.47 thf(fact_218_in__set__conv__nth,axiom,
% 0.19/0.47 ! [X2: list_a,Xs: list_list_a] :
% 0.19/0.47 ( ( member_list_a @ X2 @ ( set_list_a2 @ Xs ) )
% 0.19/0.47 = ( ? [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 & ( ( nth_list_a @ Xs @ I2 )
% 0.19/0.47 = X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % in_set_conv_nth
% 0.19/0.47 thf(fact_219_in__set__conv__nth,axiom,
% 0.19/0.47 ! [X2: nat,Xs: list_nat] :
% 0.19/0.47 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.19/0.47 = ( ? [I2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 & ( ( nth_nat @ Xs @ I2 )
% 0.19/0.47 = X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % in_set_conv_nth
% 0.19/0.47 thf(fact_220_list__ball__nth,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_a,P: a > $o] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( ! [X5: a] :
% 0.19/0.47 ( ( member_a @ X5 @ ( set_a2 @ Xs ) )
% 0.19/0.47 => ( P @ X5 ) )
% 0.19/0.47 => ( P @ ( nth_a @ Xs @ N ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_ball_nth
% 0.19/0.47 thf(fact_221_list__ball__nth,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_list_a,P: list_a > $o] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( ! [X5: list_a] :
% 0.19/0.47 ( ( member_list_a @ X5 @ ( set_list_a2 @ Xs ) )
% 0.19/0.47 => ( P @ X5 ) )
% 0.19/0.47 => ( P @ ( nth_list_a @ Xs @ N ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_ball_nth
% 0.19/0.47 thf(fact_222_list__ball__nth,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( ! [X5: nat] :
% 0.19/0.47 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 0.19/0.47 => ( P @ X5 ) )
% 0.19/0.47 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list_ball_nth
% 0.19/0.47 thf(fact_223_nth__mem,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_a] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( member_a @ ( nth_a @ Xs @ N ) @ ( set_a2 @ Xs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_mem
% 0.19/0.47 thf(fact_224_nth__mem,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_list_a] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( member_list_a @ ( nth_list_a @ Xs @ N ) @ ( set_list_a2 @ Xs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_mem
% 0.19/0.47 thf(fact_225_nth__mem,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_nat] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nth_mem
% 0.19/0.47 thf(fact_226_set__update__memI,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_a,X2: a] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( member_a @ X2 @ ( set_a2 @ ( list_update_a @ Xs @ N @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % set_update_memI
% 0.19/0.47 thf(fact_227_set__update__memI,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_list_a,X2: list_a] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( member_list_a @ X2 @ ( set_list_a2 @ ( list_update_list_a @ Xs @ N @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % set_update_memI
% 0.19/0.47 thf(fact_228_set__update__memI,axiom,
% 0.19/0.47 ! [N: nat,Xs: list_nat,X2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % set_update_memI
% 0.19/0.47 thf(fact_229_f__image__eq__set,axiom,
% 0.19/0.47 ! [Xs: list_a,A: set_nat] :
% 0.19/0.47 ( ! [N2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs ) )
% 0.19/0.47 => ( member_nat @ N2 @ A ) )
% 0.19/0.47 => ( ( f_image_a @ Xs @ A )
% 0.19/0.47 = ( set_a2 @ Xs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_eq_set
% 0.19/0.47 thf(fact_230_f__image__eq__set,axiom,
% 0.19/0.47 ! [Xs: list_list_a,A: set_nat] :
% 0.19/0.47 ( ! [N2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N2 @ ( size_s1427607542list_a @ Xs ) )
% 0.19/0.47 => ( member_nat @ N2 @ A ) )
% 0.19/0.47 => ( ( f_image_list_a @ Xs @ A )
% 0.19/0.47 = ( set_list_a2 @ Xs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_eq_set
% 0.19/0.47 thf(fact_231_f__image__eq__set,axiom,
% 0.19/0.47 ! [Xs: list_nat,A: set_nat] :
% 0.19/0.47 ( ! [N2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 0.19/0.47 => ( member_nat @ N2 @ A ) )
% 0.19/0.47 => ( ( f_image_nat @ Xs @ A )
% 0.19/0.47 = ( set_nat2 @ Xs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % f_image_eq_set
% 0.19/0.47 thf(fact_232_order__refl,axiom,
% 0.19/0.47 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 0.19/0.47
% 0.19/0.47 % order_refl
% 0.19/0.47 thf(fact_233_Nat_Oex__has__greatest__nat,axiom,
% 0.19/0.47 ! [P: nat > $o,K: nat,B2: nat] :
% 0.19/0.47 ( ( P @ K )
% 0.19/0.47 => ( ! [Y4: nat] :
% 0.19/0.47 ( ( P @ Y4 )
% 0.19/0.47 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 0.19/0.47 => ? [X5: nat] :
% 0.19/0.47 ( ( P @ X5 )
% 0.19/0.47 & ! [Y3: nat] :
% 0.19/0.47 ( ( P @ Y3 )
% 0.19/0.47 => ( ord_less_eq_nat @ Y3 @ X5 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Nat.ex_has_greatest_nat
% 0.19/0.47 thf(fact_234_nat__le__linear,axiom,
% 0.19/0.47 ! [M: nat,N: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.19/0.47 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.19/0.47
% 0.19/0.47 % nat_le_linear
% 0.19/0.47 thf(fact_235_le__antisym,axiom,
% 0.19/0.47 ! [M: nat,N: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.19/0.47 => ( ( ord_less_eq_nat @ N @ M )
% 0.19/0.47 => ( M = N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_antisym
% 0.19/0.47 thf(fact_236_eq__imp__le,axiom,
% 0.19/0.47 ! [M: nat,N: nat] :
% 0.19/0.47 ( ( M = N )
% 0.19/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.19/0.47
% 0.19/0.47 % eq_imp_le
% 0.19/0.47 thf(fact_237_le__trans,axiom,
% 0.19/0.47 ! [I3: nat,J2: nat,K: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ I3 @ J2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ J2 @ K )
% 0.19/0.47 => ( ord_less_eq_nat @ I3 @ K ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_trans
% 0.19/0.47 thf(fact_238_le__refl,axiom,
% 0.19/0.47 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.19/0.47
% 0.19/0.47 % le_refl
% 0.19/0.47 thf(fact_239_dual__order_Oantisym,axiom,
% 0.19/0.47 ! [B2: nat,A2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.19/0.47 => ( A2 = B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.antisym
% 0.19/0.47 thf(fact_240_dual__order_Oeq__iff,axiom,
% 0.19/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.19/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.19/0.47 & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.eq_iff
% 0.19/0.47 thf(fact_241_dual__order_Otrans,axiom,
% 0.19/0.47 ! [B2: nat,A2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ C @ B2 )
% 0.19/0.47 => ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.trans
% 0.19/0.47 thf(fact_242_linorder__wlog,axiom,
% 0.19/0.47 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 0.19/0.47 ( ! [A4: nat,B4: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A4 @ B4 )
% 0.19/0.47 => ( P @ A4 @ B4 ) )
% 0.19/0.47 => ( ! [A4: nat,B4: nat] :
% 0.19/0.47 ( ( P @ B4 @ A4 )
% 0.19/0.47 => ( P @ A4 @ B4 ) )
% 0.19/0.47 => ( P @ A2 @ B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % linorder_wlog
% 0.19/0.47 thf(fact_243_dual__order_Orefl,axiom,
% 0.19/0.47 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.refl
% 0.19/0.47 thf(fact_244_order__trans,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.19/0.47 => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_trans
% 0.19/0.47 thf(fact_245_order__class_Oorder_Oantisym,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.19/0.47 => ( A2 = B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_class.order.antisym
% 0.19/0.47 thf(fact_246_ord__le__eq__trans,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( B2 = C )
% 0.19/0.47 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_le_eq_trans
% 0.19/0.47 thf(fact_247_ord__eq__le__trans,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( A2 = B2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.19/0.47 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_eq_le_trans
% 0.19/0.47 thf(fact_248_order__class_Oorder_Oeq__iff,axiom,
% 0.19/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.19/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.19/0.47 & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_class.order.eq_iff
% 0.19/0.47 thf(fact_249_antisym__conv,axiom,
% 0.19/0.47 ! [Y2: nat,X2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 = ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % antisym_conv
% 0.19/0.47 thf(fact_250_le__cases3,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.19/0.47 ( ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 => ~ ( ord_less_eq_nat @ Y2 @ Z2 ) )
% 0.19/0.47 => ( ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.19/0.47 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
% 0.19/0.47 => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
% 0.19/0.47 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) )
% 0.19/0.47 => ( ( ( ord_less_eq_nat @ Z2 @ Y2 )
% 0.19/0.47 => ~ ( ord_less_eq_nat @ Y2 @ X2 ) )
% 0.19/0.47 => ( ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.19/0.47 => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
% 0.19/0.47 => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
% 0.19/0.47 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_cases3
% 0.19/0.47 thf(fact_251_order_Otrans,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.19/0.47 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.trans
% 0.19/0.47 thf(fact_252_le__cases,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ~ ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_cases
% 0.19/0.47 thf(fact_253_eq__refl,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( X2 = Y2 )
% 0.19/0.47 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % eq_refl
% 0.19/0.47 thf(fact_254_linear,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 | ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % linear
% 0.19/0.47 thf(fact_255_antisym,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.19/0.47 => ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % antisym
% 0.19/0.47 thf(fact_256_eq__iff,axiom,
% 0.19/0.47 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) )
% 0.19/0.47 = ( ^ [X3: nat,Y5: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 0.19/0.47 & ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % eq_iff
% 0.19/0.47 thf(fact_257_ord__le__eq__subst,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ( F @ B2 )
% 0.19/0.47 = C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_le_eq_subst
% 0.19/0.47 thf(fact_258_ord__eq__le__subst,axiom,
% 0.19/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( F @ B2 ) )
% 0.19/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_eq_le_subst
% 0.19/0.47 thf(fact_259_order__subst2,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_subst2
% 0.19/0.47 thf(fact_260_order__subst1,axiom,
% 0.19/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 0.19/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_subst1
% 0.19/0.47 thf(fact_261_ord__eq__less__subst,axiom,
% 0.19/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( A2
% 0.19/0.47 = ( F @ B2 ) )
% 0.19/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_eq_less_subst
% 0.19/0.47 thf(fact_262_ord__less__eq__subst,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ( F @ B2 )
% 0.19/0.47 = C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_less_eq_subst
% 0.19/0.47 thf(fact_263_order__less__subst1,axiom,
% 0.19/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ ( F @ B2 ) )
% 0.19/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_less_subst1
% 0.19/0.47 thf(fact_264_order__less__subst2,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_less_subst2
% 0.19/0.47 thf(fact_265_gt__ex,axiom,
% 0.19/0.47 ! [X2: nat] :
% 0.19/0.47 ? [X_1: nat] : ( ord_less_nat @ X2 @ X_1 ) ).
% 0.19/0.47
% 0.19/0.47 % gt_ex
% 0.19/0.47 thf(fact_266_neqE,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( X2 != Y2 )
% 0.19/0.47 => ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % neqE
% 0.19/0.47 thf(fact_267_neq__iff,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( X2 != Y2 )
% 0.19/0.47 = ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 | ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % neq_iff
% 0.19/0.47 thf(fact_268_order_Oasym,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.47 => ~ ( ord_less_nat @ B2 @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.asym
% 0.19/0.47 thf(fact_269_less__imp__neq,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( X2 != Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_neq
% 0.19/0.47 thf(fact_270_less__asym,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_asym
% 0.19/0.47 thf(fact_271_less__asym_H,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.47 => ~ ( ord_less_nat @ B2 @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_asym'
% 0.19/0.47 thf(fact_272_less__trans,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ( ord_less_nat @ Y2 @ Z2 )
% 0.19/0.47 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_trans
% 0.19/0.47 thf(fact_273_less__linear,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 | ( X2 = Y2 )
% 0.19/0.47 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_linear
% 0.19/0.47 thf(fact_274_less__irrefl,axiom,
% 0.19/0.47 ! [X2: nat] :
% 0.19/0.47 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 0.19/0.47
% 0.19/0.47 % less_irrefl
% 0.19/0.47 thf(fact_275_ord__eq__less__trans,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( A2 = B2 )
% 0.19/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.19/0.47 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_eq_less_trans
% 0.19/0.47 thf(fact_276_ord__less__eq__trans,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( B2 = C )
% 0.19/0.47 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ord_less_eq_trans
% 0.19/0.47 thf(fact_277_dual__order_Oasym,axiom,
% 0.19/0.47 ! [B2: nat,A2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.19/0.47 => ~ ( ord_less_nat @ A2 @ B2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.asym
% 0.19/0.47 thf(fact_278_less__imp__not__eq,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( X2 != Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_not_eq
% 0.19/0.47 thf(fact_279_less__not__sym,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_not_sym
% 0.19/0.47 thf(fact_280_less__induct,axiom,
% 0.19/0.47 ! [P: nat > $o,A2: nat] :
% 0.19/0.47 ( ! [X5: nat] :
% 0.19/0.47 ( ! [Y3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ Y3 @ X5 )
% 0.19/0.47 => ( P @ Y3 ) )
% 0.19/0.47 => ( P @ X5 ) )
% 0.19/0.47 => ( P @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_induct
% 0.19/0.47 thf(fact_281_antisym__conv3,axiom,
% 0.19/0.47 ! [Y2: nat,X2: nat] :
% 0.19/0.47 ( ~ ( ord_less_nat @ Y2 @ X2 )
% 0.19/0.47 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.19/0.47 = ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % antisym_conv3
% 0.19/0.47 thf(fact_282_less__imp__not__eq2,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( Y2 != X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_not_eq2
% 0.19/0.47 thf(fact_283_less__imp__triv,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat,P: $o] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ( ord_less_nat @ Y2 @ X2 )
% 0.19/0.47 => P ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_triv
% 0.19/0.47 thf(fact_284_linorder__cases,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ( X2 != Y2 )
% 0.19/0.47 => ( ord_less_nat @ Y2 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % linorder_cases
% 0.19/0.47 thf(fact_285_dual__order_Oirrefl,axiom,
% 0.19/0.47 ! [A2: nat] :
% 0.19/0.47 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.irrefl
% 0.19/0.47 thf(fact_286_order_Ostrict__trans,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.19/0.47 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.strict_trans
% 0.19/0.47 thf(fact_287_less__imp__not__less,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_not_less
% 0.19/0.47 thf(fact_288_exists__least__iff,axiom,
% 0.19/0.47 ( ( ^ [P3: nat > $o] :
% 0.19/0.47 ? [X: nat] : ( P3 @ X ) )
% 0.19/0.47 = ( ^ [P2: nat > $o] :
% 0.19/0.47 ? [N3: nat] :
% 0.19/0.47 ( ( P2 @ N3 )
% 0.19/0.47 & ! [M3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ M3 @ N3 )
% 0.19/0.47 => ~ ( P2 @ M3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_least_iff
% 0.19/0.47 thf(fact_289_linorder__less__wlog,axiom,
% 0.19/0.47 ! [P: nat > nat > $o,A2: nat,B2: nat] :
% 0.19/0.47 ( ! [A4: nat,B4: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A4 @ B4 )
% 0.19/0.47 => ( P @ A4 @ B4 ) )
% 0.19/0.47 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 0.19/0.47 => ( ! [A4: nat,B4: nat] :
% 0.19/0.47 ( ( P @ B4 @ A4 )
% 0.19/0.47 => ( P @ A4 @ B4 ) )
% 0.19/0.47 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % linorder_less_wlog
% 0.19/0.47 thf(fact_290_dual__order_Ostrict__trans,axiom,
% 0.19/0.47 ! [B2: nat,A2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.19/0.47 => ( ( ord_less_nat @ C @ B2 )
% 0.19/0.47 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.strict_trans
% 0.19/0.47 thf(fact_291_not__less__iff__gr__or__eq,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.19/0.47 = ( ( ord_less_nat @ Y2 @ X2 )
% 0.19/0.47 | ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % not_less_iff_gr_or_eq
% 0.19/0.47 thf(fact_292_order_Ostrict__implies__not__eq,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.47 => ( A2 != B2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.strict_implies_not_eq
% 0.19/0.47 thf(fact_293_dual__order_Ostrict__implies__not__eq,axiom,
% 0.19/0.47 ! [B2: nat,A2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.19/0.47 => ( A2 != B2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.strict_implies_not_eq
% 0.19/0.47 thf(fact_294_order_Onot__eq__order__implies__strict,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat] :
% 0.19/0.47 ( ( A2 != B2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.19/0.47 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.not_eq_order_implies_strict
% 0.19/0.47 thf(fact_295_dual__order_Ostrict__implies__order,axiom,
% 0.19/0.47 ! [B2: nat,A2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.19/0.47 => ( ord_less_eq_nat @ B2 @ A2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.strict_implies_order
% 0.19/0.47 thf(fact_296_dual__order_Ostrict__iff__order,axiom,
% 0.19/0.47 ( ord_less_nat
% 0.19/0.47 = ( ^ [B3: nat,A3: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.19/0.47 & ( A3 != B3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.strict_iff_order
% 0.19/0.47 thf(fact_297_dual__order_Oorder__iff__strict,axiom,
% 0.19/0.47 ( ord_less_eq_nat
% 0.19/0.47 = ( ^ [B3: nat,A3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ B3 @ A3 )
% 0.19/0.47 | ( A3 = B3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.order_iff_strict
% 0.19/0.47 thf(fact_298_order_Ostrict__implies__order,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.47 => ( ord_less_eq_nat @ A2 @ B2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.strict_implies_order
% 0.19/0.47 thf(fact_299_dual__order_Ostrict__trans2,axiom,
% 0.19/0.47 ! [B2: nat,A2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ C @ B2 )
% 0.19/0.47 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.strict_trans2
% 0.19/0.47 thf(fact_300_dual__order_Ostrict__trans1,axiom,
% 0.19/0.47 ! [B2: nat,A2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.19/0.47 => ( ( ord_less_nat @ C @ B2 )
% 0.19/0.47 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dual_order.strict_trans1
% 0.19/0.47 thf(fact_301_order_Ostrict__iff__order,axiom,
% 0.19/0.47 ( ord_less_nat
% 0.19/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.19/0.47 & ( A3 != B3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.strict_iff_order
% 0.19/0.47 thf(fact_302_order_Oorder__iff__strict,axiom,
% 0.19/0.47 ( ord_less_eq_nat
% 0.19/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A3 @ B3 )
% 0.19/0.47 | ( A3 = B3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.order_iff_strict
% 0.19/0.47 thf(fact_303_order_Ostrict__trans2,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.19/0.47 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.strict_trans2
% 0.19/0.47 thf(fact_304_order_Ostrict__trans1,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.19/0.47 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order.strict_trans1
% 0.19/0.47 thf(fact_305_not__le__imp__less,axiom,
% 0.19/0.47 ! [Y2: nat,X2: nat] :
% 0.19/0.47 ( ~ ( ord_less_eq_nat @ Y2 @ X2 )
% 0.19/0.47 => ( ord_less_nat @ X2 @ Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % not_le_imp_less
% 0.19/0.47 thf(fact_306_less__le__not__le,axiom,
% 0.19/0.47 ( ord_less_nat
% 0.19/0.47 = ( ^ [X3: nat,Y5: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 0.19/0.47 & ~ ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_le_not_le
% 0.19/0.47 thf(fact_307_le__imp__less__or__eq,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 | ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_imp_less_or_eq
% 0.19/0.47 thf(fact_308_le__less__linear,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 | ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_less_linear
% 0.19/0.47 thf(fact_309_less__le__trans,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ Y2 @ Z2 )
% 0.19/0.47 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_le_trans
% 0.19/0.47 thf(fact_310_le__less__trans,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat,Z2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ( ord_less_nat @ Y2 @ Z2 )
% 0.19/0.47 => ( ord_less_nat @ X2 @ Z2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_less_trans
% 0.19/0.47 thf(fact_311_less__imp__le,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_imp_le
% 0.19/0.47 thf(fact_312_antisym__conv2,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.19/0.47 = ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % antisym_conv2
% 0.19/0.47 thf(fact_313_antisym__conv1,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.19/0.47 = ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % antisym_conv1
% 0.19/0.47 thf(fact_314_le__neq__trans,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( A2 != B2 )
% 0.19/0.47 => ( ord_less_nat @ A2 @ B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_neq_trans
% 0.19/0.47 thf(fact_315_not__less,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) )
% 0.19/0.47 = ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % not_less
% 0.19/0.47 thf(fact_316_not__le,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ( ~ ( ord_less_eq_nat @ X2 @ Y2 ) )
% 0.19/0.47 = ( ord_less_nat @ Y2 @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % not_le
% 0.19/0.47 thf(fact_317_order__less__le__subst2,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_less_le_subst2
% 0.19/0.47 thf(fact_318_order__less__le__subst1,axiom,
% 0.19/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_nat @ A2 @ ( F @ B2 ) )
% 0.19/0.47 => ( ( ord_less_eq_nat @ B2 @ C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_less_le_subst1
% 0.19/0.47 thf(fact_319_order__le__less__subst2,axiom,
% 0.19/0.47 ! [A2: nat,B2: nat,F: nat > nat,C: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.19/0.47 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_le_less_subst2
% 0.19/0.47 thf(fact_320_order__le__less__subst1,axiom,
% 0.19/0.47 ! [A2: nat,F: nat > nat,B2: nat,C: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ A2 @ ( F @ B2 ) )
% 0.19/0.47 => ( ( ord_less_nat @ B2 @ C )
% 0.19/0.47 => ( ! [X5: nat,Y4: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ Y4 )
% 0.19/0.47 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y4 ) ) )
% 0.19/0.47 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % order_le_less_subst1
% 0.19/0.47 thf(fact_321_less__le,axiom,
% 0.19/0.47 ( ord_less_nat
% 0.19/0.47 = ( ^ [X3: nat,Y5: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 0.19/0.47 & ( X3 != Y5 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % less_le
% 0.19/0.47 thf(fact_322_le__less,axiom,
% 0.19/0.47 ( ord_less_eq_nat
% 0.19/0.47 = ( ^ [X3: nat,Y5: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X3 @ Y5 )
% 0.19/0.47 | ( X3 = Y5 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % le_less
% 0.19/0.47 thf(fact_323_leI,axiom,
% 0.19/0.47 ! [X2: nat,Y2: nat] :
% 0.19/0.47 ( ~ ( ord_less_nat @ X2 @ Y2 )
% 0.19/0.47 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % leI
% 0.19/0.47 thf(fact_324_leD,axiom,
% 0.19/0.47 ! [Y2: nat,X2: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.19/0.47 => ~ ( ord_less_nat @ X2 @ Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % leD
% 0.19/0.47 thf(fact_325_div__gr__imp__gr__divisor,axiom,
% 0.19/0.47 ! [X2: nat,N: nat,M: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X2 @ ( divide_divide_nat @ N @ M ) )
% 0.19/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.19/0.47
% 0.19/0.47 % div_gr_imp_gr_divisor
% 0.19/0.47 thf(fact_326_div__le__mono,axiom,
% 0.19/0.47 ! [M: nat,N: nat,K: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.19/0.47 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % div_le_mono
% 0.19/0.47 thf(fact_327_div__le__dividend,axiom,
% 0.19/0.47 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 0.19/0.47
% 0.19/0.47 % div_le_dividend
% 0.19/0.47 thf(fact_328_nat__descend__induct,axiom,
% 0.19/0.47 ! [N: nat,P: nat > $o,M: nat] :
% 0.19/0.47 ( ! [K3: nat] :
% 0.19/0.47 ( ( ord_less_nat @ N @ K3 )
% 0.19/0.47 => ( P @ K3 ) )
% 0.19/0.47 => ( ! [K3: nat] :
% 0.19/0.47 ( ( ord_less_eq_nat @ K3 @ N )
% 0.19/0.47 => ( ! [I5: nat] :
% 0.19/0.47 ( ( ord_less_nat @ K3 @ I5 )
% 0.19/0.47 => ( P @ I5 ) )
% 0.19/0.47 => ( P @ K3 ) ) )
% 0.19/0.47 => ( P @ M ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % nat_descend_induct
% 0.19/0.47 thf(fact_329_minf_I8_J,axiom,
% 0.19/0.47 ! [T: nat] :
% 0.19/0.47 ? [Z3: nat] :
% 0.19/0.47 ! [X6: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.19/0.47 => ~ ( ord_less_eq_nat @ T @ X6 ) ) ).
% 0.19/0.47
% 0.19/0.47 % minf(8)
% 0.19/0.47 thf(fact_330_minf_I7_J,axiom,
% 0.19/0.47 ! [T: nat] :
% 0.19/0.47 ? [Z3: nat] :
% 0.19/0.47 ! [X6: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.19/0.47 => ~ ( ord_less_nat @ T @ X6 ) ) ).
% 0.19/0.47
% 0.19/0.47 % minf(7)
% 0.19/0.47 thf(fact_331_minf_I5_J,axiom,
% 0.19/0.47 ! [T: nat] :
% 0.19/0.47 ? [Z3: nat] :
% 0.19/0.47 ! [X6: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.19/0.47 => ( ord_less_nat @ X6 @ T ) ) ).
% 0.19/0.47
% 0.19/0.47 % minf(5)
% 0.19/0.47 thf(fact_332_minf_I4_J,axiom,
% 0.19/0.47 ! [T: nat] :
% 0.19/0.47 ? [Z3: nat] :
% 0.19/0.47 ! [X6: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.19/0.47 => ( X6 != T ) ) ).
% 0.19/0.47
% 0.19/0.47 % minf(4)
% 0.19/0.47 thf(fact_333_minf_I3_J,axiom,
% 0.19/0.47 ! [T: nat] :
% 0.19/0.47 ? [Z3: nat] :
% 0.19/0.47 ! [X6: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.19/0.47 => ( X6 != T ) ) ).
% 0.19/0.47
% 0.19/0.47 % minf(3)
% 0.19/0.47 thf(fact_334_minf_I2_J,axiom,
% 0.19/0.47 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.19/0.47 ( ? [Z4: nat] :
% 0.19/0.47 ! [X5: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ Z4 )
% 0.19/0.47 => ( ( P @ X5 )
% 0.19/0.47 = ( P4 @ X5 ) ) )
% 0.19/0.47 => ( ? [Z4: nat] :
% 0.19/0.47 ! [X5: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ Z4 )
% 0.19/0.47 => ( ( Q @ X5 )
% 0.19/0.47 = ( Q2 @ X5 ) ) )
% 0.19/0.47 => ? [Z3: nat] :
% 0.19/0.47 ! [X6: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.19/0.47 => ( ( ( P @ X6 )
% 0.19/0.47 | ( Q @ X6 ) )
% 0.19/0.47 = ( ( P4 @ X6 )
% 0.19/0.47 | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % minf(2)
% 0.19/0.47 thf(fact_335_minf_I1_J,axiom,
% 0.19/0.47 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.19/0.47 ( ? [Z4: nat] :
% 0.19/0.47 ! [X5: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ Z4 )
% 0.19/0.47 => ( ( P @ X5 )
% 0.19/0.47 = ( P4 @ X5 ) ) )
% 0.19/0.47 => ( ? [Z4: nat] :
% 0.19/0.47 ! [X5: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X5 @ Z4 )
% 0.19/0.47 => ( ( Q @ X5 )
% 0.19/0.47 = ( Q2 @ X5 ) ) )
% 0.19/0.47 => ? [Z3: nat] :
% 0.19/0.47 ! [X6: nat] :
% 0.19/0.47 ( ( ord_less_nat @ X6 @ Z3 )
% 0.19/0.47 => ( ( ( P @ X6 )
% 0.19/0.47 & ( Q @ X6 ) )
% 0.19/0.47 = ( ( P4 @ X6 )
% 0.19/0.47 & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % minf(1)
% 0.19/0.47 thf(fact_336_pinf_I7_J,axiom,
% 0.19/0.47 ! [T: nat] :
% 0.19/0.47 ? [Z3: nat] :
% 0.19/0.47 ! [X6: nat] :
% 0.19/0.47 ( ( ord_less_nat @ Z3 @ X6 )
% 0.19/0.47 => ( ord_less_nat @ T @ X6 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pinf(7)
% 0.19/0.47 thf(fact_337_pinf_I5_J,axiom,
% 0.19/0.47 ! [T: nat] :
% 0.19/0.47 ? [Z3: nat] :
% 0.19/0.47 ! [X6: nat] :
% 0.19/0.47 ( ( ord_less_nat @ Z3 @ X6 )
% 0.19/0.54 => ~ ( ord_less_nat @ X6 @ T ) ) ).
% 0.19/0.54
% 0.19/0.54 % pinf(5)
% 0.19/0.54 thf(fact_338_pinf_I4_J,axiom,
% 0.19/0.54 ! [T: nat] :
% 0.19/0.54 ? [Z3: nat] :
% 0.19/0.54 ! [X6: nat] :
% 0.19/0.54 ( ( ord_less_nat @ Z3 @ X6 )
% 0.19/0.54 => ( X6 != T ) ) ).
% 0.19/0.54
% 0.19/0.54 % pinf(4)
% 0.19/0.54 thf(fact_339_pinf_I3_J,axiom,
% 0.19/0.54 ! [T: nat] :
% 0.19/0.54 ? [Z3: nat] :
% 0.19/0.54 ! [X6: nat] :
% 0.19/0.54 ( ( ord_less_nat @ Z3 @ X6 )
% 0.19/0.54 => ( X6 != T ) ) ).
% 0.19/0.54
% 0.19/0.54 % pinf(3)
% 0.19/0.54 thf(fact_340_pinf_I2_J,axiom,
% 0.19/0.54 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.19/0.54 ( ? [Z4: nat] :
% 0.19/0.54 ! [X5: nat] :
% 0.19/0.54 ( ( ord_less_nat @ Z4 @ X5 )
% 0.19/0.54 => ( ( P @ X5 )
% 0.19/0.54 = ( P4 @ X5 ) ) )
% 0.19/0.54 => ( ? [Z4: nat] :
% 0.19/0.54 ! [X5: nat] :
% 0.19/0.54 ( ( ord_less_nat @ Z4 @ X5 )
% 0.19/0.54 => ( ( Q @ X5 )
% 0.19/0.54 = ( Q2 @ X5 ) ) )
% 0.19/0.54 => ? [Z3: nat] :
% 0.19/0.54 ! [X6: nat] :
% 0.19/0.54 ( ( ord_less_nat @ Z3 @ X6 )
% 0.19/0.54 => ( ( ( P @ X6 )
% 0.19/0.54 | ( Q @ X6 ) )
% 0.19/0.54 = ( ( P4 @ X6 )
% 0.19/0.54 | ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.19/0.54
% 0.19/0.54 % pinf(2)
% 0.19/0.54 thf(fact_341_pinf_I1_J,axiom,
% 0.19/0.54 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.19/0.54 ( ? [Z4: nat] :
% 0.19/0.54 ! [X5: nat] :
% 0.19/0.54 ( ( ord_less_nat @ Z4 @ X5 )
% 0.19/0.54 => ( ( P @ X5 )
% 0.19/0.54 = ( P4 @ X5 ) ) )
% 0.19/0.54 => ( ? [Z4: nat] :
% 0.19/0.54 ! [X5: nat] :
% 0.19/0.54 ( ( ord_less_nat @ Z4 @ X5 )
% 0.19/0.54 => ( ( Q @ X5 )
% 0.19/0.54 = ( Q2 @ X5 ) ) )
% 0.19/0.54 => ? [Z3: nat] :
% 0.19/0.54 ! [X6: nat] :
% 0.19/0.54 ( ( ord_less_nat @ Z3 @ X6 )
% 0.19/0.54 => ( ( ( P @ X6 )
% 0.19/0.54 & ( Q @ X6 ) )
% 0.19/0.54 = ( ( P4 @ X6 )
% 0.19/0.54 & ( Q2 @ X6 ) ) ) ) ) ) ).
% 0.19/0.54
% 0.19/0.54 % pinf(1)
% 0.19/0.54 thf(fact_342_pinf_I6_J,axiom,
% 0.19/0.54 ! [T: nat] :
% 0.19/0.54 ? [Z3: nat] :
% 0.19/0.54 ! [X6: nat] :
% 0.19/0.54 ( ( ord_less_nat @ Z3 @ X6 )
% 0.19/0.54 => ~ ( ord_less_eq_nat @ X6 @ T ) ) ).
% 0.19/0.54
% 0.19/0.54 % pinf(6)
% 0.19/0.54 thf(fact_343_pinf_I8_J,axiom,
% 0.19/0.54 ! [T: nat] :
% 0.19/0.54 ? [Z3: nat] :
% 0.19/0.54 ! [X6: nat] :
% 0.19/0.54 ( ( ord_less_nat @ Z3 @ X6 )
% 0.19/0.54 => ( ord_less_eq_nat @ T @ X6 ) ) ).
% 0.19/0.54
% 0.19/0.54 % pinf(8)
% 0.19/0.54 thf(fact_344_minf_I6_J,axiom,
% 0.19/0.54 ! [T: nat] :
% 0.19/0.54 ? [Z3: nat] :
% 0.19/0.54 ! [X6: nat] :
% 0.19/0.54 ( ( ord_less_nat @ X6 @ Z3 )
% 0.19/0.54 => ( ord_less_eq_nat @ X6 @ T ) ) ).
% 0.19/0.54
% 0.19/0.54 % minf(6)
% 0.19/0.54 thf(fact_345_complete__interval,axiom,
% 0.19/0.54 ! [A2: nat,B2: nat,P: nat > $o] :
% 0.19/0.54 ( ( ord_less_nat @ A2 @ B2 )
% 0.19/0.54 => ( ( P @ A2 )
% 0.19/0.54 => ( ~ ( P @ B2 )
% 0.19/0.54 => ? [C2: nat] :
% 0.19/0.54 ( ( ord_less_eq_nat @ A2 @ C2 )
% 0.19/0.54 & ( ord_less_eq_nat @ C2 @ B2 )
% 0.19/0.54 & ! [X6: nat] :
% 0.19/0.54 ( ( ( ord_less_eq_nat @ A2 @ X6 )
% 0.19/0.54 & ( ord_less_nat @ X6 @ C2 ) )
% 0.19/0.54 => ( P @ X6 ) )
% 0.19/0.54 & ! [D: nat] :
% 0.19/0.54 ( ! [X5: nat] :
% 0.19/0.54 ( ( ( ord_less_eq_nat @ A2 @ X5 )
% 0.19/0.54 & ( ord_less_nat @ X5 @ D ) )
% 0.19/0.54 => ( P @ X5 ) )
% 0.19/0.54 => ( ord_less_eq_nat @ D @ C2 ) ) ) ) ) ) ).
% 0.19/0.54
% 0.19/0.54 % complete_interval
% 0.19/0.54 thf(fact_346_le__greater__neq__conv,axiom,
% 0.19/0.54 ( ord_less_eq_nat
% 0.19/0.54 = ( ^ [N3: nat,A3: nat] :
% 0.19/0.54 ! [X3: nat] :
% 0.19/0.54 ( ( ord_less_nat @ A3 @ X3 )
% 0.19/0.54 => ( N3 != X3 ) ) ) ) ).
% 0.19/0.54
% 0.19/0.54 % le_greater_neq_conv
% 0.19/0.54 thf(fact_347_ge__less__neq__conv,axiom,
% 0.19/0.54 ( ord_less_eq_nat
% 0.19/0.54 = ( ^ [A3: nat,N3: nat] :
% 0.19/0.54 ! [X3: nat] :
% 0.19/0.54 ( ( ord_less_nat @ X3 @ A3 )
% 0.19/0.54 => ( N3 != X3 ) ) ) ) ).
% 0.19/0.54
% 0.19/0.54 % ge_less_neq_conv
% 0.19/0.54
% 0.19/0.54 % Conjectures (2)
% 0.19/0.54 thf(conj_0,hypothesis,
% 0.19/0.54 ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) ).
% 0.19/0.54
% 0.19/0.54 thf(conj_1,conjecture,
% 0.19/0.54 ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
% 0.19/0.54 = k ) ).
% 0.19/0.54
% 0.19/0.54 %------------------------------------------------------------------------------
% 0.19/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.46n1OLDBRx/cvc5---1.0.5_2861.p...
% 0.19/0.54 (declare-sort $$unsorted 0)
% 0.19/0.54 (declare-sort tptp.list_l2071841302list_a 0)
% 0.19/0.54 (declare-sort tptp.list_list_list_nat 0)
% 0.19/0.54 (declare-sort tptp.list_list_list_a 0)
% 0.19/0.54 (declare-sort tptp.set_list_list_a 0)
% 0.19/0.54 (declare-sort tptp.list_set_list_a 0)
% 0.19/0.54 (declare-sort tptp.list_list_nat 0)
% 0.19/0.54 (declare-sort tptp.set_list_nat 0)
% 0.19/0.54 (declare-sort tptp.list_set_nat 0)
% 0.19/0.54 (declare-sort tptp.list_list_a 0)
% 0.19/0.54 (declare-sort tptp.set_list_a 0)
% 0.19/0.54 (declare-sort tptp.list_set_a 0)
% 0.19/0.54 (declare-sort tptp.list_nat 0)
% 0.19/0.54 (declare-sort tptp.set_nat 0)
% 0.19/0.54 (declare-sort tptp.list_a 0)
% 0.19/0.54 (declare-sort tptp.set_a 0)
% 0.19/0.54 (declare-sort tptp.nat 0)
% 0.19/0.54 (declare-sort tptp.a 0)
% 0.19/0.54 (declare-fun tptp.f_image_list_list_a (tptp.list_list_list_a tptp.set_nat) tptp.set_list_list_a)
% 0.19/0.54 (declare-fun tptp.f_image_list_nat (tptp.list_list_nat tptp.set_nat) tptp.set_list_nat)
% 0.19/0.54 (declare-fun tptp.f_image_list_a (tptp.list_list_a tptp.set_nat) tptp.set_list_a)
% 0.19/0.54 (declare-fun tptp.f_image_nat (tptp.list_nat tptp.set_nat) tptp.set_nat)
% 0.19/0.54 (declare-fun tptp.f_image_a (tptp.list_a tptp.set_nat) tptp.set_a)
% 0.19/0.54 (declare-fun tptp.list_asc_nat (tptp.list_nat) Bool)
% 0.19/0.54 (declare-fun tptp.list_asc_set_list_a (tptp.list_set_list_a) Bool)
% 0.19/0.54 (declare-fun tptp.list_asc_set_nat (tptp.list_set_nat) Bool)
% 0.19/0.54 (declare-fun tptp.list_asc_set_a (tptp.list_set_a) Bool)
% 0.19/0.54 (declare-fun tptp.list_desc_nat (tptp.list_nat) Bool)
% 0.19/0.54 (declare-fun tptp.list_desc_set_list_a (tptp.list_set_list_a) Bool)
% 0.19/0.54 (declare-fun tptp.list_desc_set_nat (tptp.list_set_nat) Bool)
% 0.19/0.54 (declare-fun tptp.list_desc_set_a (tptp.list_set_a) Bool)
% 0.19/0.54 (declare-fun tptp.list_strict_asc_nat (tptp.list_nat) Bool)
% 0.19/0.54 (declare-fun tptp.list_strict_desc_nat (tptp.list_nat) Bool)
% 0.19/0.54 (declare-fun tptp.listSl769338732list_a (tptp.list_list_list_a tptp.nat) tptp.list_l2071841302list_a)
% 0.19/0.54 (declare-fun tptp.listSl2099749758st_nat (tptp.list_list_nat tptp.nat) tptp.list_list_list_nat)
% 0.19/0.54 (declare-fun tptp.listSl703198822list_a (tptp.list_list_a tptp.nat) tptp.list_list_list_a)
% 0.19/0.54 (declare-fun tptp.listSl882585454e2_nat (tptp.list_nat tptp.nat) tptp.list_list_nat)
% 0.19/0.54 (declare-fun tptp.listSl1174287072ice2_a (tptp.list_a tptp.nat) tptp.list_list_a)
% 0.19/0.54 (declare-fun tptp.listSl2102238196list_a (tptp.list_list_list_a tptp.nat) tptp.list_l2071841302list_a)
% 0.19/0.54 (declare-fun tptp.listSl729562870st_nat (tptp.list_list_nat tptp.nat) tptp.list_list_list_nat)
% 0.19/0.54 (declare-fun tptp.listSl162220270list_a (tptp.list_list_a tptp.nat) tptp.list_list_list_a)
% 0.19/0.54 (declare-fun tptp.listSl1630398182ce_nat (tptp.list_nat tptp.nat) tptp.list_list_nat)
% 0.19/0.54 (declare-fun tptp.listSl97544552lice_a (tptp.list_a tptp.nat) tptp.list_list_a)
% 0.19/0.54 (declare-fun tptp.listSl902632890list_a (tptp.list_list_list_a tptp.nat tptp.nat) tptp.list_l2071841302list_a)
% 0.19/0.54 (declare-fun tptp.listSl1506485424st_nat (tptp.list_list_nat tptp.nat tptp.nat) tptp.list_list_list_nat)
% 0.19/0.54 (declare-fun tptp.listSl856612276list_a (tptp.list_list_a tptp.nat tptp.nat) tptp.list_list_list_a)
% 0.19/0.54 (declare-fun tptp.listSl1794011552ux_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_list_nat)
% 0.19/0.54 (declare-fun tptp.listSl1495374126_aux_a (tptp.list_a tptp.nat tptp.nat) tptp.list_list_a)
% 0.19/0.54 (declare-fun tptp.butlast_list_list_a (tptp.list_list_list_a) tptp.list_list_list_a)
% 0.19/0.54 (declare-fun tptp.butlast_list_nat (tptp.list_list_nat) tptp.list_list_nat)
% 0.19/0.54 (declare-fun tptp.butlast_list_a (tptp.list_list_a) tptp.list_list_a)
% 0.19/0.54 (declare-fun tptp.butlast_nat (tptp.list_nat) tptp.list_nat)
% 0.19/0.54 (declare-fun tptp.butlast_a (tptp.list_a) tptp.list_a)
% 0.19/0.54 (declare-fun tptp.distinct_list_list_a (tptp.list_list_list_a) Bool)
% 0.19/0.54 (declare-fun tptp.distinct_list_nat (tptp.list_list_nat) Bool)
% 0.19/0.54 (declare-fun tptp.distinct_list_a (tptp.list_list_a) Bool)
% 0.19/0.54 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 0.19/0.54 (declare-fun tptp.distinct_a (tptp.list_a) Bool)
% 0.19/0.54 (declare-fun tptp.set_list_list_a2 (tptp.list_list_list_a) tptp.set_list_list_a)
% 0.19/0.54 (declare-fun tptp.set_list_nat2 (tptp.list_list_nat) tptp.set_list_nat)
% 0.19/0.54 (declare-fun tptp.set_list_a2 (tptp.list_list_a) tptp.set_list_a)
% 0.19/0.54 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 0.19/0.54 (declare-fun tptp.set_a2 (tptp.list_a) tptp.set_a)
% 0.19/0.54 (declare-fun tptp.list_ex_list_list_a ((-> tptp.list_list_a Bool) tptp.list_list_list_a) Bool)
% 0.19/0.54 (declare-fun tptp.list_ex_list_nat ((-> tptp.list_nat Bool) tptp.list_list_nat) Bool)
% 0.19/0.54 (declare-fun tptp.list_ex_list_a ((-> tptp.list_a Bool) tptp.list_list_a) Bool)
% 0.19/0.54 (declare-fun tptp.list_ex_nat ((-> tptp.nat Bool) tptp.list_nat) Bool)
% 0.19/0.54 (declare-fun tptp.list_ex_a ((-> tptp.a Bool) tptp.list_a) Bool)
% 0.19/0.54 (declare-fun tptp.list_u1330012152list_a (tptp.list_list_list_a tptp.nat tptp.list_list_a) tptp.list_list_list_a)
% 0.19/0.54 (declare-fun tptp.list_update_list_nat (tptp.list_list_nat tptp.nat tptp.list_nat) tptp.list_list_nat)
% 0.19/0.54 (declare-fun tptp.list_update_list_a (tptp.list_list_a tptp.nat tptp.list_a) tptp.list_list_a)
% 0.19/0.54 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 0.19/0.54 (declare-fun tptp.list_update_a (tptp.list_a tptp.nat tptp.a) tptp.list_a)
% 0.19/0.54 (declare-fun tptp.nth_list_list_list_a (tptp.list_l2071841302list_a tptp.nat) tptp.list_list_list_a)
% 0.19/0.54 (declare-fun tptp.nth_list_list_nat (tptp.list_list_list_nat tptp.nat) tptp.list_list_nat)
% 0.19/0.54 (declare-fun tptp.nth_list_list_a (tptp.list_list_list_a tptp.nat) tptp.list_list_a)
% 0.19/0.54 (declare-fun tptp.nth_list_nat (tptp.list_list_nat tptp.nat) tptp.list_nat)
% 0.19/0.54 (declare-fun tptp.nth_list_a (tptp.list_list_a tptp.nat) tptp.list_a)
% 0.19/0.54 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 0.19/0.54 (declare-fun tptp.nth_set_list_a (tptp.list_set_list_a tptp.nat) tptp.set_list_a)
% 0.19/0.54 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 0.19/0.54 (declare-fun tptp.nth_set_a (tptp.list_set_a tptp.nat) tptp.set_a)
% 0.19/0.54 (declare-fun tptp.nth_a (tptp.list_a tptp.nat) tptp.a)
% 0.19/0.54 (declare-fun tptp.size_s1764310658list_a (tptp.list_l2071841302list_a) tptp.nat)
% 0.19/0.54 (declare-fun tptp.size_s1321307156st_nat (tptp.list_list_list_nat) tptp.nat)
% 0.19/0.54 (declare-fun tptp.size_s575106428list_a (tptp.list_list_list_a) tptp.nat)
% 0.19/0.54 (declare-fun tptp.size_s1898481668st_nat (tptp.list_list_nat) tptp.nat)
% 0.19/0.54 (declare-fun tptp.size_s1427607542list_a (tptp.list_list_a) tptp.nat)
% 0.19/0.54 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 0.19/0.54 (declare-fun tptp.size_s1635937238list_a (tptp.list_set_list_a) tptp.nat)
% 0.19/0.54 (declare-fun tptp.size_s577819178et_nat (tptp.list_set_nat) tptp.nat)
% 0.19/0.54 (declare-fun tptp.size_size_list_set_a (tptp.list_set_a) tptp.nat)
% 0.19/0.54 (declare-fun tptp.size_size_list_a (tptp.list_a) tptp.nat)
% 0.19/0.54 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.19/0.54 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.19/0.54 (declare-fun tptp.ord_le1756736906list_a (tptp.set_list_list_a tptp.set_list_list_a) Bool)
% 0.19/0.54 (declare-fun tptp.ord_le1747345782st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 0.19/0.54 (declare-fun tptp.ord_le1301786372list_a (tptp.set_list_a tptp.set_list_a) Bool)
% 0.19/0.54 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 0.19/0.54 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.19/0.54 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 0.19/0.54 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 0.19/0.54 (declare-fun tptp.collect_list_a ((-> tptp.list_a Bool)) tptp.set_list_a)
% 0.19/0.54 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.19/0.54 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.19/0.54 (declare-fun tptp.member_list_list_a (tptp.list_list_a tptp.set_list_list_a) Bool)
% 0.19/0.54 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 0.19/0.54 (declare-fun tptp.member_list_a (tptp.list_a tptp.set_list_a) Bool)
% 0.19/0.54 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.19/0.54 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.19/0.54 (declare-fun tptp.k () tptp.nat)
% 0.19/0.54 (declare-fun tptp.m () tptp.nat)
% 0.19/0.54 (declare-fun tptp.xs () tptp.list_a)
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_nat) (Ys tptp.list_list_nat)) (=> (= (@ tptp.size_s1898481668st_nat Xs) (@ tptp.size_s1898481668st_nat Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1898481668st_nat Xs)) (= (@ (@ tptp.nth_list_nat Xs) I) (@ (@ tptp.nth_list_nat Ys) I)))) (= Xs Ys)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_list_a) (Ys tptp.list_list_list_a)) (=> (= (@ tptp.size_s575106428list_a Xs) (@ tptp.size_s575106428list_a Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s575106428list_a Xs)) (= (@ (@ tptp.nth_list_list_a Xs) I) (@ (@ tptp.nth_list_list_a Ys) I)))) (= Xs Ys)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I) (@ (@ tptp.nth_nat Ys) I)))) (= Xs Ys)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (= (@ tptp.size_s1427607542list_a Xs) (@ tptp.size_s1427607542list_a Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) I) (@ (@ tptp.nth_list_a Ys) I)))) (= Xs Ys)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I) (@ (@ tptp.nth_a Ys) I)))) (= Xs Ys)))))
% 0.19/0.54 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.list_nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.list_nat)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_list_nat)) (and (= (@ tptp.size_s1898481668st_nat Xs2) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_list_nat Xs2) I2)))))))))
% 0.19/0.54 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.list_list_a Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.list_list_a)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_list_list_a)) (and (= (@ tptp.size_s575106428list_a Xs2) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_list_list_a Xs2) I2)))))))))
% 0.19/0.54 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.nat)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_nat Xs2) I2)))))))))
% 0.19/0.54 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.list_a Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.list_a)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_list_a)) (and (= (@ tptp.size_s1427607542list_a Xs2) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_list_a Xs2) I2)))))))))
% 0.19/0.54 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.a Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.a)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_a)) (and (= (@ tptp.size_size_list_a Xs2) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_a Xs2) I2)))))))))
% 0.19/0.54 (assert (= (lambda ((Y tptp.list_list_nat) (Z tptp.list_list_nat)) (= Y Z)) (lambda ((Xs2 tptp.list_list_nat) (Ys2 tptp.list_list_nat)) (and (= (@ tptp.size_s1898481668st_nat Xs2) (@ tptp.size_s1898481668st_nat Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1898481668st_nat Xs2)) (= (@ (@ tptp.nth_list_nat Xs2) I2) (@ (@ tptp.nth_list_nat Ys2) I2))))))))
% 0.19/0.54 (assert (= (lambda ((Y tptp.list_list_list_a) (Z tptp.list_list_list_a)) (= Y Z)) (lambda ((Xs2 tptp.list_list_list_a) (Ys2 tptp.list_list_list_a)) (and (= (@ tptp.size_s575106428list_a Xs2) (@ tptp.size_s575106428list_a Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s575106428list_a Xs2)) (= (@ (@ tptp.nth_list_list_a Xs2) I2) (@ (@ tptp.nth_list_list_a Ys2) I2))))))))
% 0.19/0.54 (assert (= (lambda ((Y tptp.list_nat) (Z tptp.list_nat)) (= Y Z)) (lambda ((Xs2 tptp.list_nat) (Ys2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I2) (@ (@ tptp.nth_nat Ys2) I2))))))))
% 0.19/0.54 (assert (= (lambda ((Y tptp.list_list_a) (Z tptp.list_list_a)) (= Y Z)) (lambda ((Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (and (= (@ tptp.size_s1427607542list_a Xs2) (@ tptp.size_s1427607542list_a Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1427607542list_a Xs2)) (= (@ (@ tptp.nth_list_a Xs2) I2) (@ (@ tptp.nth_list_a Ys2) I2))))))))
% 0.19/0.54 (assert (= (lambda ((Y tptp.list_a) (Z tptp.list_a)) (= Y Z)) (lambda ((Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs2)) (= (@ (@ tptp.nth_a Xs2) I2) (@ (@ tptp.nth_a Ys2) I2))))))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (Xs tptp.list_list_nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1898481668st_nat Xs)) K)) (= (@ (@ tptp.nth_list_list_nat (@ (@ tptp.listSl2099749758st_nat Xs) K)) M) (@ (@ tptp.nth_list_list_nat (@ (@ tptp.listSl729562870st_nat Xs) K)) M)))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (Xs tptp.list_list_list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s575106428list_a Xs)) K)) (= (@ (@ tptp.nth_list_list_list_a (@ (@ tptp.listSl769338732list_a Xs) K)) M) (@ (@ tptp.nth_list_list_list_a (@ (@ tptp.listSl2102238196list_a Xs) K)) M)))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (Xs tptp.list_list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1427607542list_a Xs)) K)) (= (@ (@ tptp.nth_list_list_a (@ (@ tptp.listSl703198822list_a Xs) K)) M) (@ (@ tptp.nth_list_list_a (@ (@ tptp.listSl162220270list_a Xs) K)) M)))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (Xs tptp.list_nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_nat Xs)) K)) (= (@ (@ tptp.nth_list_nat (@ (@ tptp.listSl882585454e2_nat Xs) K)) M) (@ (@ tptp.nth_list_nat (@ (@ tptp.listSl1630398182ce_nat Xs) K)) M)))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (Xs tptp.list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs)) K)) (= (@ (@ tptp.nth_list_a (@ (@ tptp.listSl1174287072ice2_a Xs) K)) M) (@ (@ tptp.nth_list_a (@ (@ tptp.listSl97544552lice_a Xs) K)) M)))))
% 0.19/0.54 (assert (forall ((P (-> tptp.list_list_nat Bool)) (Xs tptp.list_list_nat)) (=> (forall ((Xs3 tptp.list_list_nat)) (=> (forall ((Ys3 tptp.list_list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1898481668st_nat Ys3)) (@ tptp.size_s1898481668st_nat Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))))
% 0.19/0.54 (assert (forall ((P (-> tptp.list_list_list_a Bool)) (Xs tptp.list_list_list_a)) (=> (forall ((Xs3 tptp.list_list_list_a)) (=> (forall ((Ys3 tptp.list_list_list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s575106428list_a Ys3)) (@ tptp.size_s575106428list_a Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))))
% 0.19/0.54 (assert (forall ((P (-> tptp.list_list_a Bool)) (Xs tptp.list_list_a)) (=> (forall ((Xs3 tptp.list_list_a)) (=> (forall ((Ys3 tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1427607542list_a Ys3)) (@ tptp.size_s1427607542list_a Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))))
% 0.19/0.54 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys3)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))))
% 0.19/0.54 (assert (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (forall ((Xs3 tptp.list_a)) (=> (forall ((Ys3 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_a Ys3)) (@ tptp.size_size_list_a Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))))
% 0.19/0.54 (assert (= tptp.list_strict_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ _let_1 J)) (@ _let_1 I2))))))))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (Xs tptp.list_list_nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1898481668st_nat Xs)) K)) (= (@ tptp.size_s1898481668st_nat (@ (@ tptp.nth_list_list_nat (@ (@ tptp.listSl729562870st_nat Xs) K)) M)) K))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (Xs tptp.list_list_list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s575106428list_a Xs)) K)) (= (@ tptp.size_s575106428list_a (@ (@ tptp.nth_list_list_list_a (@ (@ tptp.listSl2102238196list_a Xs) K)) M)) K))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (Xs tptp.list_list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1427607542list_a Xs)) K)) (= (@ tptp.size_s1427607542list_a (@ (@ tptp.nth_list_list_a (@ (@ tptp.listSl162220270list_a Xs) K)) M)) K))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (Xs tptp.list_nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_nat Xs)) K)) (= (@ tptp.size_size_list_nat (@ (@ tptp.nth_list_nat (@ (@ tptp.listSl1630398182ce_nat Xs) K)) M)) K))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (Xs tptp.list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs)) K)) (= (@ tptp.size_size_list_a (@ (@ tptp.nth_list_a (@ (@ tptp.listSl97544552lice_a Xs) K)) M)) K))))
% 0.19/0.54 (assert (= tptp.list_strict_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J))))))))))
% 0.19/0.54 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_list_nat)) (= (@ tptp.size_s1898481668st_nat Xs3) N))))
% 0.19/0.54 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_list_list_a)) (= (@ tptp.size_s575106428list_a Xs3) N))))
% 0.19/0.54 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_list_a)) (= (@ tptp.size_s1427607542list_a Xs3) N))))
% 0.19/0.54 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 0.19/0.54 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_a)) (= (@ tptp.size_size_list_a Xs3) N))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_nat) (Ys tptp.list_list_nat)) (=> (not (= (@ tptp.size_s1898481668st_nat Xs) (@ tptp.size_s1898481668st_nat Ys))) (not (= Xs Ys)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_list_a) (Ys tptp.list_list_list_a)) (=> (not (= (@ tptp.size_s575106428list_a Xs) (@ tptp.size_s575106428list_a Ys))) (not (= Xs Ys)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (not (= (@ tptp.size_s1427607542list_a Xs) (@ tptp.size_s1427607542list_a Ys))) (not (= Xs Ys)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (not (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys))) (not (= Xs Ys)))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_list_nat) (Y2 tptp.list_list_nat)) (=> (not (= (@ tptp.size_s1898481668st_nat X2) (@ tptp.size_s1898481668st_nat Y2))) (not (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_list_list_a) (Y2 tptp.list_list_list_a)) (=> (not (= (@ tptp.size_s575106428list_a X2) (@ tptp.size_s575106428list_a Y2))) (not (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_a) (Y2 tptp.list_a)) (=> (not (= (@ tptp.size_size_list_a X2) (@ tptp.size_size_list_a Y2))) (not (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_list_a) (Y2 tptp.list_list_a)) (=> (not (= (@ tptp.size_s1427607542list_a X2) (@ tptp.size_s1427607542list_a Y2))) (not (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X2) (@ tptp.size_size_list_nat Y2))) (not (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_nat) (K tptp.nat)) (= (@ tptp.size_s1321307156st_nat (@ (@ tptp.listSl729562870st_nat Xs) K)) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1898481668st_nat Xs)) K))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_list_a) (K tptp.nat)) (= (@ tptp.size_s1764310658list_a (@ (@ tptp.listSl2102238196list_a Xs) K)) (@ (@ tptp.divide_divide_nat (@ tptp.size_s575106428list_a Xs)) K))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (K tptp.nat)) (= (@ tptp.size_s575106428list_a (@ (@ tptp.listSl162220270list_a Xs) K)) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1427607542list_a Xs)) K))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (K tptp.nat)) (= (@ tptp.size_s1898481668st_nat (@ (@ tptp.listSl1630398182ce_nat Xs) K)) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_nat Xs)) K))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (K tptp.nat)) (= (@ tptp.size_s1427607542list_a (@ (@ tptp.listSl97544552lice_a Xs) K)) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs)) K))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))))
% 0.19/0.54 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2)))))) (@ P N))))
% 0.19/0.54 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 0.19/0.54 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.19/0.54 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.19/0.54 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.19/0.54 (assert (= tptp.listSl729562870st_nat (lambda ((Xs2 tptp.list_list_nat) (K2 tptp.nat)) (@ (@ (@ tptp.listSl1506485424st_nat Xs2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1898481668st_nat Xs2)) K2)))))
% 0.19/0.54 (assert (= tptp.listSl2102238196list_a (lambda ((Xs2 tptp.list_list_list_a) (K2 tptp.nat)) (@ (@ (@ tptp.listSl902632890list_a Xs2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.size_s575106428list_a Xs2)) K2)))))
% 0.19/0.54 (assert (= tptp.listSl162220270list_a (lambda ((Xs2 tptp.list_list_a) (K2 tptp.nat)) (@ (@ (@ tptp.listSl856612276list_a Xs2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1427607542list_a Xs2)) K2)))))
% 0.19/0.54 (assert (= tptp.listSl1630398182ce_nat (lambda ((Xs2 tptp.list_nat) (K2 tptp.nat)) (@ (@ (@ tptp.listSl1794011552ux_nat Xs2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_nat Xs2)) K2)))))
% 0.19/0.54 (assert (= tptp.listSl97544552lice_a (lambda ((Xs2 tptp.list_a) (K2 tptp.nat)) (@ (@ (@ tptp.listSl1495374126_aux_a Xs2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs2)) K2)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_desc_nat Xs) (@ tptp.list_desc_nat Xs))))
% 0.19/0.54 (assert (= tptp.list_ex_list_nat (lambda ((P2 (-> tptp.list_nat Bool)) (Xs2 tptp.list_list_nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.size_s1898481668st_nat Xs2)) (@ P2 (@ (@ tptp.nth_list_nat Xs2) N3)))))))
% 0.19/0.54 (assert (= tptp.list_ex_list_list_a (lambda ((P2 (-> tptp.list_list_a Bool)) (Xs2 tptp.list_list_list_a)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.size_s575106428list_a Xs2)) (@ P2 (@ (@ tptp.nth_list_list_a Xs2) N3)))))))
% 0.19/0.54 (assert (= tptp.list_ex_a (lambda ((P2 (-> tptp.a Bool)) (Xs2 tptp.list_a)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.size_size_list_a Xs2)) (@ P2 (@ (@ tptp.nth_a Xs2) N3)))))))
% 0.19/0.54 (assert (= tptp.list_ex_list_a (lambda ((P2 (-> tptp.list_a Bool)) (Xs2 tptp.list_list_a)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.size_s1427607542list_a Xs2)) (@ P2 (@ (@ tptp.nth_list_a Xs2) N3)))))))
% 0.19/0.54 (assert (= tptp.list_ex_nat (lambda ((P2 (-> tptp.nat Bool)) (Xs2 tptp.list_nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.size_size_list_nat Xs2)) (@ P2 (@ (@ tptp.nth_nat Xs2) N3)))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_nat) (Xs tptp.list_list_nat) (N tptp.nat) (A tptp.set_nat)) (=> (= X2 (@ (@ tptp.nth_list_nat Xs) N)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat Xs)) (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) A)))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_list_a) (Xs tptp.list_list_list_a) (N tptp.nat) (A tptp.set_nat)) (=> (= X2 (@ (@ tptp.nth_list_list_a Xs) N)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a Xs)) (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) A)))))))
% 0.19/0.54 (assert (forall ((X2 tptp.a) (Xs tptp.list_a) (N tptp.nat) (A tptp.set_nat)) (=> (= X2 (@ (@ tptp.nth_a Xs) N)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) A)))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_a) (Xs tptp.list_list_a) (N tptp.nat) (A tptp.set_nat)) (=> (= X2 (@ (@ tptp.nth_list_a Xs) N)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) A)))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat) (N tptp.nat) (A tptp.set_nat)) (=> (= X2 (@ (@ tptp.nth_nat Xs) N)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) A)))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_asc_nat Xs) (@ tptp.list_asc_nat Xs))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_nat) (X2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1898481668st_nat Xs)) (= (@ (@ tptp.nth_list_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) X2)) I3) X2))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_list_a) (X2 tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s575106428list_a Xs)) (= (@ (@ tptp.nth_list_list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) X2)) I3) X2))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_a) (X2 tptp.a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I3) X2)) I3) X2))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) X2)) I3) X2))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) I3) X2))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_nat) (X2 tptp.list_nat)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat Xs)) (=> (= X2 (@ (@ tptp.nth_list_nat Xs) N)) (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) A)))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_list_a) (X2 tptp.list_list_a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a Xs)) (=> (= X2 (@ (@ tptp.nth_list_list_a Xs) N)) (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) A)))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_a) (X2 tptp.a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (=> (= X2 (@ (@ tptp.nth_a Xs) N)) (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) A)))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (=> (= X2 (@ (@ tptp.nth_list_a Xs) N)) (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) A)))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (= X2 (@ (@ tptp.nth_nat Xs) N)) (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) A)))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_nat) (Xs tptp.list_list_nat) (A tptp.set_nat)) (= (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s1898481668st_nat Xs)) (= X2 (@ (@ tptp.nth_list_nat Xs) X3)))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_list_a) (Xs tptp.list_list_list_a) (A tptp.set_nat)) (= (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s575106428list_a Xs)) (= X2 (@ (@ tptp.nth_list_list_a Xs) X3)))))))
% 0.19/0.54 (assert (forall ((X2 tptp.a) (Xs tptp.list_a) (A tptp.set_nat)) (= (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_a Xs)) (= X2 (@ (@ tptp.nth_a Xs) X3)))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_a) (Xs tptp.list_list_a) (A tptp.set_nat)) (= (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s1427607542list_a Xs)) (= X2 (@ (@ tptp.nth_list_a Xs) X3)))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat) (A tptp.set_nat)) (= (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_nat Xs)) (= X2 (@ (@ tptp.nth_nat Xs) X3)))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_list_nat)) (let ((_let_1 (@ tptp.butlast_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat _let_1)) (= (@ (@ tptp.nth_list_nat _let_1) N) (@ (@ tptp.nth_list_nat Xs) N))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_list_list_a)) (let ((_let_1 (@ tptp.butlast_list_list_a Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a _let_1)) (= (@ (@ tptp.nth_list_list_a _let_1) N) (@ (@ tptp.nth_list_list_a Xs) N))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.butlast_a Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a _let_1)) (= (@ (@ tptp.nth_a _let_1) N) (@ (@ tptp.nth_a Xs) N))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.butlast_list_a Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a _let_1)) (= (@ (@ tptp.nth_list_a _let_1) N) (@ (@ tptp.nth_list_a Xs) N))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.butlast_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat _let_1)) (= (@ (@ tptp.nth_nat _let_1) N) (@ (@ tptp.nth_nat Xs) N))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_nat)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat Xs)) (@ (@ tptp.member_list_nat (@ (@ tptp.nth_list_nat Xs) N)) (@ (@ tptp.f_image_list_nat Xs) A))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_list_a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a Xs)) (@ (@ tptp.member_list_list_a (@ (@ tptp.nth_list_list_a Xs) N)) (@ (@ tptp.f_image_list_list_a Xs) A))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Xs) N)) (@ (@ tptp.f_image_a Xs) A))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Xs) N)) (@ (@ tptp.f_image_list_a Xs) A))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ (@ tptp.f_image_nat Xs) A))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_nat) (Xs tptp.list_list_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) A)) (not (forall ((N2 tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_nat Xs) N2)) (=> (@ (@ tptp.member_nat N2) A) (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1898481668st_nat Xs))))))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_list_a) (Xs tptp.list_list_list_a) (A tptp.set_nat)) (=> (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) A)) (not (forall ((N2 tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_list_a Xs) N2)) (=> (@ (@ tptp.member_nat N2) A) (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s575106428list_a Xs))))))))))
% 0.19/0.54 (assert (forall ((X2 tptp.a) (Xs tptp.list_a) (A tptp.set_nat)) (=> (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) A)) (not (forall ((N2 tptp.nat)) (=> (= X2 (@ (@ tptp.nth_a Xs) N2)) (=> (@ (@ tptp.member_nat N2) A) (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs))))))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_a) (Xs tptp.list_list_a) (A tptp.set_nat)) (=> (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) A)) (not (forall ((N2 tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_a Xs) N2)) (=> (@ (@ tptp.member_nat N2) A) (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1427607542list_a Xs))))))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) A)) (not (forall ((N2 tptp.nat)) (=> (= X2 (@ (@ tptp.nth_nat Xs) N2)) (=> (@ (@ tptp.member_nat N2) A) (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs))))))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.list_update_nat Xs) I3))) (= (@ (@ (@ tptp.list_update_nat (@ _let_1 X2)) I3) Y2) (@ _let_1 Y2)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (I3 tptp.nat) (X2 tptp.list_a) (Y2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.list_update_list_a Xs) I3))) (= (@ (@ (@ tptp.list_update_list_a (@ _let_1 X2)) I3) Y2) (@ _let_1 Y2)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (I3 tptp.nat) (X2 tptp.a) (Y2 tptp.a)) (let ((_let_1 (@ (@ tptp.list_update_a Xs) I3))) (= (@ (@ (@ tptp.list_update_a (@ _let_1 X2)) I3) Y2) (@ _let_1 Y2)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_nat) (I3 tptp.nat) (X2 tptp.list_nat)) (= (@ tptp.size_s1898481668st_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) X2)) (@ tptp.size_s1898481668st_nat Xs))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_list_a) (I3 tptp.nat) (X2 tptp.list_list_a)) (= (@ tptp.size_s575106428list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) X2)) (@ tptp.size_s575106428list_a Xs))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (I3 tptp.nat) (X2 tptp.a)) (= (@ tptp.size_size_list_a (@ (@ (@ tptp.list_update_a Xs) I3) X2)) (@ tptp.size_size_list_a Xs))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (I3 tptp.nat) (X2 tptp.list_a)) (= (@ tptp.size_s1427607542list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) X2)) (@ tptp.size_s1427607542list_a Xs))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) (@ tptp.size_size_list_nat Xs))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_nat) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_update_list_nat Xs) I3) (@ (@ tptp.nth_list_nat Xs) I3)) Xs)))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_list_a) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) (@ (@ tptp.nth_list_list_a Xs) I3)) Xs)))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_update_list_a Xs) I3) (@ (@ tptp.nth_list_a Xs) I3)) Xs)))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_update_a Xs) I3) (@ (@ tptp.nth_a Xs) I3)) Xs)))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I3) (@ (@ tptp.nth_nat Xs) I3)) Xs)))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (Xs tptp.list_list_nat) (X2 tptp.list_nat)) (=> (not (= I3 J2)) (= (@ (@ tptp.nth_list_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) X2)) J2) (@ (@ tptp.nth_list_nat Xs) J2)))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (Xs tptp.list_list_list_a) (X2 tptp.list_list_a)) (=> (not (= I3 J2)) (= (@ (@ tptp.nth_list_list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) X2)) J2) (@ (@ tptp.nth_list_list_a Xs) J2)))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (not (= I3 J2)) (= (@ (@ tptp.nth_list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) X2)) J2) (@ (@ tptp.nth_list_a Xs) J2)))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (Xs tptp.list_a) (X2 tptp.a)) (=> (not (= I3 J2)) (= (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I3) X2)) J2) (@ (@ tptp.nth_a Xs) J2)))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (not (= I3 J2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) J2) (@ (@ tptp.nth_nat Xs) J2)))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (I4 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.list_update_nat Xs))) (=> (not (= I3 I4)) (= (@ (@ (@ tptp.list_update_nat (@ (@ _let_1 I3) X2)) I4) X4) (@ (@ (@ tptp.list_update_nat (@ (@ _let_1 I4) X4)) I3) X2))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (I4 tptp.nat) (Xs tptp.list_list_a) (X2 tptp.list_a) (X4 tptp.list_a)) (let ((_let_1 (@ tptp.list_update_list_a Xs))) (=> (not (= I3 I4)) (= (@ (@ (@ tptp.list_update_list_a (@ (@ _let_1 I3) X2)) I4) X4) (@ (@ (@ tptp.list_update_list_a (@ (@ _let_1 I4) X4)) I3) X2))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (I4 tptp.nat) (Xs tptp.list_a) (X2 tptp.a) (X4 tptp.a)) (let ((_let_1 (@ tptp.list_update_a Xs))) (=> (not (= I3 I4)) (= (@ (@ (@ tptp.list_update_a (@ (@ _let_1 I3) X2)) I4) X4) (@ (@ (@ tptp.list_update_a (@ (@ _let_1 I4) X4)) I3) X2))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (K tptp.nat) (N tptp.nat)) (= (@ tptp.size_s1898481668st_nat (@ (@ (@ tptp.listSl1794011552ux_nat Xs) K) N)) N)))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (K tptp.nat) (N tptp.nat)) (= (@ tptp.size_s575106428list_a (@ (@ (@ tptp.listSl856612276list_a Xs) K) N)) N)))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (K tptp.nat) (N tptp.nat)) (= (@ tptp.size_s1427607542list_a (@ (@ (@ tptp.listSl1495374126_aux_a Xs) K) N)) N)))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_nat) (J2 tptp.nat) (X2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_list_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) X2)) J2))) (let ((_let_2 (= I3 J2))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1898481668st_nat Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_list_nat Xs) J2)))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_list_a) (J2 tptp.nat) (X2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.nth_list_list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) X2)) J2))) (let ((_let_2 (= I3 J2))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s575106428list_a Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_list_list_a Xs) J2)))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_a) (J2 tptp.nat) (X2 tptp.a)) (let ((_let_1 (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I3) X2)) J2))) (let ((_let_2 (= I3 J2))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_a Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_a Xs) J2)))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_a) (J2 tptp.nat) (X2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.nth_list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) X2)) J2))) (let ((_let_2 (= I3 J2))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1427607542list_a Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_list_a Xs) J2)))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_nat) (J2 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) J2))) (let ((_let_2 (= I3 J2))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) J2)))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_nat) (X2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1898481668st_nat Xs)) (= (= (@ (@ (@ tptp.list_update_list_nat Xs) I3) X2) Xs) (= (@ (@ tptp.nth_list_nat Xs) I3) X2)))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_list_a) (X2 tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s575106428list_a Xs)) (= (= (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) X2) Xs) (= (@ (@ tptp.nth_list_list_a Xs) I3) X2)))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_a) (X2 tptp.a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_a Xs)) (= (= (@ (@ (@ tptp.list_update_a Xs) I3) X2) Xs) (= (@ (@ tptp.nth_a Xs) I3) X2)))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1427607542list_a Xs)) (= (= (@ (@ (@ tptp.list_update_list_a Xs) I3) X2) Xs) (= (@ (@ tptp.nth_list_a Xs) I3) X2)))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ (@ tptp.list_update_nat Xs) I3) X2) Xs) (= (@ (@ tptp.nth_nat Xs) I3) X2)))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_nat Xs))) (let ((_let_2 (@ tptp.size_s1898481668st_nat Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_list_nat2 (@ (@ (@ tptp.list_update_list_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.set_list_nat2 Xs))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_list_a Xs))) (let ((_let_2 (@ tptp.size_s575106428list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_list_list_a2 (@ (@ (@ tptp.list_u1330012152list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.set_list_list_a2 Xs))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_a Xs))) (let ((_let_2 (@ tptp.size_size_list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_a2 (@ (@ (@ tptp.list_update_a (@ (@ (@ tptp.list_update_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.set_a2 Xs))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_a Xs))) (let ((_let_2 (@ tptp.size_s1427607542list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_list_a2 (@ (@ (@ tptp.list_update_list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.set_list_a2 Xs))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.set_nat2 Xs))))))))
% 0.19/0.54 (assert (= tptp.list_desc_set_nat (lambda ((Xs2 tptp.list_set_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s577819178et_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 J)) (@ _let_1 I2))))))))))
% 0.19/0.54 (assert (= tptp.list_desc_set_list_a (lambda ((Xs2 tptp.list_set_list_a)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s1635937238list_a Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_list_a Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_le1301786372list_a (@ _let_1 J)) (@ _let_1 I2))))))))))
% 0.19/0.54 (assert (= tptp.list_desc_set_a (lambda ((Xs2 tptp.list_set_a)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_set_a Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_a Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 J)) (@ _let_1 I2))))))))))
% 0.19/0.54 (assert (= tptp.list_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I2))))))))))
% 0.19/0.54 (assert (= tptp.list_asc_set_nat (lambda ((Xs2 tptp.list_set_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s577819178et_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 I2)) (@ _let_1 J))))))))))
% 0.19/0.54 (assert (= tptp.list_asc_set_list_a (lambda ((Xs2 tptp.list_set_list_a)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s1635937238list_a Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_list_a Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_le1301786372list_a (@ _let_1 I2)) (@ _let_1 J))))))))))
% 0.19/0.54 (assert (= tptp.list_asc_set_a (lambda ((Xs2 tptp.list_set_a)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_set_a Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_a Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 I2)) (@ _let_1 J))))))))))
% 0.19/0.54 (assert (= tptp.list_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))))
% 0.19/0.54 (assert (forall ((A2 tptp.list_a) (P (-> tptp.list_a Bool))) (= (@ (@ tptp.member_list_a A2) (@ tptp.collect_list_a P)) (@ P A2))))
% 0.19/0.54 (assert (forall ((A2 tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A2) (@ tptp.collect_a P)) (@ P A2))))
% 0.19/0.54 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A))) A)))
% 0.19/0.54 (assert (forall ((A tptp.set_list_a)) (= (@ tptp.collect_list_a (lambda ((X3 tptp.list_a)) (@ (@ tptp.member_list_a X3) A))) A)))
% 0.19/0.54 (assert (forall ((A tptp.set_a)) (= (@ tptp.collect_a (lambda ((X3 tptp.a)) (@ (@ tptp.member_a X3) A))) A)))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_nat Xs))) (let ((_let_2 (@ tptp.size_s1898481668st_nat Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_list_nat (@ (@ (@ tptp.list_update_list_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.distinct_list_nat Xs))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_list_a Xs))) (let ((_let_2 (@ tptp.size_s575106428list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_list_list_a (@ (@ (@ tptp.list_u1330012152list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.distinct_list_list_a Xs))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_a Xs))) (let ((_let_2 (@ tptp.size_size_list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_a (@ (@ (@ tptp.list_update_a (@ (@ (@ tptp.list_update_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.distinct_a Xs))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_a Xs))) (let ((_let_2 (@ tptp.size_s1427607542list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_list_a (@ (@ (@ tptp.list_update_list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.distinct_list_a Xs))))))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (Xs tptp.list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_nat (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.distinct_nat Xs))))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_nat) (Xs tptp.list_list_nat)) (=> (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) tptp.top_top_set_nat)) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1898481668st_nat Xs)) (not (= X2 (@ (@ tptp.nth_list_nat Xs) N2)))))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_list_a) (Xs tptp.list_list_list_a)) (=> (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) tptp.top_top_set_nat)) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s575106428list_a Xs)) (not (= X2 (@ (@ tptp.nth_list_list_a Xs) N2)))))))))
% 0.19/0.54 (assert (forall ((X2 tptp.a) (Xs tptp.list_a)) (=> (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) tptp.top_top_set_nat)) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs)) (not (= X2 (@ (@ tptp.nth_a Xs) N2)))))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_a) (Xs tptp.list_list_a)) (=> (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) tptp.top_top_set_nat)) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1427607542list_a Xs)) (not (= X2 (@ (@ tptp.nth_list_a Xs) N2)))))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) tptp.top_top_set_nat)) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (not (= X2 (@ (@ tptp.nth_nat Xs) N2)))))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat Xs)) (@ (@ tptp.member_list_nat (@ (@ tptp.nth_list_nat Xs) N)) (@ (@ tptp.f_image_list_nat Xs) tptp.top_top_set_nat)))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_list_list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a Xs)) (@ (@ tptp.member_list_list_a (@ (@ tptp.nth_list_list_a Xs) N)) (@ (@ tptp.f_image_list_list_a Xs) tptp.top_top_set_nat)))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Xs) N)) (@ (@ tptp.f_image_a Xs) tptp.top_top_set_nat)))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Xs) N)) (@ (@ tptp.f_image_list_a Xs) tptp.top_top_set_nat)))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ (@ tptp.f_image_nat Xs) tptp.top_top_set_nat)))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_nat) (Xs tptp.list_list_nat) (N tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_nat Xs) N)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat Xs)) (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) tptp.top_top_set_nat))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_list_a) (Xs tptp.list_list_list_a) (N tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_list_a Xs) N)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a Xs)) (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) tptp.top_top_set_nat))))))
% 0.19/0.54 (assert (forall ((X2 tptp.a) (Xs tptp.list_a) (N tptp.nat)) (=> (= X2 (@ (@ tptp.nth_a Xs) N)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) tptp.top_top_set_nat))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_a) (Xs tptp.list_list_a) (N tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_a Xs) N)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) tptp.top_top_set_nat))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (= X2 (@ (@ tptp.nth_nat Xs) N)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) tptp.top_top_set_nat))))))
% 0.19/0.54 (assert (forall ((A tptp.set_nat) (Xs tptp.list_list_nat) (B tptp.set_list_nat)) (=> (forall ((N2 tptp.nat)) (=> (and (@ (@ tptp.member_nat N2) A) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1898481668st_nat Xs))) (@ (@ tptp.member_list_nat (@ (@ tptp.nth_list_nat Xs) N2)) B))) (@ (@ tptp.ord_le1747345782st_nat (@ (@ tptp.f_image_list_nat Xs) A)) B))))
% 0.19/0.54 (assert (forall ((A tptp.set_nat) (Xs tptp.list_list_list_a) (B tptp.set_list_list_a)) (=> (forall ((N2 tptp.nat)) (=> (and (@ (@ tptp.member_nat N2) A) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s575106428list_a Xs))) (@ (@ tptp.member_list_list_a (@ (@ tptp.nth_list_list_a Xs) N2)) B))) (@ (@ tptp.ord_le1756736906list_a (@ (@ tptp.f_image_list_list_a Xs) A)) B))))
% 0.19/0.54 (assert (forall ((A tptp.set_nat) (Xs tptp.list_a) (B tptp.set_a)) (=> (forall ((N2 tptp.nat)) (=> (and (@ (@ tptp.member_nat N2) A) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs))) (@ (@ tptp.member_a (@ (@ tptp.nth_a Xs) N2)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.f_image_a Xs) A)) B))))
% 0.19/0.54 (assert (forall ((A tptp.set_nat) (Xs tptp.list_list_a) (B tptp.set_list_a)) (=> (forall ((N2 tptp.nat)) (=> (and (@ (@ tptp.member_nat N2) A) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1427607542list_a Xs))) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Xs) N2)) B))) (@ (@ tptp.ord_le1301786372list_a (@ (@ tptp.f_image_list_a Xs) A)) B))))
% 0.19/0.54 (assert (forall ((A tptp.set_nat) (Xs tptp.list_nat) (B tptp.set_nat)) (=> (forall ((N2 tptp.nat)) (=> (and (@ (@ tptp.member_nat N2) A) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs))) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N2)) B))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.f_image_nat Xs) A)) B))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (A tptp.set_nat) (B tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.f_image_a Xs) A)) B) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Xs) X3)) B)))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (A tptp.set_nat) (B tptp.set_list_a)) (= (@ (@ tptp.ord_le1301786372list_a (@ (@ tptp.f_image_list_a Xs) A)) B) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Xs) X3)) B)))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.f_image_nat Xs) A)) B) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) X3)) B)))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (I3 tptp.nat) (X2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_a Xs)) I3) (= (@ (@ (@ tptp.list_update_a Xs) I3) X2) Xs))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (I3 tptp.nat) (X2 tptp.list_a)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1427607542list_a Xs)) I3) (= (@ (@ (@ tptp.list_update_list_a Xs) I3) X2) Xs))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I3) (= (@ (@ (@ tptp.list_update_nat Xs) I3) X2) Xs))))
% 0.19/0.54 (assert (forall ((F (-> tptp.nat tptp.nat)) (I3 tptp.nat) (J2 tptp.nat)) (=> (forall ((I tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (@ (@ tptp.ord_less_nat (@ F I)) (@ F J3)))) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ F J2))))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.19/0.54 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N3) (= M3 N3)))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.19/0.54 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N3) (not (= M3 N3))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (X2 tptp.a)) (=> (@ tptp.distinct_a Xs) (=> (@ (@ tptp.member_a X2) (@ tptp.set_a2 Xs)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X5) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) X5) X2) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) Y3) X2)) (= Y3 X5)))))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (@ tptp.distinct_list_a Xs) (=> (@ (@ tptp.member_list_a X2) (@ tptp.set_list_a2 Xs)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X5) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) X5) X2) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) Y3) X2)) (= Y3 X5)))))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X5) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) X5) X2) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) Y3) X2)) (= Y3 X5)))))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_asc_nat Xs) (@ tptp.distinct_nat Xs))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_desc_nat Xs) (@ tptp.distinct_nat Xs))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_asc_nat Xs) (forall ((J4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J4) (@ tptp.size_size_list_nat Xs)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I5) J4) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I5)) (@ _let_1 J4))))))))))
% 0.19/0.54 (assert (= tptp.list_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))))))
% 0.19/0.54 (assert (= tptp.list_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I2))))))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (I3 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_a Xs))) (let ((_let_2 (@ tptp.size_size_list_a Xs))) (=> (@ tptp.distinct_a Xs) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I3) (@ _let_1 J2)) (= I3 J2)))))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (I3 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_a Xs))) (let ((_let_2 (@ tptp.size_s1427607542list_a Xs))) (=> (@ tptp.distinct_list_a Xs) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I3) (@ _let_1 J2)) (= I3 J2)))))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I3) (@ _let_1 J2)) (= I3 J2)))))))))
% 0.19/0.54 (assert (= tptp.distinct_a (lambda ((Xs2 tptp.list_a)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs2)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_a Xs2))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_a Xs2)) (=> (not (= I2 J)) (not (= (@ _let_1 I2) (@ _let_1 J))))))))))))
% 0.19/0.54 (assert (= tptp.distinct_list_a (lambda ((Xs2 tptp.list_list_a)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1427607542list_a Xs2)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_list_a Xs2))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s1427607542list_a Xs2)) (=> (not (= I2 J)) (not (= (@ _let_1 I2) (@ _let_1 J))))))))))))
% 0.19/0.54 (assert (= tptp.distinct_nat (lambda ((Xs2 tptp.list_nat)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (=> (not (= I2 J)) (not (= (@ _let_1 I2) (@ _let_1 J))))))))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (P (-> tptp.a Bool))) (= (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) (@ tptp.set_a2 Xs)) (@ P X3))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs)) (@ P (@ (@ tptp.nth_a Xs) I2)))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (P (-> tptp.list_a Bool))) (= (forall ((X3 tptp.list_a)) (=> (@ (@ tptp.member_list_a X3) (@ tptp.set_list_a2 Xs)) (@ P X3))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1427607542list_a Xs)) (@ P (@ (@ tptp.nth_list_a Xs) I2)))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I2)))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (P (-> tptp.a Bool)) (X2 tptp.a)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (@ P (@ (@ tptp.nth_a Xs) I)))) (=> (@ (@ tptp.member_a X2) (@ tptp.set_a2 Xs)) (@ P X2)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (P (-> tptp.list_a Bool)) (X2 tptp.list_a)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1427607542list_a Xs)) (@ P (@ (@ tptp.nth_list_a Xs) I)))) (=> (@ (@ tptp.member_list_a X2) (@ tptp.set_list_a2 Xs)) (@ P X2)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I)))) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ P X2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.a) (Xs tptp.list_a)) (= (@ (@ tptp.member_a X2) (@ tptp.set_a2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I2) X2))))))
% 0.19/0.54 (assert (forall ((X2 tptp.list_a) (Xs tptp.list_list_a)) (= (@ (@ tptp.member_list_a X2) (@ tptp.set_list_a2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) I2) X2))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I2) X2))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_a) (P (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (=> (forall ((X5 tptp.a)) (=> (@ (@ tptp.member_a X5) (@ tptp.set_a2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_a Xs) N))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_list_a) (P (-> tptp.list_a Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (=> (forall ((X5 tptp.list_a)) (=> (@ (@ tptp.member_list_a X5) (@ tptp.set_list_a2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_list_a Xs) N))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Xs) N)) (@ tptp.set_a2 Xs)))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Xs) N)) (@ tptp.set_list_a2 Xs)))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ tptp.set_nat2 Xs)))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_a) (X2 tptp.a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a X2) (@ tptp.set_a2 (@ (@ (@ tptp.list_update_a Xs) N) X2))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a X2) (@ tptp.set_list_a2 (@ (@ (@ tptp.list_update_list_a Xs) N) X2))))))
% 0.19/0.54 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X2))))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_a) (A tptp.set_nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_nat N2) A))) (= (@ (@ tptp.f_image_a Xs) A) (@ tptp.set_a2 Xs)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_list_a) (A tptp.set_nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_nat N2) A))) (= (@ (@ tptp.f_image_list_a Xs) A) (@ tptp.set_list_a2 Xs)))))
% 0.19/0.54 (assert (forall ((Xs tptp.list_nat) (A tptp.set_nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat N2) A))) (= (@ (@ tptp.f_image_nat Xs) A) (@ tptp.set_nat2 Xs)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)))
% 0.19/0.54 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B2))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) X5)))))))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.19/0.54 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I3))) (=> (@ _let_1 J2) (=> (@ (@ tptp.ord_less_eq_nat J2) K) (@ _let_1 K))))))
% 0.19/0.54 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.19/0.54 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= A2 B2)))))
% 0.19/0.54 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (@ (@ tptp.ord_less_eq_nat A3) B3)))))
% 0.19/0.54 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 0.19/0.54 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= A2 B2)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_eq_nat A2) C)))))
% 0.19/0.54 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ tptp.ord_less_eq_nat B3) A3)))))
% 0.19/0.54 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y2) (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y2))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y2))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= X2 Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat Y2) X2))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= X2 Y2)))))
% 0.19/0.54 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((X3 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X3)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C)))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A2) (@ F C)))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_1))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (= X2 Y2)) (or (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat Y2) X2)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (@ (@ tptp.ord_less_nat B2) A2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (@ (@ tptp.ord_less_nat B2) A2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_nat Y2) Z2) (@ _let_1 Z2))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y2) (= X2 Y2) (@ (@ tptp.ord_less_nat Y2) X2))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A2) C)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 0.19/0.54 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (not (@ (@ tptp.ord_less_nat A2) B2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2)))))
% 0.19/0.54 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y3) X5) (@ P Y3))) (@ P X5))) (@ P A2))))
% 0.19/0.54 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y2) X2)) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= Y2 X2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (=> (@ (@ tptp.ord_less_nat Y2) X2) P))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (=> (not (= X2 Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ _let_1 C))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2)))))
% 0.19/0.54 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X tptp.nat)) (@ P3 X))) (lambda ((P2 (-> tptp.nat Bool))) (exists ((N3 tptp.nat)) (and (@ P2 N3) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (not (@ P2 M3)))))))))
% 0.19/0.54 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2))))))
% 0.19/0.54 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (or (@ (@ tptp.ord_less_nat Y2) X2) (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (= A2 B2)))))
% 0.19/0.54 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (not (= A2 B2)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_nat A2) B2)))))
% 0.19/0.54 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (@ (@ tptp.ord_less_eq_nat B2) A2))))
% 0.19/0.54 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (= A3 B3))))))
% 0.19/0.54 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A3) (= A3 B3)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_eq_nat A2) B2))))
% 0.19/0.54 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_nat C) A2)))))
% 0.19/0.54 (assert (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 0.19/0.54 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (= A3 B3))))))
% 0.19/0.54 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B3) (= A3 B3)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A2) C)))))
% 0.19/0.54 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y2) X2)) (@ (@ tptp.ord_less_nat X2) Y2))))
% 0.19/0.54 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y5) (not (@ (@ tptp.ord_less_eq_nat Y5) X3))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (or (@ (@ tptp.ord_less_nat X2) Y2) (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_nat Y2) X2))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2))))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (=> (@ (@ tptp.ord_less_nat Y2) Z2) (@ (@ tptp.ord_less_nat X2) Z2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (= (@ (@ tptp.ord_less_eq_nat X2) Y2) (= X2 Y2)))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_nat A2) B2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A2) (@ F C)))))))
% 0.19/0.54 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y5) (not (= X3 Y5))))))
% 0.19/0.54 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y5 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y5) (= X3 Y5)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2))))
% 0.19/0.54 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (not (@ (@ tptp.ord_less_nat X2) Y2)))))
% 0.19/0.54 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.divide_divide_nat N) M)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N) K)))))
% 0.19/0.54 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 0.19/0.54 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K3) (@ P K3))) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) I5) (@ P I5))) (@ P K3)))) (@ P M)))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (@ (@ tptp.ord_less_eq_nat T) X6)))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (@ (@ tptp.ord_less_nat T) X6)))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X6))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (= X6 T)))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (= X6 T)))))))
% 0.19/0.54 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (= (or (@ P X6) (@ Q X6)) (or (@ P4 X6) (@ Q2 X6))))))))))
% 0.19/0.54 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (= (and (@ P X6) (@ Q X6)) (and (@ P4 X6) (@ Q2 X6))))))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (@ (@ tptp.ord_less_nat T) X6))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (@ (@ tptp.ord_less_nat X6) T)))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (= X6 T)))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (= X6 T)))))))
% 0.19/0.54 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (= (or (@ P X6) (@ Q X6)) (or (@ P4 X6) (@ Q2 X6))))))))))
% 0.19/0.54 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (= (and (@ P X6) (@ Q X6)) (and (@ P4 X6) (@ Q2 X6))))))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (@ (@ tptp.ord_less_eq_nat X6) T)))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (@ (@ tptp.ord_less_eq_nat T) X6))))))
% 0.19/0.54 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (@ (@ tptp.ord_less_eq_nat X6) T))))))
% 0.19/0.54 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ P A2) (=> (not (@ P B2)) (exists ((C2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) C2) (@ (@ tptp.ord_less_eq_nat C2) B2) (forall ((X6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A2) X6) (@ (@ tptp.ord_less_nat X6) C2)) (@ P X6))) (forall ((D tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A2) X5) (@ (@ tptp.ord_less_nat X5) D)) (@ P X5))) (@ (@ tptp.ord_less_eq_nat D) C2))))))))))
% 0.69/0.88 (assert (= tptp.ord_less_eq_nat (lambda ((N3 tptp.nat) (A3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) X3) (not (= N3 X3)))))))
% 0.69/0.88 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (N3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) A3) (not (= N3 X3)))))))
% 0.69/0.88 (assert (@ (@ tptp.ord_less_nat tptp.m) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a tptp.xs)) tptp.k)))
% 0.69/0.88 (assert (not (= (@ tptp.size_size_list_a (@ (@ tptp.nth_list_a (@ (@ tptp.listSl1174287072ice2_a tptp.xs) tptp.k)) tptp.m)) tptp.k)))
% 0.69/0.88 (set-info :filename cvc5---1.0.5_2861)
% 0.69/0.88 (check-sat-assuming ( true ))
% 0.69/0.88 ------- get file name : TPTP file name is ITP104^1
% 0.69/0.88 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2861.smt2...
% 0.69/0.88 --- Run --ho-elim --full-saturate-quant at 10...
% 0.69/0.88 % SZS status Theorem for ITP104^1
% 0.69/0.88 % SZS output start Proof for ITP104^1
% 0.69/0.88 (
% 0.69/0.88 (let ((_let_1 (@ tptp.size_size_list_a (@ (@ tptp.nth_list_a (@ (@ tptp.listSl1174287072ice2_a tptp.xs) tptp.k)) tptp.m)))) (let ((_let_2 (not (= _let_1 tptp.k)))) (let ((_let_3 (@ (@ tptp.ord_less_nat tptp.m) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a tptp.xs)) tptp.k)))) (let ((_let_4 (= tptp.distinct_nat (lambda ((Xs2 tptp.list_nat)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (=> (not (= I2 J)) (not (= (@ _let_1 I2) (@ _let_1 J))))))))))))) (let ((_let_5 (= tptp.distinct_list_a (lambda ((Xs2 tptp.list_list_a)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1427607542list_a Xs2)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_list_a Xs2))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s1427607542list_a Xs2)) (=> (not (= I2 J)) (not (= (@ _let_1 I2) (@ _let_1 J))))))))))))) (let ((_let_6 (= tptp.distinct_a (lambda ((Xs2 tptp.list_a)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs2)) (forall ((J tptp.nat)) (let ((_let_1 (@ tptp.nth_a Xs2))) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_a Xs2)) (=> (not (= I2 J)) (not (= (@ _let_1 I2) (@ _let_1 J))))))))))))) (let ((_let_7 (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N3) (= M3 N3)))))) (let ((_let_8 (= tptp.list_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))))))) (let ((_let_9 (= tptp.list_asc_set_a (lambda ((Xs2 tptp.list_set_a)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_set_a Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_a Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 I2)) (@ _let_1 J))))))))))) (let ((_let_10 (= tptp.list_asc_set_list_a (lambda ((Xs2 tptp.list_set_list_a)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s1635937238list_a Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_list_a Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_le1301786372list_a (@ _let_1 I2)) (@ _let_1 J))))))))))) (let ((_let_11 (= tptp.list_asc_set_nat (lambda ((Xs2 tptp.list_set_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s577819178et_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 I2)) (@ _let_1 J))))))))))) (let ((_let_12 (= tptp.list_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I2))))))))))) (let ((_let_13 (= tptp.list_desc_set_a (lambda ((Xs2 tptp.list_set_a)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_set_a Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_a Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_set_a (@ _let_1 J)) (@ _let_1 I2))))))))))) (let ((_let_14 (= tptp.list_desc_set_list_a (lambda ((Xs2 tptp.list_set_list_a)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s1635937238list_a Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_list_a Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_le1301786372list_a (@ _let_1 J)) (@ _let_1 I2))))))))))) (let ((_let_15 (= tptp.list_desc_set_nat (lambda ((Xs2 tptp.list_set_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_s577819178et_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_set_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 J)) (@ _let_1 I2))))))))))) (let ((_let_16 (= tptp.list_ex_nat (lambda ((P2 (-> tptp.nat Bool)) (Xs2 tptp.list_nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.size_size_list_nat Xs2)) (@ P2 (@ (@ tptp.nth_nat Xs2) N3)))))))) (let ((_let_17 (= tptp.list_ex_list_a (lambda ((P2 (-> tptp.list_a Bool)) (Xs2 tptp.list_list_a)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.size_s1427607542list_a Xs2)) (@ P2 (@ (@ tptp.nth_list_a Xs2) N3)))))))) (let ((_let_18 (= tptp.list_ex_a (lambda ((P2 (-> tptp.a Bool)) (Xs2 tptp.list_a)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.size_size_list_a Xs2)) (@ P2 (@ (@ tptp.nth_a Xs2) N3)))))))) (let ((_let_19 (= tptp.list_ex_list_list_a (lambda ((P2 (-> tptp.list_list_a Bool)) (Xs2 tptp.list_list_list_a)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.size_s575106428list_a Xs2)) (@ P2 (@ (@ tptp.nth_list_list_a Xs2) N3)))))))) (let ((_let_20 (= tptp.list_ex_list_nat (lambda ((P2 (-> tptp.list_nat Bool)) (Xs2 tptp.list_list_nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat N3) (@ tptp.size_s1898481668st_nat Xs2)) (@ P2 (@ (@ tptp.nth_list_nat Xs2) N3)))))))) (let ((_let_21 (= tptp.listSl97544552lice_a (lambda ((Xs2 tptp.list_a) (K2 tptp.nat)) (@ (@ (@ tptp.listSl1495374126_aux_a Xs2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs2)) K2)))))) (let ((_let_22 (= tptp.listSl1630398182ce_nat (lambda ((Xs2 tptp.list_nat) (K2 tptp.nat)) (@ (@ (@ tptp.listSl1794011552ux_nat Xs2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_nat Xs2)) K2)))))) (let ((_let_23 (= tptp.listSl162220270list_a (lambda ((Xs2 tptp.list_list_a) (K2 tptp.nat)) (@ (@ (@ tptp.listSl856612276list_a Xs2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1427607542list_a Xs2)) K2)))))) (let ((_let_24 (= tptp.listSl2102238196list_a (lambda ((Xs2 tptp.list_list_list_a) (K2 tptp.nat)) (@ (@ (@ tptp.listSl902632890list_a Xs2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.size_s575106428list_a Xs2)) K2)))))) (let ((_let_25 (= tptp.listSl729562870st_nat (lambda ((Xs2 tptp.list_list_nat) (K2 tptp.nat)) (@ (@ (@ tptp.listSl1506485424st_nat Xs2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1898481668st_nat Xs2)) K2)))))) (let ((_let_26 (= tptp.list_strict_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J))))))))))) (let ((_let_27 (forall ((M tptp.nat) (Xs tptp.list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs)) K)) (= (@ tptp.size_size_list_a (@ (@ tptp.nth_list_a (@ (@ tptp.listSl97544552lice_a Xs) K)) M)) K))))) (let ((_let_28 (= tptp.list_strict_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ _let_1 J)) (@ _let_1 I2))))))))))) (let ((_let_29 (forall ((M tptp.nat) (Xs tptp.list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs)) K)) (= (@ (@ tptp.nth_list_a (@ (@ tptp.listSl1174287072ice2_a Xs) K)) M) (@ (@ tptp.nth_list_a (@ (@ tptp.listSl97544552lice_a Xs) K)) M)))))) (let ((_let_30 (ho_102 (ho_101 k_100 (ho_114 (ho_164 k_163 tptp.xs) tptp.k)) tptp.m))) (let ((_let_31 (= tptp.k (ho_95 k_94 _let_30)))) (let ((_let_32 (ho_64 (ho_131 k_130 (ho_95 k_94 tptp.xs)) tptp.k))) (let ((_let_33 (ho_102 (ho_101 k_100 (ho_114 (ho_162 (ho_161 k_160 tptp.xs) tptp.k) _let_32)) tptp.m))) (let ((_let_34 (= _let_30 _let_33))) (let ((_let_35 (= tptp.k (ho_95 k_94 _let_33)))) (let ((_let_36 (not _let_31))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (= tptp.k _let_1)) _let_36))))))) (let ((_let_38 (ho_40 (ho_39 k_41 tptp.m) _let_32))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_34))) (let ((_let_41 (forall ((M tptp.nat) (Xs tptp.list_a) (K tptp.nat)) (let ((_let_1 (ho_64 (ho_131 k_130 (ho_95 k_94 Xs)) K))) (or (not (ho_40 (ho_39 k_41 M) _let_1)) (= (ho_102 (ho_101 k_100 (ho_114 (ho_162 (ho_161 k_160 Xs) K) _let_1)) M) (ho_102 (ho_101 k_100 (ho_114 (ho_164 k_163 Xs) K)) M))))))) (let ((_let_42 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_7)) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_21)) (ASSUME :args (_let_22)) (ASSUME :args (_let_23)) (ASSUME :args (_let_24)) (ASSUME :args (_let_25)) (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_29)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_42 :args ((forall ((M tptp.nat) (Xs tptp.list_a) (K tptp.nat)) (or (not (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs)) K))) (= (@ (@ tptp.nth_list_a (@ (@ tptp.listSl1174287072ice2_a Xs) K)) M) (@ (@ tptp.nth_list_a (@ (@ tptp.listSl97544552lice_a Xs) K)) M)))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((M tptp.nat) (Xs tptp.list_a) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs)) K))) (or (not (@ (@ tptp.ord_less_nat M) _let_1)) (= (@ (@ tptp.nth_list_a (@ (@ tptp.listSl1174287072ice2_a Xs) K)) M) (@ (@ tptp.nth_list_a (@ (@ (@ tptp.listSl1495374126_aux_a Xs) K) _let_1)) M))))) _let_41))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 _let_38)))))) (let ((_let_45 (or _let_39 _let_35))) (let ((_let_46 (forall ((M tptp.nat) (Xs tptp.list_a) (K tptp.nat)) (let ((_let_1 (ho_64 (ho_131 k_130 (ho_95 k_94 Xs)) K))) (or (not (ho_40 (ho_39 k_41 M) _let_1)) (= K (ho_95 k_94 (ho_102 (ho_101 k_100 (ho_114 (ho_162 (ho_161 k_160 Xs) K) _let_1)) M)))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_27)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_42 :args ((forall ((M tptp.nat) (Xs tptp.list_a) (K tptp.nat)) (or (not (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs)) K))) (= K (@ tptp.size_size_list_a (@ (@ tptp.nth_list_a (@ (@ tptp.listSl97544552lice_a Xs) K)) M))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((M tptp.nat) (Xs tptp.list_a) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs)) K))) (or (not (@ (@ tptp.ord_less_nat M) _let_1)) (= K (@ tptp.size_size_list_a (@ (@ tptp.nth_list_a (@ (@ (@ tptp.listSl1495374126_aux_a Xs) K) _let_1)) M)))))) _let_46))))))) (let ((_let_48 (and _let_36 _let_34))) (let ((_let_49 (_let_36 _let_34))) (let ((_let_50 (ASSUME :args (_let_34)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_48)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_37 _let_50) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.k)) (CONG (REFL :args (k_94)) (SYMM _let_50) :args (APPLY_UF ho_95)) :args (=)) (FALSE_INTRO _let_37))) :args _let_49)) :args _let_49)) :args (true _let_48)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_31))) (REFL :args ((not _let_34))) (REFL :args ((not _let_35))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_39 _let_35 (not _let_45)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.m tptp.xs tptp.k QUANTIFIERS_INST_E_MATCHING ((not (= (ho_40 (ho_39 k_41 M) (ho_64 (ho_131 k_130 (ho_95 k_94 Xs)) K)) false))))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_35 false _let_38 false _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_34 (not _let_40)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_43 :args (tptp.m tptp.xs tptp.k QUANTIFIERS_INST_E_MATCHING ((not (= (ho_40 (ho_39 k_41 M) (ho_64 (ho_131 k_130 (ho_95 k_94 Xs)) K)) false))))) :args (_let_41)))) _let_43 :args (_let_40 false _let_41)) :args (_let_34 false _let_38 false _let_40)) _let_37 :args (false false _let_35 false _let_34 true _let_31)) :args ((forall ((Xs tptp.list_list_nat) (Ys tptp.list_list_nat)) (=> (= (@ tptp.size_s1898481668st_nat Xs) (@ tptp.size_s1898481668st_nat Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1898481668st_nat Xs)) (= (@ (@ tptp.nth_list_nat Xs) I) (@ (@ tptp.nth_list_nat Ys) I)))) (= Xs Ys)))) (forall ((Xs tptp.list_list_list_a) (Ys tptp.list_list_list_a)) (=> (= (@ tptp.size_s575106428list_a Xs) (@ tptp.size_s575106428list_a Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s575106428list_a Xs)) (= (@ (@ tptp.nth_list_list_a Xs) I) (@ (@ tptp.nth_list_list_a Ys) I)))) (= Xs Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I) (@ (@ tptp.nth_nat Ys) I)))) (= Xs Ys)))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (= (@ tptp.size_s1427607542list_a Xs) (@ tptp.size_s1427607542list_a Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) I) (@ (@ tptp.nth_list_a Ys) I)))) (= Xs Ys)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I) (@ (@ tptp.nth_a Ys) I)))) (= Xs Ys)))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.list_nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.list_nat)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_list_nat)) (and (= (@ tptp.size_s1898481668st_nat Xs2) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_list_nat Xs2) I2)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.list_list_a Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.list_list_a)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_list_list_a)) (and (= (@ tptp.size_s575106428list_a Xs2) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_list_list_a Xs2) I2)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.nat)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_nat Xs2) I2)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.list_a Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.list_a)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_list_a)) (and (= (@ tptp.size_s1427607542list_a Xs2) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_list_a Xs2) I2)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.a Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.a)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_a)) (and (= (@ tptp.size_size_list_a Xs2) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_a Xs2) I2)))))))) (= (lambda ((Y tptp.list_list_nat) (Z tptp.list_list_nat)) (= Y Z)) (lambda ((Xs2 tptp.list_list_nat) (Ys2 tptp.list_list_nat)) (and (= (@ tptp.size_s1898481668st_nat Xs2) (@ tptp.size_s1898481668st_nat Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1898481668st_nat Xs2)) (= (@ (@ tptp.nth_list_nat Xs2) I2) (@ (@ tptp.nth_list_nat Ys2) I2))))))) (= (lambda ((Y tptp.list_list_list_a) (Z tptp.list_list_list_a)) (= Y Z)) (lambda ((Xs2 tptp.list_list_list_a) (Ys2 tptp.list_list_list_a)) (and (= (@ tptp.size_s575106428list_a Xs2) (@ tptp.size_s575106428list_a Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s575106428list_a Xs2)) (= (@ (@ tptp.nth_list_list_a Xs2) I2) (@ (@ tptp.nth_list_list_a Ys2) I2))))))) (= (lambda ((Y tptp.list_nat) (Z tptp.list_nat)) (= Y Z)) (lambda ((Xs2 tptp.list_nat) (Ys2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I2) (@ (@ tptp.nth_nat Ys2) I2))))))) (= (lambda ((Y tptp.list_list_a) (Z tptp.list_list_a)) (= Y Z)) (lambda ((Xs2 tptp.list_list_a) (Ys2 tptp.list_list_a)) (and (= (@ tptp.size_s1427607542list_a Xs2) (@ tptp.size_s1427607542list_a Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1427607542list_a Xs2)) (= (@ (@ tptp.nth_list_a Xs2) I2) (@ (@ tptp.nth_list_a Ys2) I2))))))) (= (lambda ((Y tptp.list_a) (Z tptp.list_a)) (= Y Z)) (lambda ((Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs2)) (= (@ (@ tptp.nth_a Xs2) I2) (@ (@ tptp.nth_a Ys2) I2))))))) (forall ((M tptp.nat) (Xs tptp.list_list_nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1898481668st_nat Xs)) K)) (= (@ (@ tptp.nth_list_list_nat (@ (@ tptp.listSl2099749758st_nat Xs) K)) M) (@ (@ tptp.nth_list_list_nat (@ (@ tptp.listSl729562870st_nat Xs) K)) M)))) (forall ((M tptp.nat) (Xs tptp.list_list_list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s575106428list_a Xs)) K)) (= (@ (@ tptp.nth_list_list_list_a (@ (@ tptp.listSl769338732list_a Xs) K)) M) (@ (@ tptp.nth_list_list_list_a (@ (@ tptp.listSl2102238196list_a Xs) K)) M)))) (forall ((M tptp.nat) (Xs tptp.list_list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1427607542list_a Xs)) K)) (= (@ (@ tptp.nth_list_list_a (@ (@ tptp.listSl703198822list_a Xs) K)) M) (@ (@ tptp.nth_list_list_a (@ (@ tptp.listSl162220270list_a Xs) K)) M)))) (forall ((M tptp.nat) (Xs tptp.list_nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_nat Xs)) K)) (= (@ (@ tptp.nth_list_nat (@ (@ tptp.listSl882585454e2_nat Xs) K)) M) (@ (@ tptp.nth_list_nat (@ (@ tptp.listSl1630398182ce_nat Xs) K)) M)))) _let_29 (forall ((P (-> tptp.list_list_nat Bool)) (Xs tptp.list_list_nat)) (=> (forall ((Xs3 tptp.list_list_nat)) (=> (forall ((Ys3 tptp.list_list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1898481668st_nat Ys3)) (@ tptp.size_s1898481668st_nat Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) (forall ((P (-> tptp.list_list_list_a Bool)) (Xs tptp.list_list_list_a)) (=> (forall ((Xs3 tptp.list_list_list_a)) (=> (forall ((Ys3 tptp.list_list_list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s575106428list_a Ys3)) (@ tptp.size_s575106428list_a Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) (forall ((P (-> tptp.list_list_a Bool)) (Xs tptp.list_list_a)) (=> (forall ((Xs3 tptp.list_list_a)) (=> (forall ((Ys3 tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1427607542list_a Ys3)) (@ tptp.size_s1427607542list_a Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys3)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (forall ((Xs3 tptp.list_a)) (=> (forall ((Ys3 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_a Ys3)) (@ tptp.size_size_list_a Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) _let_28 (forall ((M tptp.nat) (Xs tptp.list_list_nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1898481668st_nat Xs)) K)) (= (@ tptp.size_s1898481668st_nat (@ (@ tptp.nth_list_list_nat (@ (@ tptp.listSl729562870st_nat Xs) K)) M)) K))) (forall ((M tptp.nat) (Xs tptp.list_list_list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s575106428list_a Xs)) K)) (= (@ tptp.size_s575106428list_a (@ (@ tptp.nth_list_list_list_a (@ (@ tptp.listSl2102238196list_a Xs) K)) M)) K))) (forall ((M tptp.nat) (Xs tptp.list_list_a) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1427607542list_a Xs)) K)) (= (@ tptp.size_s1427607542list_a (@ (@ tptp.nth_list_list_a (@ (@ tptp.listSl162220270list_a Xs) K)) M)) K))) (forall ((M tptp.nat) (Xs tptp.list_nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_nat Xs)) K)) (= (@ tptp.size_size_list_nat (@ (@ tptp.nth_list_nat (@ (@ tptp.listSl1630398182ce_nat Xs) K)) M)) K))) _let_27 _let_26 (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_list_nat)) (= (@ tptp.size_s1898481668st_nat Xs3) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_list_list_a)) (= (@ tptp.size_s575106428list_a Xs3) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_list_a)) (= (@ tptp.size_s1427607542list_a Xs3) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_a)) (= (@ tptp.size_size_list_a Xs3) N))) (forall ((Xs tptp.list_list_nat) (Ys tptp.list_list_nat)) (=> (not (= (@ tptp.size_s1898481668st_nat Xs) (@ tptp.size_s1898481668st_nat Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_list_list_a) (Ys tptp.list_list_list_a)) (=> (not (= (@ tptp.size_s575106428list_a Xs) (@ tptp.size_s575106428list_a Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (not (= (@ tptp.size_s1427607542list_a Xs) (@ tptp.size_s1427607542list_a Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (not (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys))) (not (= Xs Ys)))) (forall ((X2 tptp.list_list_nat) (Y2 tptp.list_list_nat)) (=> (not (= (@ tptp.size_s1898481668st_nat X2) (@ tptp.size_s1898481668st_nat Y2))) (not (= X2 Y2)))) (forall ((X2 tptp.list_list_list_a) (Y2 tptp.list_list_list_a)) (=> (not (= (@ tptp.size_s575106428list_a X2) (@ tptp.size_s575106428list_a Y2))) (not (= X2 Y2)))) (forall ((X2 tptp.list_a) (Y2 tptp.list_a)) (=> (not (= (@ tptp.size_size_list_a X2) (@ tptp.size_size_list_a Y2))) (not (= X2 Y2)))) (forall ((X2 tptp.list_list_a) (Y2 tptp.list_list_a)) (=> (not (= (@ tptp.size_s1427607542list_a X2) (@ tptp.size_s1427607542list_a Y2))) (not (= X2 Y2)))) (forall ((X2 tptp.list_nat) (Y2 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X2) (@ tptp.size_size_list_nat Y2))) (not (= X2 Y2)))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))) (forall ((Xs tptp.list_list_nat) (K tptp.nat)) (= (@ tptp.size_s1321307156st_nat (@ (@ tptp.listSl729562870st_nat Xs) K)) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1898481668st_nat Xs)) K))) (forall ((Xs tptp.list_list_list_a) (K tptp.nat)) (= (@ tptp.size_s1764310658list_a (@ (@ tptp.listSl2102238196list_a Xs) K)) (@ (@ tptp.divide_divide_nat (@ tptp.size_s575106428list_a Xs)) K))) (forall ((Xs tptp.list_list_a) (K tptp.nat)) (= (@ tptp.size_s575106428list_a (@ (@ tptp.listSl162220270list_a Xs) K)) (@ (@ tptp.divide_divide_nat (@ tptp.size_s1427607542list_a Xs)) K))) (forall ((Xs tptp.list_nat) (K tptp.nat)) (= (@ tptp.size_s1898481668st_nat (@ (@ tptp.listSl1630398182ce_nat Xs) K)) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_nat Xs)) K))) (forall ((Xs tptp.list_a) (K tptp.nat)) (= (@ tptp.size_s1427607542list_a (@ (@ tptp.listSl97544552lice_a Xs) K)) (@ (@ tptp.divide_divide_nat (@ tptp.size_size_list_a Xs)) K))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2)))))) (@ P N))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P M2))) (@ P N2))) (@ P N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) _let_25 _let_24 _let_23 _let_22 _let_21 (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_desc_nat Xs) (@ tptp.list_desc_nat Xs))) _let_20 _let_19 _let_18 _let_17 _let_16 (forall ((X2 tptp.list_nat) (Xs tptp.list_list_nat) (N tptp.nat) (A tptp.set_nat)) (=> (= X2 (@ (@ tptp.nth_list_nat Xs) N)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat Xs)) (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) A)))))) (forall ((X2 tptp.list_list_a) (Xs tptp.list_list_list_a) (N tptp.nat) (A tptp.set_nat)) (=> (= X2 (@ (@ tptp.nth_list_list_a Xs) N)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a Xs)) (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) A)))))) (forall ((X2 tptp.a) (Xs tptp.list_a) (N tptp.nat) (A tptp.set_nat)) (=> (= X2 (@ (@ tptp.nth_a Xs) N)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) A)))))) (forall ((X2 tptp.list_a) (Xs tptp.list_list_a) (N tptp.nat) (A tptp.set_nat)) (=> (= X2 (@ (@ tptp.nth_list_a Xs) N)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) A)))))) (forall ((X2 tptp.nat) (Xs tptp.list_nat) (N tptp.nat) (A tptp.set_nat)) (=> (= X2 (@ (@ tptp.nth_nat Xs) N)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) A)))))) (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_asc_nat Xs) (@ tptp.list_asc_nat Xs))) (forall ((I3 tptp.nat) (Xs tptp.list_list_nat) (X2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1898481668st_nat Xs)) (= (@ (@ tptp.nth_list_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) X2)) I3) X2))) (forall ((I3 tptp.nat) (Xs tptp.list_list_list_a) (X2 tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s575106428list_a Xs)) (= (@ (@ tptp.nth_list_list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) X2)) I3) X2))) (forall ((I3 tptp.nat) (Xs tptp.list_a) (X2 tptp.a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I3) X2)) I3) X2))) (forall ((I3 tptp.nat) (Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) X2)) I3) X2))) (forall ((I3 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) I3) X2))) (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_nat) (X2 tptp.list_nat)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat Xs)) (=> (= X2 (@ (@ tptp.nth_list_nat Xs) N)) (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) A)))))) (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_list_a) (X2 tptp.list_list_a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a Xs)) (=> (= X2 (@ (@ tptp.nth_list_list_a Xs) N)) (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) A)))))) (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_a) (X2 tptp.a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (=> (= X2 (@ (@ tptp.nth_a Xs) N)) (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) A)))))) (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (=> (= X2 (@ (@ tptp.nth_list_a Xs) N)) (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) A)))))) (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (= X2 (@ (@ tptp.nth_nat Xs) N)) (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) A)))))) (forall ((X2 tptp.list_nat) (Xs tptp.list_list_nat) (A tptp.set_nat)) (= (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s1898481668st_nat Xs)) (= X2 (@ (@ tptp.nth_list_nat Xs) X3)))))) (forall ((X2 tptp.list_list_a) (Xs tptp.list_list_list_a) (A tptp.set_nat)) (= (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s575106428list_a Xs)) (= X2 (@ (@ tptp.nth_list_list_a Xs) X3)))))) (forall ((X2 tptp.a) (Xs tptp.list_a) (A tptp.set_nat)) (= (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_a Xs)) (= X2 (@ (@ tptp.nth_a Xs) X3)))))) (forall ((X2 tptp.list_a) (Xs tptp.list_list_a) (A tptp.set_nat)) (= (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s1427607542list_a Xs)) (= X2 (@ (@ tptp.nth_list_a Xs) X3)))))) (forall ((X2 tptp.nat) (Xs tptp.list_nat) (A tptp.set_nat)) (= (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_nat Xs)) (= X2 (@ (@ tptp.nth_nat Xs) X3)))))) (forall ((N tptp.nat) (Xs tptp.list_list_nat)) (let ((_let_1 (@ tptp.butlast_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat _let_1)) (= (@ (@ tptp.nth_list_nat _let_1) N) (@ (@ tptp.nth_list_nat Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_list_list_a)) (let ((_let_1 (@ tptp.butlast_list_list_a Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a _let_1)) (= (@ (@ tptp.nth_list_list_a _let_1) N) (@ (@ tptp.nth_list_list_a Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.butlast_a Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a _let_1)) (= (@ (@ tptp.nth_a _let_1) N) (@ (@ tptp.nth_a Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.butlast_list_a Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a _let_1)) (= (@ (@ tptp.nth_list_a _let_1) N) (@ (@ tptp.nth_list_a Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.butlast_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat _let_1)) (= (@ (@ tptp.nth_nat _let_1) N) (@ (@ tptp.nth_nat Xs) N))))) (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_nat)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat Xs)) (@ (@ tptp.member_list_nat (@ (@ tptp.nth_list_nat Xs) N)) (@ (@ tptp.f_image_list_nat Xs) A))))) (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_list_a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a Xs)) (@ (@ tptp.member_list_list_a (@ (@ tptp.nth_list_list_a Xs) N)) (@ (@ tptp.f_image_list_list_a Xs) A))))) (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Xs) N)) (@ (@ tptp.f_image_a Xs) A))))) (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_list_a)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Xs) N)) (@ (@ tptp.f_image_list_a Xs) A))))) (forall ((N tptp.nat) (A tptp.set_nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat N) A) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ (@ tptp.f_image_nat Xs) A))))) (forall ((X2 tptp.list_nat) (Xs tptp.list_list_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) A)) (not (forall ((N2 tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_nat Xs) N2)) (=> (@ (@ tptp.member_nat N2) A) (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1898481668st_nat Xs))))))))) (forall ((X2 tptp.list_list_a) (Xs tptp.list_list_list_a) (A tptp.set_nat)) (=> (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) A)) (not (forall ((N2 tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_list_a Xs) N2)) (=> (@ (@ tptp.member_nat N2) A) (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s575106428list_a Xs))))))))) (forall ((X2 tptp.a) (Xs tptp.list_a) (A tptp.set_nat)) (=> (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) A)) (not (forall ((N2 tptp.nat)) (=> (= X2 (@ (@ tptp.nth_a Xs) N2)) (=> (@ (@ tptp.member_nat N2) A) (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs))))))))) (forall ((X2 tptp.list_a) (Xs tptp.list_list_a) (A tptp.set_nat)) (=> (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) A)) (not (forall ((N2 tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_a Xs) N2)) (=> (@ (@ tptp.member_nat N2) A) (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1427607542list_a Xs))))))))) (forall ((X2 tptp.nat) (Xs tptp.list_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) A)) (not (forall ((N2 tptp.nat)) (=> (= X2 (@ (@ tptp.nth_nat Xs) N2)) (=> (@ (@ tptp.member_nat N2) A) (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs))))))))) (forall ((Xs tptp.list_nat) (I3 tptp.nat) (X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.list_update_nat Xs) I3))) (= (@ (@ (@ tptp.list_update_nat (@ _let_1 X2)) I3) Y2) (@ _let_1 Y2)))) (forall ((Xs tptp.list_list_a) (I3 tptp.nat) (X2 tptp.list_a) (Y2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.list_update_list_a Xs) I3))) (= (@ (@ (@ tptp.list_update_list_a (@ _let_1 X2)) I3) Y2) (@ _let_1 Y2)))) (forall ((Xs tptp.list_a) (I3 tptp.nat) (X2 tptp.a) (Y2 tptp.a)) (let ((_let_1 (@ (@ tptp.list_update_a Xs) I3))) (= (@ (@ (@ tptp.list_update_a (@ _let_1 X2)) I3) Y2) (@ _let_1 Y2)))) (forall ((Xs tptp.list_list_nat) (I3 tptp.nat) (X2 tptp.list_nat)) (= (@ tptp.size_s1898481668st_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) X2)) (@ tptp.size_s1898481668st_nat Xs))) (forall ((Xs tptp.list_list_list_a) (I3 tptp.nat) (X2 tptp.list_list_a)) (= (@ tptp.size_s575106428list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) X2)) (@ tptp.size_s575106428list_a Xs))) (forall ((Xs tptp.list_a) (I3 tptp.nat) (X2 tptp.a)) (= (@ tptp.size_size_list_a (@ (@ (@ tptp.list_update_a Xs) I3) X2)) (@ tptp.size_size_list_a Xs))) (forall ((Xs tptp.list_list_a) (I3 tptp.nat) (X2 tptp.list_a)) (= (@ tptp.size_s1427607542list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) X2)) (@ tptp.size_s1427607542list_a Xs))) (forall ((Xs tptp.list_nat) (I3 tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) (@ tptp.size_size_list_nat Xs))) (forall ((Xs tptp.list_list_nat) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_update_list_nat Xs) I3) (@ (@ tptp.nth_list_nat Xs) I3)) Xs)) (forall ((Xs tptp.list_list_list_a) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) (@ (@ tptp.nth_list_list_a Xs) I3)) Xs)) (forall ((Xs tptp.list_list_a) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_update_list_a Xs) I3) (@ (@ tptp.nth_list_a Xs) I3)) Xs)) (forall ((Xs tptp.list_a) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_update_a Xs) I3) (@ (@ tptp.nth_a Xs) I3)) Xs)) (forall ((Xs tptp.list_nat) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I3) (@ (@ tptp.nth_nat Xs) I3)) Xs)) (forall ((I3 tptp.nat) (J2 tptp.nat) (Xs tptp.list_list_nat) (X2 tptp.list_nat)) (=> (not (= I3 J2)) (= (@ (@ tptp.nth_list_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) X2)) J2) (@ (@ tptp.nth_list_nat Xs) J2)))) (forall ((I3 tptp.nat) (J2 tptp.nat) (Xs tptp.list_list_list_a) (X2 tptp.list_list_a)) (=> (not (= I3 J2)) (= (@ (@ tptp.nth_list_list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) X2)) J2) (@ (@ tptp.nth_list_list_a Xs) J2)))) (forall ((I3 tptp.nat) (J2 tptp.nat) (Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (not (= I3 J2)) (= (@ (@ tptp.nth_list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) X2)) J2) (@ (@ tptp.nth_list_a Xs) J2)))) (forall ((I3 tptp.nat) (J2 tptp.nat) (Xs tptp.list_a) (X2 tptp.a)) (=> (not (= I3 J2)) (= (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I3) X2)) J2) (@ (@ tptp.nth_a Xs) J2)))) (forall ((I3 tptp.nat) (J2 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (not (= I3 J2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) J2) (@ (@ tptp.nth_nat Xs) J2)))) (forall ((I3 tptp.nat) (I4 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.list_update_nat Xs))) (=> (not (= I3 I4)) (= (@ (@ (@ tptp.list_update_nat (@ (@ _let_1 I3) X2)) I4) X4) (@ (@ (@ tptp.list_update_nat (@ (@ _let_1 I4) X4)) I3) X2))))) (forall ((I3 tptp.nat) (I4 tptp.nat) (Xs tptp.list_list_a) (X2 tptp.list_a) (X4 tptp.list_a)) (let ((_let_1 (@ tptp.list_update_list_a Xs))) (=> (not (= I3 I4)) (= (@ (@ (@ tptp.list_update_list_a (@ (@ _let_1 I3) X2)) I4) X4) (@ (@ (@ tptp.list_update_list_a (@ (@ _let_1 I4) X4)) I3) X2))))) (forall ((I3 tptp.nat) (I4 tptp.nat) (Xs tptp.list_a) (X2 tptp.a) (X4 tptp.a)) (let ((_let_1 (@ tptp.list_update_a Xs))) (=> (not (= I3 I4)) (= (@ (@ (@ tptp.list_update_a (@ (@ _let_1 I3) X2)) I4) X4) (@ (@ (@ tptp.list_update_a (@ (@ _let_1 I4) X4)) I3) X2))))) (forall ((Xs tptp.list_nat) (K tptp.nat) (N tptp.nat)) (= (@ tptp.size_s1898481668st_nat (@ (@ (@ tptp.listSl1794011552ux_nat Xs) K) N)) N)) (forall ((Xs tptp.list_list_a) (K tptp.nat) (N tptp.nat)) (= (@ tptp.size_s575106428list_a (@ (@ (@ tptp.listSl856612276list_a Xs) K) N)) N)) (forall ((Xs tptp.list_a) (K tptp.nat) (N tptp.nat)) (= (@ tptp.size_s1427607542list_a (@ (@ (@ tptp.listSl1495374126_aux_a Xs) K) N)) N)) (forall ((I3 tptp.nat) (Xs tptp.list_list_nat) (J2 tptp.nat) (X2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_list_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) X2)) J2))) (let ((_let_2 (= I3 J2))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1898481668st_nat Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_list_nat Xs) J2)))))))) (forall ((I3 tptp.nat) (Xs tptp.list_list_list_a) (J2 tptp.nat) (X2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.nth_list_list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) X2)) J2))) (let ((_let_2 (= I3 J2))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s575106428list_a Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_list_list_a Xs) J2)))))))) (forall ((I3 tptp.nat) (Xs tptp.list_a) (J2 tptp.nat) (X2 tptp.a)) (let ((_let_1 (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I3) X2)) J2))) (let ((_let_2 (= I3 J2))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_a Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_a Xs) J2)))))))) (forall ((I3 tptp.nat) (Xs tptp.list_list_a) (J2 tptp.nat) (X2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.nth_list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) X2)) J2))) (let ((_let_2 (= I3 J2))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1427607542list_a Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_list_a Xs) J2)))))))) (forall ((I3 tptp.nat) (Xs tptp.list_nat) (J2 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) J2))) (let ((_let_2 (= I3 J2))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) J2)))))))) (forall ((I3 tptp.nat) (Xs tptp.list_list_nat) (X2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1898481668st_nat Xs)) (= (= (@ (@ (@ tptp.list_update_list_nat Xs) I3) X2) Xs) (= (@ (@ tptp.nth_list_nat Xs) I3) X2)))) (forall ((I3 tptp.nat) (Xs tptp.list_list_list_a) (X2 tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s575106428list_a Xs)) (= (= (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) X2) Xs) (= (@ (@ tptp.nth_list_list_a Xs) I3) X2)))) (forall ((I3 tptp.nat) (Xs tptp.list_a) (X2 tptp.a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_a Xs)) (= (= (@ (@ (@ tptp.list_update_a Xs) I3) X2) Xs) (= (@ (@ tptp.nth_a Xs) I3) X2)))) (forall ((I3 tptp.nat) (Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1427607542list_a Xs)) (= (= (@ (@ (@ tptp.list_update_list_a Xs) I3) X2) Xs) (= (@ (@ tptp.nth_list_a Xs) I3) X2)))) (forall ((I3 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ (@ tptp.list_update_nat Xs) I3) X2) Xs) (= (@ (@ tptp.nth_nat Xs) I3) X2)))) (forall ((I3 tptp.nat) (Xs tptp.list_list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_nat Xs))) (let ((_let_2 (@ tptp.size_s1898481668st_nat Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_list_nat2 (@ (@ (@ tptp.list_update_list_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.set_list_nat2 Xs))))))) (forall ((I3 tptp.nat) (Xs tptp.list_list_list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_list_a Xs))) (let ((_let_2 (@ tptp.size_s575106428list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_list_list_a2 (@ (@ (@ tptp.list_u1330012152list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.set_list_list_a2 Xs))))))) (forall ((I3 tptp.nat) (Xs tptp.list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_a Xs))) (let ((_let_2 (@ tptp.size_size_list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_a2 (@ (@ (@ tptp.list_update_a (@ (@ (@ tptp.list_update_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.set_a2 Xs))))))) (forall ((I3 tptp.nat) (Xs tptp.list_list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_a Xs))) (let ((_let_2 (@ tptp.size_s1427607542list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_list_a2 (@ (@ (@ tptp.list_update_list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.set_list_a2 Xs))))))) (forall ((I3 tptp.nat) (Xs tptp.list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.set_nat2 Xs))))))) _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))) (forall ((A2 tptp.list_a) (P (-> tptp.list_a Bool))) (= (@ (@ tptp.member_list_a A2) (@ tptp.collect_list_a P)) (@ P A2))) (forall ((A2 tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A2) (@ tptp.collect_a P)) (@ P A2))) (forall ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A))) A)) (forall ((A tptp.set_list_a)) (= (@ tptp.collect_list_a (lambda ((X3 tptp.list_a)) (@ (@ tptp.member_list_a X3) A))) A)) (forall ((A tptp.set_a)) (= (@ tptp.collect_a (lambda ((X3 tptp.a)) (@ (@ tptp.member_a X3) A))) A)) (forall ((I3 tptp.nat) (Xs tptp.list_list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_nat Xs))) (let ((_let_2 (@ tptp.size_s1898481668st_nat Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_list_nat (@ (@ (@ tptp.list_update_list_nat (@ (@ (@ tptp.list_update_list_nat Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.distinct_list_nat Xs))))))) (forall ((I3 tptp.nat) (Xs tptp.list_list_list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_list_a Xs))) (let ((_let_2 (@ tptp.size_s575106428list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_list_list_a (@ (@ (@ tptp.list_u1330012152list_a (@ (@ (@ tptp.list_u1330012152list_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.distinct_list_list_a Xs))))))) (forall ((I3 tptp.nat) (Xs tptp.list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_a Xs))) (let ((_let_2 (@ tptp.size_size_list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_a (@ (@ (@ tptp.list_update_a (@ (@ (@ tptp.list_update_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.distinct_a Xs))))))) (forall ((I3 tptp.nat) (Xs tptp.list_list_a) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_a Xs))) (let ((_let_2 (@ tptp.size_s1427607542list_a Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_list_a (@ (@ (@ tptp.list_update_list_a (@ (@ (@ tptp.list_update_list_a Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.distinct_list_a Xs))))))) (forall ((I3 tptp.nat) (Xs tptp.list_nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (@ tptp.distinct_nat (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I3) (@ _let_1 J2))) J2) (@ _let_1 I3))) (@ tptp.distinct_nat Xs))))))) (forall ((X2 tptp.list_nat) (Xs tptp.list_list_nat)) (=> (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) tptp.top_top_set_nat)) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1898481668st_nat Xs)) (not (= X2 (@ (@ tptp.nth_list_nat Xs) N2)))))))) (forall ((X2 tptp.list_list_a) (Xs tptp.list_list_list_a)) (=> (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) tptp.top_top_set_nat)) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s575106428list_a Xs)) (not (= X2 (@ (@ tptp.nth_list_list_a Xs) N2)))))))) (forall ((X2 tptp.a) (Xs tptp.list_a)) (=> (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) tptp.top_top_set_nat)) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs)) (not (= X2 (@ (@ tptp.nth_a Xs) N2)))))))) (forall ((X2 tptp.list_a) (Xs tptp.list_list_a)) (=> (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) tptp.top_top_set_nat)) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1427607542list_a Xs)) (not (= X2 (@ (@ tptp.nth_list_a Xs) N2)))))))) (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) tptp.top_top_set_nat)) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (not (= X2 (@ (@ tptp.nth_nat Xs) N2)))))))) (forall ((N tptp.nat) (Xs tptp.list_list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat Xs)) (@ (@ tptp.member_list_nat (@ (@ tptp.nth_list_nat Xs) N)) (@ (@ tptp.f_image_list_nat Xs) tptp.top_top_set_nat)))) (forall ((N tptp.nat) (Xs tptp.list_list_list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a Xs)) (@ (@ tptp.member_list_list_a (@ (@ tptp.nth_list_list_a Xs) N)) (@ (@ tptp.f_image_list_list_a Xs) tptp.top_top_set_nat)))) (forall ((N tptp.nat) (Xs tptp.list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Xs) N)) (@ (@ tptp.f_image_a Xs) tptp.top_top_set_nat)))) (forall ((N tptp.nat) (Xs tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Xs) N)) (@ (@ tptp.f_image_list_a Xs) tptp.top_top_set_nat)))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ (@ tptp.f_image_nat Xs) tptp.top_top_set_nat)))) (forall ((X2 tptp.list_nat) (Xs tptp.list_list_nat) (N tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_nat Xs) N)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1898481668st_nat Xs)) (@ (@ tptp.member_list_nat X2) (@ (@ tptp.f_image_list_nat Xs) tptp.top_top_set_nat))))) (forall ((X2 tptp.list_list_a) (Xs tptp.list_list_list_a) (N tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_list_a Xs) N)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s575106428list_a Xs)) (@ (@ tptp.member_list_list_a X2) (@ (@ tptp.f_image_list_list_a Xs) tptp.top_top_set_nat))))) (forall ((X2 tptp.a) (Xs tptp.list_a) (N tptp.nat)) (=> (= X2 (@ (@ tptp.nth_a Xs) N)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a X2) (@ (@ tptp.f_image_a Xs) tptp.top_top_set_nat))))) (forall ((X2 tptp.list_a) (Xs tptp.list_list_a) (N tptp.nat)) (=> (= X2 (@ (@ tptp.nth_list_a Xs) N)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a X2) (@ (@ tptp.f_image_list_a Xs) tptp.top_top_set_nat))))) (forall ((X2 tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (= X2 (@ (@ tptp.nth_nat Xs) N)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X2) (@ (@ tptp.f_image_nat Xs) tptp.top_top_set_nat))))) (forall ((A tptp.set_nat) (Xs tptp.list_list_nat) (B tptp.set_list_nat)) (=> (forall ((N2 tptp.nat)) (=> (and (@ (@ tptp.member_nat N2) A) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1898481668st_nat Xs))) (@ (@ tptp.member_list_nat (@ (@ tptp.nth_list_nat Xs) N2)) B))) (@ (@ tptp.ord_le1747345782st_nat (@ (@ tptp.f_image_list_nat Xs) A)) B))) (forall ((A tptp.set_nat) (Xs tptp.list_list_list_a) (B tptp.set_list_list_a)) (=> (forall ((N2 tptp.nat)) (=> (and (@ (@ tptp.member_nat N2) A) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s575106428list_a Xs))) (@ (@ tptp.member_list_list_a (@ (@ tptp.nth_list_list_a Xs) N2)) B))) (@ (@ tptp.ord_le1756736906list_a (@ (@ tptp.f_image_list_list_a Xs) A)) B))) (forall ((A tptp.set_nat) (Xs tptp.list_a) (B tptp.set_a)) (=> (forall ((N2 tptp.nat)) (=> (and (@ (@ tptp.member_nat N2) A) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs))) (@ (@ tptp.member_a (@ (@ tptp.nth_a Xs) N2)) B))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.f_image_a Xs) A)) B))) (forall ((A tptp.set_nat) (Xs tptp.list_list_a) (B tptp.set_list_a)) (=> (forall ((N2 tptp.nat)) (=> (and (@ (@ tptp.member_nat N2) A) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1427607542list_a Xs))) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Xs) N2)) B))) (@ (@ tptp.ord_le1301786372list_a (@ (@ tptp.f_image_list_a Xs) A)) B))) (forall ((A tptp.set_nat) (Xs tptp.list_nat) (B tptp.set_nat)) (=> (forall ((N2 tptp.nat)) (=> (and (@ (@ tptp.member_nat N2) A) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs))) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N2)) B))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.f_image_nat Xs) A)) B))) (forall ((Xs tptp.list_a) (A tptp.set_nat) (B tptp.set_a)) (= (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.f_image_a Xs) A)) B) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Xs) X3)) B)))))) (forall ((Xs tptp.list_list_a) (A tptp.set_nat) (B tptp.set_list_a)) (= (@ (@ tptp.ord_le1301786372list_a (@ (@ tptp.f_image_list_a Xs) A)) B) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.ord_less_nat X3) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Xs) X3)) B)))))) (forall ((Xs tptp.list_nat) (A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.f_image_nat Xs) A)) B) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.ord_less_nat X3) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) X3)) B)))))) (forall ((Xs tptp.list_a) (I3 tptp.nat) (X2 tptp.a)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_a Xs)) I3) (= (@ (@ (@ tptp.list_update_a Xs) I3) X2) Xs))) (forall ((Xs tptp.list_list_a) (I3 tptp.nat) (X2 tptp.list_a)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1427607542list_a Xs)) I3) (= (@ (@ (@ tptp.list_update_list_a Xs) I3) X2) Xs))) (forall ((Xs tptp.list_nat) (I3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I3) (= (@ (@ (@ tptp.list_update_nat Xs) I3) X2) Xs))) (forall ((F (-> tptp.nat tptp.nat)) (I3 tptp.nat) (J2 tptp.nat)) (=> (forall ((I tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (@ (@ tptp.ord_less_nat (@ F I)) (@ F J3)))) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ F J2))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))) _let_7 (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))) (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N3) (not (= M3 N3))))) (forall ((Xs tptp.list_a) (X2 tptp.a)) (=> (@ tptp.distinct_a Xs) (=> (@ (@ tptp.member_a X2) (@ tptp.set_a2 Xs)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X5) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) X5) X2) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) Y3) X2)) (= Y3 X5)))))))) (forall ((Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (@ tptp.distinct_list_a Xs) (=> (@ (@ tptp.member_list_a X2) (@ tptp.set_list_a2 Xs)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X5) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) X5) X2) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) Y3) X2)) (= Y3 X5)))))))) (forall ((Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.ord_less_nat X5) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) X5) X2) (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat Y3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) Y3) X2)) (= Y3 X5)))))))) (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_asc_nat Xs) (@ tptp.distinct_nat Xs))) (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_desc_nat Xs) (@ tptp.distinct_nat Xs))) (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_asc_nat Xs) (forall ((J4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J4) (@ tptp.size_size_list_nat Xs)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I5) J4) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I5)) (@ _let_1 J4))))))))) (= tptp.list_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))))) (= tptp.list_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I2))))))))) (forall ((Xs tptp.list_a) (I3 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_a Xs))) (let ((_let_2 (@ tptp.size_size_list_a Xs))) (=> (@ tptp.distinct_a Xs) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I3) (@ _let_1 J2)) (= I3 J2)))))))) (forall ((Xs tptp.list_list_a) (I3 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_list_a Xs))) (let ((_let_2 (@ tptp.size_s1427607542list_a Xs))) (=> (@ tptp.distinct_list_a Xs) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I3) (@ _let_1 J2)) (= I3 J2)))))))) (forall ((Xs tptp.list_nat) (I3 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J2) _let_2) (= (= (@ _let_1 I3) (@ _let_1 J2)) (= I3 J2)))))))) _let_6 _let_5 _let_4 (forall ((Xs tptp.list_a) (P (-> tptp.a Bool))) (= (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) (@ tptp.set_a2 Xs)) (@ P X3))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs)) (@ P (@ (@ tptp.nth_a Xs) I2)))))) (forall ((Xs tptp.list_list_a) (P (-> tptp.list_a Bool))) (= (forall ((X3 tptp.list_a)) (=> (@ (@ tptp.member_list_a X3) (@ tptp.set_list_a2 Xs)) (@ P X3))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1427607542list_a Xs)) (@ P (@ (@ tptp.nth_list_a Xs) I2)))))) (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I2)))))) (forall ((Xs tptp.list_a) (P (-> tptp.a Bool)) (X2 tptp.a)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (@ P (@ (@ tptp.nth_a Xs) I)))) (=> (@ (@ tptp.member_a X2) (@ tptp.set_a2 Xs)) (@ P X2)))) (forall ((Xs tptp.list_list_a) (P (-> tptp.list_a Bool)) (X2 tptp.list_a)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1427607542list_a Xs)) (@ P (@ (@ tptp.nth_list_a Xs) I)))) (=> (@ (@ tptp.member_list_a X2) (@ tptp.set_list_a2 Xs)) (@ P X2)))) (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I)))) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ P X2)))) (forall ((X2 tptp.a) (Xs tptp.list_a)) (= (@ (@ tptp.member_a X2) (@ tptp.set_a2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I2) X2))))) (forall ((X2 tptp.list_a) (Xs tptp.list_list_a)) (= (@ (@ tptp.member_list_a X2) (@ tptp.set_list_a2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) I2) X2))))) (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I2) X2))))) (forall ((N tptp.nat) (Xs tptp.list_a) (P (-> tptp.a Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (=> (forall ((X5 tptp.a)) (=> (@ (@ tptp.member_a X5) (@ tptp.set_a2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_a Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_list_a) (P (-> tptp.list_a Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (=> (forall ((X5 tptp.list_a)) (=> (@ (@ tptp.member_list_a X5) (@ tptp.set_list_a2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_list_a Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_nat Xs) N))))) (forall ((N tptp.nat) (Xs tptp.list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Xs) N)) (@ tptp.set_a2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Xs) N)) (@ tptp.set_list_a2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ tptp.set_nat2 Xs)))) (forall ((N tptp.nat) (Xs tptp.list_a) (X2 tptp.a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_a X2) (@ tptp.set_a2 (@ (@ (@ tptp.list_update_a Xs) N) X2))))) (forall ((N tptp.nat) (Xs tptp.list_list_a) (X2 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_list_a X2) (@ tptp.set_list_a2 (@ (@ (@ tptp.list_update_list_a Xs) N) X2))))) (forall ((N tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X2))))) (forall ((Xs tptp.list_a) (A tptp.set_nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs)) (@ (@ tptp.member_nat N2) A))) (= (@ (@ tptp.f_image_a Xs) A) (@ tptp.set_a2 Xs)))) (forall ((Xs tptp.list_list_a) (A tptp.set_nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s1427607542list_a Xs)) (@ (@ tptp.member_nat N2) A))) (= (@ (@ tptp.f_image_list_a Xs) A) (@ tptp.set_list_a2 Xs)))) (forall ((Xs tptp.list_nat) (A tptp.set_nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat N2) A))) (= (@ (@ tptp.f_image_nat Xs) A) (@ tptp.set_nat2 Xs)))) (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B2))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) X5)))))))) (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((I3 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I3))) (=> (@ _let_1 J2) (=> (@ (@ tptp.ord_less_eq_nat J2) K) (@ _let_1 K))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (= A2 B2)))) (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (@ (@ tptp.ord_less_eq_nat A3) B3)))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2)))) (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)) (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2))))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (= A2 B2)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_eq_nat A2) C)))) (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ tptp.ord_less_eq_nat B3) A3)))) (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y2) (= X2 Y2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y2))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y2))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= X2 Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat Y2) X2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= X2 Y2)))) (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((X3 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X3)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))) (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))) (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A2) (@ F C)))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (= (@ F B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))) (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))) (forall ((X2 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_1))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (= X2 Y2)) (or (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (@ (@ tptp.ord_less_nat B2) A2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= X2 Y2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (@ (@ tptp.ord_less_nat B2) A2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_nat Y2) Z2) (@ _let_1 Z2))))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y2) (= X2 Y2) (@ (@ tptp.ord_less_nat Y2) X2))) (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A2 B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A2) C)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (not (@ (@ tptp.ord_less_nat A2) B2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= X2 Y2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y3) X5) (@ P Y3))) (@ P X5))) (@ P A2))) (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y2) X2)) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (= X2 Y2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= Y2 X2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (=> (@ (@ tptp.ord_less_nat Y2) X2) P))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (=> (not (= X2 Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ _let_1 C))))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2)))) (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X tptp.nat)) (@ P3 X))) (lambda ((P2 (-> tptp.nat Bool))) (exists ((N3 tptp.nat)) (and (@ P2 N3) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (not (@ P2 M3)))))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B2 tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A2) B2))))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (or (@ (@ tptp.ord_less_nat Y2) X2) (= X2 Y2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (not (= A2 B2)))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (not (= A2 B2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (not (= A2 B2)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_nat A2) B2)))) (forall ((B2 tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (@ (@ tptp.ord_less_eq_nat B2) A2))) (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (= A3 B3))))) (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A3) (= A3 B3)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (@ (@ tptp.ord_less_eq_nat A2) B2))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A2) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_nat C) A2)))) (forall ((B2 tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (= A3 B3))))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B3) (= A3 B3)))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A2) C)))) (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y2) X2)) (@ (@ tptp.ord_less_nat X2) Y2))) (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y5) (not (@ (@ tptp.ord_less_eq_nat Y5) X3))))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (or (@ (@ tptp.ord_less_nat X2) Y2) (= X2 Y2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_nat Y2) X2))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2))))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (=> (@ (@ tptp.ord_less_nat Y2) Z2) (@ (@ tptp.ord_less_nat X2) Z2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (= X2 Y2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (= (@ (@ tptp.ord_less_eq_nat X2) Y2) (= X2 Y2)))) (forall ((A2 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_nat A2) B2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))) (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))) (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X5 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y4) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A2) (@ F C)))))) (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y5) (not (= X3 Y5))))) (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y5 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y5) (= X3 Y5)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2))) (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (not (@ (@ tptp.ord_less_nat X2) Y2)))) (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.divide_divide_nat N) M)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N) K)))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)) (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K3) (@ P K3))) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N) (=> (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) I5) (@ P I5))) (@ P K3)))) (@ P M)))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (@ (@ tptp.ord_less_eq_nat T) X6)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (@ (@ tptp.ord_less_nat T) X6)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X6))) (=> (@ _let_1 Z3) (@ _let_1 T)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (= X6 T)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (not (= X6 T)))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (= (or (@ P X6) (@ Q X6)) (or (@ P4 X6) (@ Q2 X6))))))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (= (and (@ P X6) (@ Q X6)) (and (@ P4 X6) (@ Q2 X6))))))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (@ (@ tptp.ord_less_nat T) X6))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (@ (@ tptp.ord_less_nat X6) T)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (= X6 T)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (= X6 T)))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (= (or (@ P X6) (@ Q X6)) (or (@ P4 X6) (@ Q2 X6))))))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P4 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q2 X5))))) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (= (and (@ P X6) (@ Q X6)) (and (@ P4 X6) (@ Q2 X6))))))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (not (@ (@ tptp.ord_less_eq_nat X6) T)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X6) (@ (@ tptp.ord_less_eq_nat T) X6))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z3) (@ (@ tptp.ord_less_eq_nat X6) T))))) (forall ((A2 tptp.nat) (B2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ P A2) (=> (not (@ P B2)) (exists ((C2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) C2) (@ (@ tptp.ord_less_eq_nat C2) B2) (forall ((X6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A2) X6) (@ (@ tptp.ord_less_nat X6) C2)) (@ P X6))) (forall ((D tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A2) X5) (@ (@ tptp.ord_less_nat X5) D)) (@ P X5))) (@ (@ tptp.ord_less_eq_nat D) C2))))))))) (= tptp.ord_less_eq_nat (lambda ((N3 tptp.nat) (A3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) X3) (not (= N3 X3)))))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (N3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) A3) (not (= N3 X3)))))) _let_3 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.69/0.88 )
% 0.69/0.88 % SZS output end Proof for ITP104^1
% 0.69/0.88 % cvc5---1.0.5 exiting
% 0.69/0.89 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------