TSTP Solution File: ITP100^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP100^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 03:18:14 EDT 2023
% Result : Theorem 0.87s 1.10s
% Output : Proof 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17 % Problem : ITP100^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.18 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n007.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Sun Aug 27 15:27:12 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.25/0.58 %----Proving TH0
% 0.25/0.59 %------------------------------------------------------------------------------
% 0.25/0.59 % File : ITP100^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.59 % Domain : Interactive Theorem Proving
% 0.25/0.59 % Problem : Sledgehammer ListInf problem prob_52__5408414_1
% 0.25/0.59 % Version : Especial.
% 0.25/0.59 % English :
% 0.25/0.59
% 0.25/0.59 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.59 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.59 % Source : [Des21]
% 0.25/0.59 % Names : ListInf/prob_52__5408414_1 [Des21]
% 0.25/0.59
% 0.25/0.59 % Status : Theorem
% 0.25/0.59 % Rating : 0.38 v8.1.0, 0.27 v7.5.0
% 0.25/0.59 % Syntax : Number of formulae : 450 ( 197 unt; 94 typ; 0 def)
% 0.25/0.59 % Number of atoms : 947 ( 705 equ; 0 cnn)
% 0.25/0.59 % Maximal formula atoms : 13 ( 2 avg)
% 0.25/0.59 % Number of connectives : 3688 ( 230 ~; 53 |; 136 &;2783 @)
% 0.25/0.59 % ( 0 <=>; 486 =>; 0 <=; 0 <~>)
% 0.25/0.59 % Maximal formula depth : 29 ( 7 avg)
% 0.25/0.59 % Number of types : 10 ( 9 usr)
% 0.25/0.59 % Number of type conns : 477 ( 477 >; 0 *; 0 +; 0 <<)
% 0.25/0.59 % Number of symbols : 88 ( 85 usr; 8 con; 0-3 aty)
% 0.25/0.59 % Number of variables : 1277 ( 28 ^;1135 !; 114 ?;1277 :)
% 0.25/0.59 % SPC : TH0_THM_EQU_NAR
% 0.25/0.59
% 0.25/0.59 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:11.750
% 0.25/0.59 %------------------------------------------------------------------------------
% 0.25/0.59 % Could-be-implicit typings (9)
% 0.25/0.59 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.25/0.59 list_list_list_a: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_n_t__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.25/0.59 set_list_list_a: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.25/0.59 list_list_a: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_n_t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.25/0.59 set_list_a: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.25/0.59 list_nat: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.25/0.59 list_a: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.25/0.59 set_a: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_n_t__Nat__Onat,type,
% 0.25/0.59 nat: $tType ).
% 0.25/0.59
% 0.25/0.59 thf(ty_n_tf__a,type,
% 0.25/0.59 a: $tType ).
% 0.25/0.59
% 0.25/0.59 % Explicit typings (85)
% 0.25/0.59 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 bNF_Gr1972240547list_a: set_list_list_a > list_a > set_list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001tf__a,type,
% 0.25/0.59 bNF_Greatest_Shift_a: set_list_a > a > set_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 bNF_Gr1046450207list_a: set_list_list_a > list_list_a > set_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001tf__a,type,
% 0.25/0.59 bNF_Greatest_Succ_a: set_list_a > list_a > set_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_If_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 if_list_a: $o > list_a > list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List2_Olist__ord_001t__Nat__Onat,type,
% 0.25/0.59 list_ord_nat: ( nat > nat > $o ) > list_nat > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List2_Olist__strict__asc_001t__Nat__Onat,type,
% 0.25/0.59 list_strict_asc_nat: list_nat > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List2_Omap2_001tf__a_001tf__a_001tf__a,type,
% 0.25/0.59 map2_a_a_a: ( a > a > a ) > list_a > list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_ListInf__Mirabelle__akbajwqfbr_Oi__append_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 listIn1753026346list_a: list_list_a > ( nat > list_a ) > nat > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_ListInf__Mirabelle__akbajwqfbr_Oi__append_001tf__a,type,
% 0.25/0.59 listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oappend_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.25/0.59 append_list_list_a: list_list_list_a > list_list_list_a > list_list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oappend_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 append_list_a: list_list_a > list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 0.25/0.59 append_nat: list_nat > list_nat > list_nat ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oappend_001tf__a,type,
% 0.25/0.59 append_a: list_a > list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.25/0.59 bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Obind_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Obind_001tf__a_001tf__a,type,
% 0.25/0.59 bind_a_a: list_a > ( a > list_a ) > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 butlast_list_a: list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Obutlast_001tf__a,type,
% 0.25/0.59 butlast_a: list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oconcat_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 concat_list_a: list_list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oconcat_001tf__a,type,
% 0.25/0.59 concat_a: list_list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Odistinct__adj_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 distinct_adj_list_a: list_list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Odistinct__adj_001tf__a,type,
% 0.25/0.59 distinct_adj_a: list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Ofoldr_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.25/0.59 foldr_769741863list_a: ( list_list_a > list_list_a > list_list_a ) > list_list_list_a > list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Ofoldr_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 foldr_list_a_list_a: ( list_a > list_a > list_a ) > list_list_a > list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oinsert_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 insert_list_a: list_a > list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oinsert_001tf__a,type,
% 0.25/0.59 insert_a: a > list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olast_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 last_list_a: list_list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olast_001tf__a,type,
% 0.25/0.59 last_a: list_a > a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.25/0.59 cons_list_list_a: list_list_a > list_list_list_a > list_list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 cons_list_a: list_a > list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.25/0.59 cons_nat: nat > list_nat > list_nat ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_OCons_001tf__a,type,
% 0.25/0.59 cons_a: a > list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.25/0.59 nil_list_list_a: list_list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 nil_list_a: list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.25/0.59 nil_nat: list_nat ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_ONil_001tf__a,type,
% 0.25/0.59 nil_a: list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.25/0.59 hd_list_list_a: list_list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_Ohd_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 hd_list_a: list_list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_Ohd_001tf__a,type,
% 0.25/0.59 hd_a: list_a > a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_Otl_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 tl_list_a: list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist_Otl_001tf__a,type,
% 0.25/0.59 tl_a: list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist__ex1_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olist__ex1_001tf__a,type,
% 0.25/0.59 list_ex1_a: ( a > $o ) > list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olistrelp_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 listre1221556159list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olistrelp_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.25/0.59 listrelp_list_a_a: ( list_a > a > $o ) > list_list_a > list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olistrelp_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 listrelp_a_list_a: ( a > list_a > $o ) > list_a > list_list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Olistrelp_001tf__a_001tf__a,type,
% 0.25/0.59 listrelp_a_a: ( a > a > $o ) > list_a > list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Omap__tailrec__rev_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 map_ta982122357list_a: ( list_a > list_a ) > list_list_a > list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Omap__tailrec__rev_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.25/0.59 map_ta2002079599st_a_a: ( list_a > a ) > list_list_a > list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Omap__tailrec__rev_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 map_ta41997947list_a: ( a > list_a ) > list_a > list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Omap__tailrec__rev_001tf__a_001tf__a,type,
% 0.25/0.59 map_tailrec_rev_a_a: ( a > a ) > list_a > list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.25/0.59 maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Omaps_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Omaps_001tf__a_001tf__a,type,
% 0.25/0.59 maps_a_a: ( a > list_a ) > list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Omember_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 member_list_a: list_list_a > list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Omember_001tf__a,type,
% 0.25/0.59 member_a: list_a > a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oord_Olexordp__eq_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 lexordp_eq_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oord_Olexordp__eq_001tf__a,type,
% 0.25/0.59 lexordp_eq_a: ( a > a > $o ) > list_a > list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oord__class_Olexordp_001t__Nat__Onat,type,
% 0.25/0.59 ord_lexordp_nat: list_nat > list_nat > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oord__class_Olexordp__eq_001t__Nat__Onat,type,
% 0.25/0.59 ord_lexordp_eq_nat: list_nat > list_nat > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oproduct__lists_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 product_lists_list_a: list_list_list_a > list_list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oproduct__lists_001tf__a,type,
% 0.25/0.59 product_lists_a: list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oremdups__adj_001tf__a,type,
% 0.25/0.59 remdups_adj_a: list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Orotate1_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 rotate1_list_a: list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Orotate1_001tf__a,type,
% 0.25/0.59 rotate1_a: list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Oshuffles_001tf__a,type,
% 0.25/0.59 shuffles_a: list_a > list_a > set_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Osplice_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 splice_list_a: list_list_a > list_list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Osplice_001tf__a,type,
% 0.25/0.59 splice_a: list_a > list_a > list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Osubseqs_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 subseqs_list_a: list_list_a > list_list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Osubseqs_001tf__a,type,
% 0.25/0.59 subseqs_a: list_a > list_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Osuccessively_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 successively_list_a: ( list_a > list_a > $o ) > list_list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_List_Osuccessively_001tf__a,type,
% 0.25/0.59 successively_a: ( a > a > $o ) > list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 size_size_list_a: list_a > nat ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.25/0.59 ord_less_nat: nat > nat > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_OCollect_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 collect_list_a: ( list_a > $o ) > set_list_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.25/0.59 collect_a: ( a > $o ) > set_a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_member_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.25/0.59 member_list_list_a: list_list_a > set_list_list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_member_001t__List__Olist_Itf__a_J,type,
% 0.25/0.59 member_list_a2: list_a > set_list_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_c_member_001tf__a,type,
% 0.25/0.59 member_a2: a > set_a > $o ).
% 0.25/0.59
% 0.25/0.59 thf(sy_v_f,type,
% 0.25/0.59 f: nat > a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_v_x,type,
% 0.25/0.59 x: a ).
% 0.25/0.59
% 0.25/0.59 thf(sy_v_xs,type,
% 0.25/0.59 xs: list_a ).
% 0.25/0.59
% 0.25/0.59 % Relevant facts (352)
% 0.25/0.59 thf(fact_0_i__append__Nil,axiom,
% 0.25/0.59 ! [F: nat > list_a] :
% 0.25/0.59 ( ( listIn1753026346list_a @ nil_list_a @ F )
% 0.25/0.59 = F ) ).
% 0.25/0.59
% 0.25/0.59 % i_append_Nil
% 0.25/0.59 thf(fact_1_i__append__Nil,axiom,
% 0.25/0.59 ! [F: nat > a] :
% 0.25/0.59 ( ( listIn1312259492pend_a @ nil_a @ F )
% 0.25/0.59 = F ) ).
% 0.25/0.59
% 0.25/0.59 % i_append_Nil
% 0.25/0.59 thf(fact_2_list_Oinject,axiom,
% 0.25/0.59 ! [X21: list_a,X22: list_list_a,Y21: list_a,Y22: list_list_a] :
% 0.25/0.59 ( ( ( cons_list_a @ X21 @ X22 )
% 0.25/0.59 = ( cons_list_a @ Y21 @ Y22 ) )
% 0.25/0.59 = ( ( X21 = Y21 )
% 0.25/0.59 & ( X22 = Y22 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.inject
% 0.25/0.59 thf(fact_3_list_Oinject,axiom,
% 0.25/0.59 ! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
% 0.25/0.59 ( ( ( cons_a @ X21 @ X22 )
% 0.25/0.59 = ( cons_a @ Y21 @ Y22 ) )
% 0.25/0.59 = ( ( X21 = Y21 )
% 0.25/0.59 & ( X22 = Y22 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.inject
% 0.25/0.59 thf(fact_4_list_Odistinct_I1_J,axiom,
% 0.25/0.59 ! [X21: list_a,X22: list_list_a] :
% 0.25/0.59 ( nil_list_a
% 0.25/0.59 != ( cons_list_a @ X21 @ X22 ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.distinct(1)
% 0.25/0.59 thf(fact_5_list_Odistinct_I1_J,axiom,
% 0.25/0.59 ! [X21: a,X22: list_a] :
% 0.25/0.59 ( nil_a
% 0.25/0.59 != ( cons_a @ X21 @ X22 ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.distinct(1)
% 0.25/0.59 thf(fact_6_list_OdiscI,axiom,
% 0.25/0.59 ! [List: list_list_a,X21: list_a,X22: list_list_a] :
% 0.25/0.59 ( ( List
% 0.25/0.59 = ( cons_list_a @ X21 @ X22 ) )
% 0.25/0.59 => ( List != nil_list_a ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.discI
% 0.25/0.59 thf(fact_7_list_OdiscI,axiom,
% 0.25/0.59 ! [List: list_a,X21: a,X22: list_a] :
% 0.25/0.59 ( ( List
% 0.25/0.59 = ( cons_a @ X21 @ X22 ) )
% 0.25/0.59 => ( List != nil_a ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.discI
% 0.25/0.59 thf(fact_8_list_Oexhaust,axiom,
% 0.25/0.59 ! [Y: list_list_a] :
% 0.25/0.59 ( ( Y != nil_list_a )
% 0.25/0.59 => ~ ! [X212: list_a,X222: list_list_a] :
% 0.25/0.59 ( Y
% 0.25/0.59 != ( cons_list_a @ X212 @ X222 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.exhaust
% 0.25/0.59 thf(fact_9_list_Oexhaust,axiom,
% 0.25/0.59 ! [Y: list_a] :
% 0.25/0.59 ( ( Y != nil_a )
% 0.25/0.59 => ~ ! [X212: a,X222: list_a] :
% 0.25/0.59 ( Y
% 0.25/0.59 != ( cons_a @ X212 @ X222 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.exhaust
% 0.25/0.59 thf(fact_10_list_Oinducts,axiom,
% 0.25/0.59 ! [P: list_list_a > $o,List: list_list_a] :
% 0.25/0.59 ( ( P @ nil_list_a )
% 0.25/0.59 => ( ! [X1: list_a,X2: list_list_a] :
% 0.25/0.59 ( ( P @ X2 )
% 0.25/0.59 => ( P @ ( cons_list_a @ X1 @ X2 ) ) )
% 0.25/0.59 => ( P @ List ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.inducts
% 0.25/0.59 thf(fact_11_list_Oinducts,axiom,
% 0.25/0.59 ! [P: list_a > $o,List: list_a] :
% 0.25/0.59 ( ( P @ nil_a )
% 0.25/0.59 => ( ! [X1: a,X2: list_a] :
% 0.25/0.59 ( ( P @ X2 )
% 0.25/0.59 => ( P @ ( cons_a @ X1 @ X2 ) ) )
% 0.25/0.59 => ( P @ List ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.inducts
% 0.25/0.59 thf(fact_12_neq__Nil__conv,axiom,
% 0.25/0.59 ! [Xs: list_list_a] :
% 0.25/0.59 ( ( Xs != nil_list_a )
% 0.25/0.59 = ( ? [Y2: list_a,Ys: list_list_a] :
% 0.25/0.59 ( Xs
% 0.25/0.59 = ( cons_list_a @ Y2 @ Ys ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % neq_Nil_conv
% 0.25/0.59 thf(fact_13_neq__Nil__conv,axiom,
% 0.25/0.59 ! [Xs: list_a] :
% 0.25/0.59 ( ( Xs != nil_a )
% 0.25/0.59 = ( ? [Y2: a,Ys: list_a] :
% 0.25/0.59 ( Xs
% 0.25/0.59 = ( cons_a @ Y2 @ Ys ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % neq_Nil_conv
% 0.25/0.59 thf(fact_14_list__induct2_H,axiom,
% 0.25/0.59 ! [P: list_a > list_list_a > $o,Xs: list_a,Ys2: list_list_a] :
% 0.25/0.59 ( ( P @ nil_a @ nil_list_a )
% 0.25/0.59 => ( ! [X: a,Xs2: list_a] : ( P @ ( cons_a @ X @ Xs2 ) @ nil_list_a )
% 0.25/0.59 => ( ! [Y3: list_a,Ys3: list_list_a] : ( P @ nil_a @ ( cons_list_a @ Y3 @ Ys3 ) )
% 0.25/0.59 => ( ! [X: a,Xs2: list_a,Y3: list_a,Ys3: list_list_a] :
% 0.25/0.59 ( ( P @ Xs2 @ Ys3 )
% 0.25/0.59 => ( P @ ( cons_a @ X @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys3 ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2'
% 0.25/0.59 thf(fact_15_list__induct2_H,axiom,
% 0.25/0.59 ! [P: list_list_a > list_a > $o,Xs: list_list_a,Ys2: list_a] :
% 0.25/0.59 ( ( P @ nil_list_a @ nil_a )
% 0.25/0.59 => ( ! [X: list_a,Xs2: list_list_a] : ( P @ ( cons_list_a @ X @ Xs2 ) @ nil_a )
% 0.25/0.59 => ( ! [Y3: a,Ys3: list_a] : ( P @ nil_list_a @ ( cons_a @ Y3 @ Ys3 ) )
% 0.25/0.59 => ( ! [X: list_a,Xs2: list_list_a,Y3: a,Ys3: list_a] :
% 0.25/0.59 ( ( P @ Xs2 @ Ys3 )
% 0.25/0.59 => ( P @ ( cons_list_a @ X @ Xs2 ) @ ( cons_a @ Y3 @ Ys3 ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2'
% 0.25/0.59 thf(fact_16_list__induct2_H,axiom,
% 0.25/0.59 ! [P: list_list_a > list_list_a > $o,Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.59 ( ( P @ nil_list_a @ nil_list_a )
% 0.25/0.59 => ( ! [X: list_a,Xs2: list_list_a] : ( P @ ( cons_list_a @ X @ Xs2 ) @ nil_list_a )
% 0.25/0.59 => ( ! [Y3: list_a,Ys3: list_list_a] : ( P @ nil_list_a @ ( cons_list_a @ Y3 @ Ys3 ) )
% 0.25/0.59 => ( ! [X: list_a,Xs2: list_list_a,Y3: list_a,Ys3: list_list_a] :
% 0.25/0.59 ( ( P @ Xs2 @ Ys3 )
% 0.25/0.59 => ( P @ ( cons_list_a @ X @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys3 ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2'
% 0.25/0.59 thf(fact_17_list__induct2_H,axiom,
% 0.25/0.59 ! [P: list_a > list_a > $o,Xs: list_a,Ys2: list_a] :
% 0.25/0.59 ( ( P @ nil_a @ nil_a )
% 0.25/0.59 => ( ! [X: a,Xs2: list_a] : ( P @ ( cons_a @ X @ Xs2 ) @ nil_a )
% 0.25/0.59 => ( ! [Y3: a,Ys3: list_a] : ( P @ nil_a @ ( cons_a @ Y3 @ Ys3 ) )
% 0.25/0.59 => ( ! [X: a,Xs2: list_a,Y3: a,Ys3: list_a] :
% 0.25/0.59 ( ( P @ Xs2 @ Ys3 )
% 0.25/0.59 => ( P @ ( cons_a @ X @ Xs2 ) @ ( cons_a @ Y3 @ Ys3 ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2'
% 0.25/0.59 thf(fact_18_splice_Oinduct,axiom,
% 0.25/0.59 ! [P: list_list_a > list_list_a > $o,A0: list_list_a,A1: list_list_a] :
% 0.25/0.59 ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 0.25/0.59 => ( ! [X: list_a,Xs2: list_list_a,Ys3: list_list_a] :
% 0.25/0.59 ( ( P @ Ys3 @ Xs2 )
% 0.25/0.59 => ( P @ ( cons_list_a @ X @ Xs2 ) @ Ys3 ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % splice.induct
% 0.25/0.59 thf(fact_19_splice_Oinduct,axiom,
% 0.25/0.59 ! [P: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.25/0.59 ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.25/0.59 => ( ! [X: a,Xs2: list_a,Ys3: list_a] :
% 0.25/0.59 ( ( P @ Ys3 @ Xs2 )
% 0.25/0.59 => ( P @ ( cons_a @ X @ Xs2 ) @ Ys3 ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % splice.induct
% 0.25/0.59 thf(fact_20_induct__list012,axiom,
% 0.25/0.59 ! [P: list_list_a > $o,Xs: list_list_a] :
% 0.25/0.59 ( ( P @ nil_list_a )
% 0.25/0.59 => ( ! [X: list_a] : ( P @ ( cons_list_a @ X @ nil_list_a ) )
% 0.25/0.59 => ( ! [X: list_a,Y3: list_a,Zs: list_list_a] :
% 0.25/0.59 ( ( P @ Zs )
% 0.25/0.59 => ( ( P @ ( cons_list_a @ Y3 @ Zs ) )
% 0.25/0.59 => ( P @ ( cons_list_a @ X @ ( cons_list_a @ Y3 @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % induct_list012
% 0.25/0.59 thf(fact_21_induct__list012,axiom,
% 0.25/0.59 ! [P: list_a > $o,Xs: list_a] :
% 0.25/0.59 ( ( P @ nil_a )
% 0.25/0.59 => ( ! [X: a] : ( P @ ( cons_a @ X @ nil_a ) )
% 0.25/0.59 => ( ! [X: a,Y3: a,Zs: list_a] :
% 0.25/0.59 ( ( P @ Zs )
% 0.25/0.59 => ( ( P @ ( cons_a @ Y3 @ Zs ) )
% 0.25/0.59 => ( P @ ( cons_a @ X @ ( cons_a @ Y3 @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % induct_list012
% 0.25/0.59 thf(fact_22_shuffles_Oinduct,axiom,
% 0.25/0.59 ! [P: list_list_a > list_list_a > $o,A0: list_list_a,A1: list_list_a] :
% 0.25/0.59 ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 0.25/0.59 => ( ! [Xs2: list_list_a] : ( P @ Xs2 @ nil_list_a )
% 0.25/0.59 => ( ! [X: list_a,Xs2: list_list_a,Y3: list_a,Ys3: list_list_a] :
% 0.25/0.59 ( ( P @ Xs2 @ ( cons_list_a @ Y3 @ Ys3 ) )
% 0.25/0.59 => ( ( P @ ( cons_list_a @ X @ Xs2 ) @ Ys3 )
% 0.25/0.59 => ( P @ ( cons_list_a @ X @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys3 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % shuffles.induct
% 0.25/0.59 thf(fact_23_shuffles_Oinduct,axiom,
% 0.25/0.59 ! [P: list_a > list_a > $o,A0: list_a,A1: list_a] :
% 0.25/0.59 ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.25/0.59 => ( ! [Xs2: list_a] : ( P @ Xs2 @ nil_a )
% 0.25/0.59 => ( ! [X: a,Xs2: list_a,Y3: a,Ys3: list_a] :
% 0.25/0.59 ( ( P @ Xs2 @ ( cons_a @ Y3 @ Ys3 ) )
% 0.25/0.59 => ( ( P @ ( cons_a @ X @ Xs2 ) @ Ys3 )
% 0.25/0.59 => ( P @ ( cons_a @ X @ Xs2 ) @ ( cons_a @ Y3 @ Ys3 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % shuffles.induct
% 0.25/0.59 thf(fact_24_not__Cons__self2,axiom,
% 0.25/0.59 ! [X3: list_a,Xs: list_list_a] :
% 0.25/0.59 ( ( cons_list_a @ X3 @ Xs )
% 0.25/0.59 != Xs ) ).
% 0.25/0.59
% 0.25/0.59 % not_Cons_self2
% 0.25/0.59 thf(fact_25_not__Cons__self2,axiom,
% 0.25/0.59 ! [X3: a,Xs: list_a] :
% 0.25/0.59 ( ( cons_a @ X3 @ Xs )
% 0.25/0.59 != Xs ) ).
% 0.25/0.59
% 0.25/0.59 % not_Cons_self2
% 0.25/0.59 thf(fact_26_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.59 ! [P: ( list_a > a ) > list_list_a > list_a > $o,A0: list_a > a,A1: list_list_a,A2: list_a] :
% 0.25/0.59 ( ! [F2: list_a > a,X_1: list_a] : ( P @ F2 @ nil_list_a @ X_1 )
% 0.25/0.59 => ( ! [F2: list_a > a,A: list_a,As: list_list_a,Bs: list_a] :
% 0.25/0.59 ( ( P @ F2 @ As @ ( cons_a @ ( F2 @ A ) @ Bs ) )
% 0.25/0.59 => ( P @ F2 @ ( cons_list_a @ A @ As ) @ Bs ) )
% 0.25/0.59 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % map_tailrec_rev.induct
% 0.25/0.59 thf(fact_27_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.59 ! [P: ( a > list_a ) > list_a > list_list_a > $o,A0: a > list_a,A1: list_a,A2: list_list_a] :
% 0.25/0.59 ( ! [F2: a > list_a,X_1: list_list_a] : ( P @ F2 @ nil_a @ X_1 )
% 0.25/0.59 => ( ! [F2: a > list_a,A: a,As: list_a,Bs: list_list_a] :
% 0.25/0.59 ( ( P @ F2 @ As @ ( cons_list_a @ ( F2 @ A ) @ Bs ) )
% 0.25/0.59 => ( P @ F2 @ ( cons_a @ A @ As ) @ Bs ) )
% 0.25/0.59 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % map_tailrec_rev.induct
% 0.25/0.59 thf(fact_28_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.59 ! [P: ( list_a > list_a ) > list_list_a > list_list_a > $o,A0: list_a > list_a,A1: list_list_a,A2: list_list_a] :
% 0.25/0.59 ( ! [F2: list_a > list_a,X_1: list_list_a] : ( P @ F2 @ nil_list_a @ X_1 )
% 0.25/0.59 => ( ! [F2: list_a > list_a,A: list_a,As: list_list_a,Bs: list_list_a] :
% 0.25/0.59 ( ( P @ F2 @ As @ ( cons_list_a @ ( F2 @ A ) @ Bs ) )
% 0.25/0.59 => ( P @ F2 @ ( cons_list_a @ A @ As ) @ Bs ) )
% 0.25/0.59 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % map_tailrec_rev.induct
% 0.25/0.59 thf(fact_29_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.59 ! [P: ( a > a ) > list_a > list_a > $o,A0: a > a,A1: list_a,A2: list_a] :
% 0.25/0.59 ( ! [F2: a > a,X_1: list_a] : ( P @ F2 @ nil_a @ X_1 )
% 0.25/0.59 => ( ! [F2: a > a,A: a,As: list_a,Bs: list_a] :
% 0.25/0.59 ( ( P @ F2 @ As @ ( cons_a @ ( F2 @ A ) @ Bs ) )
% 0.25/0.59 => ( P @ F2 @ ( cons_a @ A @ As ) @ Bs ) )
% 0.25/0.59 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % map_tailrec_rev.induct
% 0.25/0.59 thf(fact_30_list__nonempty__induct,axiom,
% 0.25/0.59 ! [Xs: list_list_a,P: list_list_a > $o] :
% 0.25/0.59 ( ( Xs != nil_list_a )
% 0.25/0.59 => ( ! [X: list_a] : ( P @ ( cons_list_a @ X @ nil_list_a ) )
% 0.25/0.59 => ( ! [X: list_a,Xs2: list_list_a] :
% 0.25/0.59 ( ( Xs2 != nil_list_a )
% 0.25/0.59 => ( ( P @ Xs2 )
% 0.25/0.59 => ( P @ ( cons_list_a @ X @ Xs2 ) ) ) )
% 0.25/0.59 => ( P @ Xs ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_nonempty_induct
% 0.25/0.59 thf(fact_31_list__nonempty__induct,axiom,
% 0.25/0.59 ! [Xs: list_a,P: list_a > $o] :
% 0.25/0.59 ( ( Xs != nil_a )
% 0.25/0.59 => ( ! [X: a] : ( P @ ( cons_a @ X @ nil_a ) )
% 0.25/0.59 => ( ! [X: a,Xs2: list_a] :
% 0.25/0.59 ( ( Xs2 != nil_a )
% 0.25/0.59 => ( ( P @ Xs2 )
% 0.25/0.59 => ( P @ ( cons_a @ X @ Xs2 ) ) ) )
% 0.25/0.59 => ( P @ Xs ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_nonempty_induct
% 0.25/0.59 thf(fact_32_successively_Oinduct,axiom,
% 0.25/0.59 ! [P: ( list_a > list_a > $o ) > list_list_a > $o,A0: list_a > list_a > $o,A1: list_list_a] :
% 0.25/0.59 ( ! [P2: list_a > list_a > $o] : ( P @ P2 @ nil_list_a )
% 0.25/0.59 => ( ! [P2: list_a > list_a > $o,X: list_a] : ( P @ P2 @ ( cons_list_a @ X @ nil_list_a ) )
% 0.25/0.59 => ( ! [P2: list_a > list_a > $o,X: list_a,Y3: list_a,Xs2: list_list_a] :
% 0.25/0.59 ( ( P @ P2 @ ( cons_list_a @ Y3 @ Xs2 ) )
% 0.25/0.59 => ( P @ P2 @ ( cons_list_a @ X @ ( cons_list_a @ Y3 @ Xs2 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % successively.induct
% 0.25/0.59 thf(fact_33_successively_Oinduct,axiom,
% 0.25/0.59 ! [P: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 0.25/0.59 ( ! [P2: a > a > $o] : ( P @ P2 @ nil_a )
% 0.25/0.59 => ( ! [P2: a > a > $o,X: a] : ( P @ P2 @ ( cons_a @ X @ nil_a ) )
% 0.25/0.59 => ( ! [P2: a > a > $o,X: a,Y3: a,Xs2: list_a] :
% 0.25/0.59 ( ( P @ P2 @ ( cons_a @ Y3 @ Xs2 ) )
% 0.25/0.59 => ( P @ P2 @ ( cons_a @ X @ ( cons_a @ Y3 @ Xs2 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % successively.induct
% 0.25/0.59 thf(fact_34_remdups__adj_Oinduct,axiom,
% 0.25/0.59 ! [P: list_list_a > $o,A0: list_list_a] :
% 0.25/0.59 ( ( P @ nil_list_a )
% 0.25/0.59 => ( ! [X: list_a] : ( P @ ( cons_list_a @ X @ nil_list_a ) )
% 0.25/0.59 => ( ! [X: list_a,Y3: list_a,Xs2: list_list_a] :
% 0.25/0.59 ( ( ( X = Y3 )
% 0.25/0.59 => ( P @ ( cons_list_a @ X @ Xs2 ) ) )
% 0.25/0.59 => ( ( ( X != Y3 )
% 0.25/0.59 => ( P @ ( cons_list_a @ Y3 @ Xs2 ) ) )
% 0.25/0.59 => ( P @ ( cons_list_a @ X @ ( cons_list_a @ Y3 @ Xs2 ) ) ) ) )
% 0.25/0.59 => ( P @ A0 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.induct
% 0.25/0.59 thf(fact_35_remdups__adj_Oinduct,axiom,
% 0.25/0.59 ! [P: list_a > $o,A0: list_a] :
% 0.25/0.59 ( ( P @ nil_a )
% 0.25/0.59 => ( ! [X: a] : ( P @ ( cons_a @ X @ nil_a ) )
% 0.25/0.59 => ( ! [X: a,Y3: a,Xs2: list_a] :
% 0.25/0.59 ( ( ( X = Y3 )
% 0.25/0.59 => ( P @ ( cons_a @ X @ Xs2 ) ) )
% 0.25/0.59 => ( ( ( X != Y3 )
% 0.25/0.59 => ( P @ ( cons_a @ Y3 @ Xs2 ) ) )
% 0.25/0.59 => ( P @ ( cons_a @ X @ ( cons_a @ Y3 @ Xs2 ) ) ) ) )
% 0.25/0.59 => ( P @ A0 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.induct
% 0.25/0.59 thf(fact_36_sorted__wrt_Oinduct,axiom,
% 0.25/0.59 ! [P: ( list_a > list_a > $o ) > list_list_a > $o,A0: list_a > list_a > $o,A1: list_list_a] :
% 0.25/0.59 ( ! [P2: list_a > list_a > $o] : ( P @ P2 @ nil_list_a )
% 0.25/0.59 => ( ! [P2: list_a > list_a > $o,X: list_a,Ys3: list_list_a] :
% 0.25/0.59 ( ( P @ P2 @ Ys3 )
% 0.25/0.59 => ( P @ P2 @ ( cons_list_a @ X @ Ys3 ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sorted_wrt.induct
% 0.25/0.59 thf(fact_37_sorted__wrt_Oinduct,axiom,
% 0.25/0.59 ! [P: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
% 0.25/0.59 ( ! [P2: a > a > $o] : ( P @ P2 @ nil_a )
% 0.25/0.59 => ( ! [P2: a > a > $o,X: a,Ys3: list_a] :
% 0.25/0.59 ( ( P @ P2 @ Ys3 )
% 0.25/0.59 => ( P @ P2 @ ( cons_a @ X @ Ys3 ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sorted_wrt.induct
% 0.25/0.59 thf(fact_38_remdups__adj_Ocases,axiom,
% 0.25/0.59 ! [X3: list_list_a] :
% 0.25/0.59 ( ( X3 != nil_list_a )
% 0.25/0.59 => ( ! [X: list_a] :
% 0.25/0.59 ( X3
% 0.25/0.59 != ( cons_list_a @ X @ nil_list_a ) )
% 0.25/0.59 => ~ ! [X: list_a,Y3: list_a,Xs2: list_list_a] :
% 0.25/0.59 ( X3
% 0.25/0.59 != ( cons_list_a @ X @ ( cons_list_a @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.cases
% 0.25/0.59 thf(fact_39_remdups__adj_Ocases,axiom,
% 0.25/0.59 ! [X3: list_a] :
% 0.25/0.59 ( ( X3 != nil_a )
% 0.25/0.59 => ( ! [X: a] :
% 0.25/0.59 ( X3
% 0.25/0.59 != ( cons_a @ X @ nil_a ) )
% 0.25/0.59 => ~ ! [X: a,Y3: a,Xs2: list_a] :
% 0.25/0.59 ( X3
% 0.25/0.59 != ( cons_a @ X @ ( cons_a @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.cases
% 0.25/0.59 thf(fact_40_transpose_Ocases,axiom,
% 0.25/0.59 ! [X3: list_list_list_a] :
% 0.25/0.59 ( ( X3 != nil_list_list_a )
% 0.25/0.59 => ( ! [Xss: list_list_list_a] :
% 0.25/0.59 ( X3
% 0.25/0.59 != ( cons_list_list_a @ nil_list_a @ Xss ) )
% 0.25/0.59 => ~ ! [X: list_a,Xs2: list_list_a,Xss: list_list_list_a] :
% 0.25/0.59 ( X3
% 0.25/0.59 != ( cons_list_list_a @ ( cons_list_a @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transpose.cases
% 0.25/0.59 thf(fact_41_transpose_Ocases,axiom,
% 0.25/0.59 ! [X3: list_list_a] :
% 0.25/0.59 ( ( X3 != nil_list_a )
% 0.25/0.59 => ( ! [Xss: list_list_a] :
% 0.25/0.59 ( X3
% 0.25/0.59 != ( cons_list_a @ nil_a @ Xss ) )
% 0.25/0.59 => ~ ! [X: a,Xs2: list_a,Xss: list_list_a] :
% 0.25/0.59 ( X3
% 0.25/0.59 != ( cons_list_a @ ( cons_a @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transpose.cases
% 0.25/0.59 thf(fact_42_insert__Nil,axiom,
% 0.25/0.59 ! [X3: list_a] :
% 0.25/0.59 ( ( insert_list_a @ X3 @ nil_list_a )
% 0.25/0.59 = ( cons_list_a @ X3 @ nil_list_a ) ) ).
% 0.25/0.59
% 0.25/0.59 % insert_Nil
% 0.25/0.59 thf(fact_43_insert__Nil,axiom,
% 0.25/0.59 ! [X3: a] :
% 0.25/0.59 ( ( insert_a @ X3 @ nil_a )
% 0.25/0.59 = ( cons_a @ X3 @ nil_a ) ) ).
% 0.25/0.59
% 0.25/0.59 % insert_Nil
% 0.25/0.59 thf(fact_44_list__ex1__simps_I1_J,axiom,
% 0.25/0.59 ! [P: list_a > $o] :
% 0.25/0.59 ~ ( list_ex1_list_a @ P @ nil_list_a ) ).
% 0.25/0.59
% 0.25/0.59 % list_ex1_simps(1)
% 0.25/0.59 thf(fact_45_list__ex1__simps_I1_J,axiom,
% 0.25/0.59 ! [P: a > $o] :
% 0.25/0.59 ~ ( list_ex1_a @ P @ nil_a ) ).
% 0.25/0.59
% 0.25/0.59 % list_ex1_simps(1)
% 0.25/0.59 thf(fact_46_map__tailrec__rev_Oelims,axiom,
% 0.25/0.59 ! [X3: a > list_a,Xa: list_a,Xb: list_list_a,Y: list_list_a] :
% 0.25/0.59 ( ( ( map_ta41997947list_a @ X3 @ Xa @ Xb )
% 0.25/0.59 = Y )
% 0.25/0.59 => ( ( ( Xa = nil_a )
% 0.25/0.59 => ( Y != Xb ) )
% 0.25/0.59 => ~ ! [A: a,As: list_a] :
% 0.25/0.59 ( ( Xa
% 0.25/0.59 = ( cons_a @ A @ As ) )
% 0.25/0.59 => ( Y
% 0.25/0.59 != ( map_ta41997947list_a @ X3 @ As @ ( cons_list_a @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % map_tailrec_rev.elims
% 0.25/0.59 thf(fact_47_map__tailrec__rev_Oelims,axiom,
% 0.25/0.59 ! [X3: list_a > a,Xa: list_list_a,Xb: list_a,Y: list_a] :
% 0.25/0.59 ( ( ( map_ta2002079599st_a_a @ X3 @ Xa @ Xb )
% 0.25/0.59 = Y )
% 0.25/0.59 => ( ( ( Xa = nil_list_a )
% 0.25/0.59 => ( Y != Xb ) )
% 0.25/0.59 => ~ ! [A: list_a,As: list_list_a] :
% 0.25/0.59 ( ( Xa
% 0.25/0.59 = ( cons_list_a @ A @ As ) )
% 0.25/0.59 => ( Y
% 0.25/0.59 != ( map_ta2002079599st_a_a @ X3 @ As @ ( cons_a @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % map_tailrec_rev.elims
% 0.25/0.59 thf(fact_48_map__tailrec__rev_Oelims,axiom,
% 0.25/0.59 ! [X3: list_a > list_a,Xa: list_list_a,Xb: list_list_a,Y: list_list_a] :
% 0.25/0.59 ( ( ( map_ta982122357list_a @ X3 @ Xa @ Xb )
% 0.25/0.59 = Y )
% 0.25/0.59 => ( ( ( Xa = nil_list_a )
% 0.25/0.59 => ( Y != Xb ) )
% 0.25/0.59 => ~ ! [A: list_a,As: list_list_a] :
% 0.25/0.59 ( ( Xa
% 0.25/0.59 = ( cons_list_a @ A @ As ) )
% 0.25/0.59 => ( Y
% 0.25/0.59 != ( map_ta982122357list_a @ X3 @ As @ ( cons_list_a @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % map_tailrec_rev.elims
% 0.25/0.59 thf(fact_49_map__tailrec__rev_Oelims,axiom,
% 0.25/0.59 ! [X3: a > a,Xa: list_a,Xb: list_a,Y: list_a] :
% 0.25/0.59 ( ( ( map_tailrec_rev_a_a @ X3 @ Xa @ Xb )
% 0.25/0.59 = Y )
% 0.25/0.59 => ( ( ( Xa = nil_a )
% 0.25/0.59 => ( Y != Xb ) )
% 0.25/0.59 => ~ ! [A: a,As: list_a] :
% 0.25/0.59 ( ( Xa
% 0.25/0.59 = ( cons_a @ A @ As ) )
% 0.25/0.59 => ( Y
% 0.25/0.59 != ( map_tailrec_rev_a_a @ X3 @ As @ ( cons_a @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % map_tailrec_rev.elims
% 0.25/0.59 thf(fact_50_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.25/0.59 ! [Less: list_a > list_a > $o,X3: list_a,Xs: list_list_a] :
% 0.25/0.59 ~ ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X3 @ Xs ) @ nil_list_a ) ).
% 0.25/0.59
% 0.25/0.59 % ord.lexordp_eq_simps(3)
% 0.25/0.59 thf(fact_51_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.25/0.59 ! [Less: a > a > $o,X3: a,Xs: list_a] :
% 0.25/0.59 ~ ( lexordp_eq_a @ Less @ ( cons_a @ X3 @ Xs ) @ nil_a ) ).
% 0.25/0.59
% 0.25/0.59 % ord.lexordp_eq_simps(3)
% 0.25/0.59 thf(fact_52_bind__simps_I1_J,axiom,
% 0.25/0.59 ! [F: a > list_list_a] :
% 0.25/0.59 ( ( bind_a_list_a @ nil_a @ F )
% 0.25/0.59 = nil_list_a ) ).
% 0.25/0.59
% 0.25/0.59 % bind_simps(1)
% 0.25/0.59 thf(fact_53_bind__simps_I1_J,axiom,
% 0.25/0.59 ! [F: list_a > list_a] :
% 0.25/0.59 ( ( bind_list_a_a @ nil_list_a @ F )
% 0.25/0.59 = nil_a ) ).
% 0.25/0.59
% 0.25/0.59 % bind_simps(1)
% 0.25/0.59 thf(fact_54_bind__simps_I1_J,axiom,
% 0.25/0.59 ! [F: list_a > list_list_a] :
% 0.25/0.59 ( ( bind_list_a_list_a @ nil_list_a @ F )
% 0.25/0.59 = nil_list_a ) ).
% 0.25/0.59
% 0.25/0.59 % bind_simps(1)
% 0.25/0.59 thf(fact_55_bind__simps_I1_J,axiom,
% 0.25/0.59 ! [F: a > list_a] :
% 0.25/0.59 ( ( bind_a_a @ nil_a @ F )
% 0.25/0.59 = nil_a ) ).
% 0.25/0.59
% 0.25/0.59 % bind_simps(1)
% 0.25/0.59 thf(fact_56_listrelp_Oinducts,axiom,
% 0.25/0.59 ! [R: a > list_a > $o,X12: list_a,X23: list_list_a,P: list_a > list_list_a > $o] :
% 0.25/0.59 ( ( listrelp_a_list_a @ R @ X12 @ X23 )
% 0.25/0.59 => ( ( P @ nil_a @ nil_list_a )
% 0.25/0.59 => ( ! [X: a,Y3: list_a,Xs2: list_a,Ys3: list_list_a] :
% 0.25/0.59 ( ( R @ X @ Y3 )
% 0.25/0.59 => ( ( listrelp_a_list_a @ R @ Xs2 @ Ys3 )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys3 )
% 0.25/0.59 => ( P @ ( cons_a @ X @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys3 ) ) ) ) )
% 0.25/0.59 => ( P @ X12 @ X23 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.inducts
% 0.25/0.59 thf(fact_57_listrelp_Oinducts,axiom,
% 0.25/0.59 ! [R: list_a > a > $o,X12: list_list_a,X23: list_a,P: list_list_a > list_a > $o] :
% 0.25/0.59 ( ( listrelp_list_a_a @ R @ X12 @ X23 )
% 0.25/0.59 => ( ( P @ nil_list_a @ nil_a )
% 0.25/0.59 => ( ! [X: list_a,Y3: a,Xs2: list_list_a,Ys3: list_a] :
% 0.25/0.59 ( ( R @ X @ Y3 )
% 0.25/0.59 => ( ( listrelp_list_a_a @ R @ Xs2 @ Ys3 )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys3 )
% 0.25/0.59 => ( P @ ( cons_list_a @ X @ Xs2 ) @ ( cons_a @ Y3 @ Ys3 ) ) ) ) )
% 0.25/0.59 => ( P @ X12 @ X23 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.inducts
% 0.25/0.59 thf(fact_58_listrelp_Oinducts,axiom,
% 0.25/0.59 ! [R: list_a > list_a > $o,X12: list_list_a,X23: list_list_a,P: list_list_a > list_list_a > $o] :
% 0.25/0.59 ( ( listre1221556159list_a @ R @ X12 @ X23 )
% 0.25/0.59 => ( ( P @ nil_list_a @ nil_list_a )
% 0.25/0.59 => ( ! [X: list_a,Y3: list_a,Xs2: list_list_a,Ys3: list_list_a] :
% 0.25/0.59 ( ( R @ X @ Y3 )
% 0.25/0.59 => ( ( listre1221556159list_a @ R @ Xs2 @ Ys3 )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys3 )
% 0.25/0.59 => ( P @ ( cons_list_a @ X @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys3 ) ) ) ) )
% 0.25/0.59 => ( P @ X12 @ X23 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.inducts
% 0.25/0.59 thf(fact_59_listrelp_Oinducts,axiom,
% 0.25/0.59 ! [R: a > a > $o,X12: list_a,X23: list_a,P: list_a > list_a > $o] :
% 0.25/0.59 ( ( listrelp_a_a @ R @ X12 @ X23 )
% 0.25/0.59 => ( ( P @ nil_a @ nil_a )
% 0.25/0.59 => ( ! [X: a,Y3: a,Xs2: list_a,Ys3: list_a] :
% 0.25/0.59 ( ( R @ X @ Y3 )
% 0.25/0.59 => ( ( listrelp_a_a @ R @ Xs2 @ Ys3 )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys3 )
% 0.25/0.59 => ( P @ ( cons_a @ X @ Xs2 ) @ ( cons_a @ Y3 @ Ys3 ) ) ) ) )
% 0.25/0.59 => ( P @ X12 @ X23 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.inducts
% 0.25/0.59 thf(fact_60_listrelp_Osimps,axiom,
% 0.25/0.59 ( listrelp_a_list_a
% 0.25/0.59 = ( ^ [R2: a > list_a > $o,A12: list_a,A22: list_list_a] :
% 0.25/0.59 ( ( ( A12 = nil_a )
% 0.25/0.59 & ( A22 = nil_list_a ) )
% 0.25/0.59 | ? [X4: a,Y2: list_a,Xs3: list_a,Ys: list_list_a] :
% 0.25/0.59 ( ( A12
% 0.25/0.59 = ( cons_a @ X4 @ Xs3 ) )
% 0.25/0.59 & ( A22
% 0.25/0.59 = ( cons_list_a @ Y2 @ Ys ) )
% 0.25/0.59 & ( R2 @ X4 @ Y2 )
% 0.25/0.59 & ( listrelp_a_list_a @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.simps
% 0.25/0.59 thf(fact_61_listrelp_Osimps,axiom,
% 0.25/0.59 ( listrelp_list_a_a
% 0.25/0.59 = ( ^ [R2: list_a > a > $o,A12: list_list_a,A22: list_a] :
% 0.25/0.59 ( ( ( A12 = nil_list_a )
% 0.25/0.59 & ( A22 = nil_a ) )
% 0.25/0.59 | ? [X4: list_a,Y2: a,Xs3: list_list_a,Ys: list_a] :
% 0.25/0.59 ( ( A12
% 0.25/0.59 = ( cons_list_a @ X4 @ Xs3 ) )
% 0.25/0.59 & ( A22
% 0.25/0.59 = ( cons_a @ Y2 @ Ys ) )
% 0.25/0.59 & ( R2 @ X4 @ Y2 )
% 0.25/0.59 & ( listrelp_list_a_a @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.simps
% 0.25/0.59 thf(fact_62_listrelp_Osimps,axiom,
% 0.25/0.59 ( listre1221556159list_a
% 0.25/0.59 = ( ^ [R2: list_a > list_a > $o,A12: list_list_a,A22: list_list_a] :
% 0.25/0.59 ( ( ( A12 = nil_list_a )
% 0.25/0.59 & ( A22 = nil_list_a ) )
% 0.25/0.59 | ? [X4: list_a,Y2: list_a,Xs3: list_list_a,Ys: list_list_a] :
% 0.25/0.59 ( ( A12
% 0.25/0.59 = ( cons_list_a @ X4 @ Xs3 ) )
% 0.25/0.59 & ( A22
% 0.25/0.59 = ( cons_list_a @ Y2 @ Ys ) )
% 0.25/0.59 & ( R2 @ X4 @ Y2 )
% 0.25/0.59 & ( listre1221556159list_a @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.simps
% 0.25/0.59 thf(fact_63_listrelp_Osimps,axiom,
% 0.25/0.59 ( listrelp_a_a
% 0.25/0.59 = ( ^ [R2: a > a > $o,A12: list_a,A22: list_a] :
% 0.25/0.59 ( ( ( A12 = nil_a )
% 0.25/0.59 & ( A22 = nil_a ) )
% 0.25/0.59 | ? [X4: a,Y2: a,Xs3: list_a,Ys: list_a] :
% 0.25/0.59 ( ( A12
% 0.25/0.59 = ( cons_a @ X4 @ Xs3 ) )
% 0.25/0.59 & ( A22
% 0.25/0.59 = ( cons_a @ Y2 @ Ys ) )
% 0.25/0.59 & ( R2 @ X4 @ Y2 )
% 0.25/0.59 & ( listrelp_a_a @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.simps
% 0.25/0.59 thf(fact_64_listrelp_Ocases,axiom,
% 0.25/0.59 ! [R: a > list_a > $o,A1: list_a,A2: list_list_a] :
% 0.25/0.59 ( ( listrelp_a_list_a @ R @ A1 @ A2 )
% 0.25/0.59 => ( ( ( A1 = nil_a )
% 0.25/0.59 => ( A2 != nil_list_a ) )
% 0.25/0.59 => ~ ! [X: a,Y3: list_a,Xs2: list_a] :
% 0.25/0.59 ( ( A1
% 0.25/0.59 = ( cons_a @ X @ Xs2 ) )
% 0.25/0.59 => ! [Ys3: list_list_a] :
% 0.25/0.59 ( ( A2
% 0.25/0.59 = ( cons_list_a @ Y3 @ Ys3 ) )
% 0.25/0.59 => ( ( R @ X @ Y3 )
% 0.25/0.59 => ~ ( listrelp_a_list_a @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.cases
% 0.25/0.59 thf(fact_65_listrelp_Ocases,axiom,
% 0.25/0.59 ! [R: list_a > a > $o,A1: list_list_a,A2: list_a] :
% 0.25/0.59 ( ( listrelp_list_a_a @ R @ A1 @ A2 )
% 0.25/0.59 => ( ( ( A1 = nil_list_a )
% 0.25/0.59 => ( A2 != nil_a ) )
% 0.25/0.59 => ~ ! [X: list_a,Y3: a,Xs2: list_list_a] :
% 0.25/0.59 ( ( A1
% 0.25/0.59 = ( cons_list_a @ X @ Xs2 ) )
% 0.25/0.59 => ! [Ys3: list_a] :
% 0.25/0.59 ( ( A2
% 0.25/0.59 = ( cons_a @ Y3 @ Ys3 ) )
% 0.25/0.59 => ( ( R @ X @ Y3 )
% 0.25/0.59 => ~ ( listrelp_list_a_a @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.cases
% 0.25/0.59 thf(fact_66_listrelp_Ocases,axiom,
% 0.25/0.59 ! [R: list_a > list_a > $o,A1: list_list_a,A2: list_list_a] :
% 0.25/0.59 ( ( listre1221556159list_a @ R @ A1 @ A2 )
% 0.25/0.59 => ( ( ( A1 = nil_list_a )
% 0.25/0.59 => ( A2 != nil_list_a ) )
% 0.25/0.59 => ~ ! [X: list_a,Y3: list_a,Xs2: list_list_a] :
% 0.25/0.59 ( ( A1
% 0.25/0.59 = ( cons_list_a @ X @ Xs2 ) )
% 0.25/0.59 => ! [Ys3: list_list_a] :
% 0.25/0.59 ( ( A2
% 0.25/0.59 = ( cons_list_a @ Y3 @ Ys3 ) )
% 0.25/0.59 => ( ( R @ X @ Y3 )
% 0.25/0.59 => ~ ( listre1221556159list_a @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.cases
% 0.25/0.59 thf(fact_67_listrelp_Ocases,axiom,
% 0.25/0.59 ! [R: a > a > $o,A1: list_a,A2: list_a] :
% 0.25/0.59 ( ( listrelp_a_a @ R @ A1 @ A2 )
% 0.25/0.59 => ( ( ( A1 = nil_a )
% 0.25/0.59 => ( A2 != nil_a ) )
% 0.25/0.59 => ~ ! [X: a,Y3: a,Xs2: list_a] :
% 0.25/0.59 ( ( A1
% 0.25/0.59 = ( cons_a @ X @ Xs2 ) )
% 0.25/0.59 => ! [Ys3: list_a] :
% 0.25/0.59 ( ( A2
% 0.25/0.59 = ( cons_a @ Y3 @ Ys3 ) )
% 0.25/0.59 => ( ( R @ X @ Y3 )
% 0.25/0.59 => ~ ( listrelp_a_a @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % listrelp.cases
% 0.25/0.59 thf(fact_68_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.25/0.59 ! [Less: list_a > list_a > $o,X3: list_a,Xs: list_list_a,Y: list_a,Ys2: list_list_a] :
% 0.25/0.59 ( ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X3 @ Xs ) @ ( cons_list_a @ Y @ Ys2 ) )
% 0.25/0.59 = ( ( Less @ X3 @ Y )
% 0.25/0.59 | ( ~ ( Less @ Y @ X3 )
% 0.25/0.59 & ( lexordp_eq_list_a @ Less @ Xs @ Ys2 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord.lexordp_eq_simps(4)
% 0.25/0.59 thf(fact_69_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.25/0.59 ! [Less: a > a > $o,X3: a,Xs: list_a,Y: a,Ys2: list_a] :
% 0.25/0.59 ( ( lexordp_eq_a @ Less @ ( cons_a @ X3 @ Xs ) @ ( cons_a @ Y @ Ys2 ) )
% 0.25/0.59 = ( ( Less @ X3 @ Y )
% 0.25/0.59 | ( ~ ( Less @ Y @ X3 )
% 0.25/0.59 & ( lexordp_eq_a @ Less @ Xs @ Ys2 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord.lexordp_eq_simps(4)
% 0.25/0.59 thf(fact_70_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.25/0.59 ! [Less: list_a > list_a > $o,Xs: list_list_a] :
% 0.25/0.59 ( ( lexordp_eq_list_a @ Less @ Xs @ nil_list_a )
% 0.25/0.59 = ( Xs = nil_list_a ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord.lexordp_eq_simps(2)
% 0.25/0.59 thf(fact_71_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.25/0.59 ! [Less: a > a > $o,Xs: list_a] :
% 0.25/0.59 ( ( lexordp_eq_a @ Less @ Xs @ nil_a )
% 0.25/0.59 = ( Xs = nil_a ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord.lexordp_eq_simps(2)
% 0.25/0.59 thf(fact_72_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.25/0.59 ! [Less: list_a > list_a > $o,Ys2: list_list_a] : ( lexordp_eq_list_a @ Less @ nil_list_a @ Ys2 ) ).
% 0.25/0.59
% 0.25/0.59 % ord.lexordp_eq_simps(1)
% 0.25/0.59 thf(fact_73_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.25/0.59 ! [Less: a > a > $o,Ys2: list_a] : ( lexordp_eq_a @ Less @ nil_a @ Ys2 ) ).
% 0.25/0.59
% 0.25/0.59 % ord.lexordp_eq_simps(1)
% 0.25/0.59 thf(fact_74_ord_Olexordp__eq_Ocong,axiom,
% 0.25/0.59 lexordp_eq_a = lexordp_eq_a ).
% 0.25/0.59
% 0.25/0.59 % ord.lexordp_eq.cong
% 0.25/0.59 thf(fact_75_ord_Olexordp__eq__refl,axiom,
% 0.25/0.59 ! [Less: a > a > $o,Xs: list_a] : ( lexordp_eq_a @ Less @ Xs @ Xs ) ).
% 0.25/0.59
% 0.25/0.59 % ord.lexordp_eq_refl
% 0.25/0.59 thf(fact_76_mem__Collect__eq,axiom,
% 0.25/0.59 ! [A3: list_a,P: list_a > $o] :
% 0.25/0.59 ( ( member_list_a2 @ A3 @ ( collect_list_a @ P ) )
% 0.25/0.59 = ( P @ A3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % mem_Collect_eq
% 0.25/0.59 thf(fact_77_mem__Collect__eq,axiom,
% 0.25/0.59 ! [A3: a,P: a > $o] :
% 0.25/0.59 ( ( member_a2 @ A3 @ ( collect_a @ P ) )
% 0.25/0.59 = ( P @ A3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % mem_Collect_eq
% 0.25/0.59 thf(fact_78_Collect__mem__eq,axiom,
% 0.25/0.59 ! [A4: set_list_a] :
% 0.25/0.59 ( ( collect_list_a
% 0.25/0.59 @ ^ [X4: list_a] : ( member_list_a2 @ X4 @ A4 ) )
% 0.25/0.59 = A4 ) ).
% 0.25/0.59
% 0.25/0.59 % Collect_mem_eq
% 0.25/0.59 thf(fact_79_Collect__mem__eq,axiom,
% 0.25/0.60 ! [A4: set_a] :
% 0.25/0.60 ( ( collect_a
% 0.25/0.60 @ ^ [X4: a] : ( member_a2 @ X4 @ A4 ) )
% 0.25/0.60 = A4 ) ).
% 0.25/0.60
% 0.25/0.60 % Collect_mem_eq
% 0.25/0.60 thf(fact_80_ord_Olexordp__eq_OCons,axiom,
% 0.25/0.60 ! [Less: list_a > list_a > $o,X3: list_a,Y: list_a,Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( Less @ X3 @ Y )
% 0.25/0.60 => ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X3 @ Xs ) @ ( cons_list_a @ Y @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.Cons
% 0.25/0.60 thf(fact_81_ord_Olexordp__eq_OCons,axiom,
% 0.25/0.60 ! [Less: a > a > $o,X3: a,Y: a,Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( Less @ X3 @ Y )
% 0.25/0.60 => ( lexordp_eq_a @ Less @ ( cons_a @ X3 @ Xs ) @ ( cons_a @ Y @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.Cons
% 0.25/0.60 thf(fact_82_ord_Olexordp__eq_OCons__eq,axiom,
% 0.25/0.60 ! [Less: list_a > list_a > $o,X3: list_a,Y: list_a,Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ~ ( Less @ X3 @ Y )
% 0.25/0.60 => ( ~ ( Less @ Y @ X3 )
% 0.25/0.60 => ( ( lexordp_eq_list_a @ Less @ Xs @ Ys2 )
% 0.25/0.60 => ( lexordp_eq_list_a @ Less @ ( cons_list_a @ X3 @ Xs ) @ ( cons_list_a @ Y @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.Cons_eq
% 0.25/0.60 thf(fact_83_ord_Olexordp__eq_OCons__eq,axiom,
% 0.25/0.60 ! [Less: a > a > $o,X3: a,Y: a,Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ~ ( Less @ X3 @ Y )
% 0.25/0.60 => ( ~ ( Less @ Y @ X3 )
% 0.25/0.60 => ( ( lexordp_eq_a @ Less @ Xs @ Ys2 )
% 0.25/0.60 => ( lexordp_eq_a @ Less @ ( cons_a @ X3 @ Xs ) @ ( cons_a @ Y @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.Cons_eq
% 0.25/0.60 thf(fact_84_ord_Olexordp__eq_ONil,axiom,
% 0.25/0.60 ! [Less: list_a > list_a > $o,Ys2: list_list_a] : ( lexordp_eq_list_a @ Less @ nil_list_a @ Ys2 ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.Nil
% 0.25/0.60 thf(fact_85_ord_Olexordp__eq_ONil,axiom,
% 0.25/0.60 ! [Less: a > a > $o,Ys2: list_a] : ( lexordp_eq_a @ Less @ nil_a @ Ys2 ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.Nil
% 0.25/0.60 thf(fact_86_listrelp_OCons,axiom,
% 0.25/0.60 ! [R: a > list_a > $o,X3: a,Y: list_a,Xs: list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( R @ X3 @ Y )
% 0.25/0.60 => ( ( listrelp_a_list_a @ R @ Xs @ Ys2 )
% 0.25/0.60 => ( listrelp_a_list_a @ R @ ( cons_a @ X3 @ Xs ) @ ( cons_list_a @ Y @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % listrelp.Cons
% 0.25/0.60 thf(fact_87_listrelp_OCons,axiom,
% 0.25/0.60 ! [R: list_a > a > $o,X3: list_a,Y: a,Xs: list_list_a,Ys2: list_a] :
% 0.25/0.60 ( ( R @ X3 @ Y )
% 0.25/0.60 => ( ( listrelp_list_a_a @ R @ Xs @ Ys2 )
% 0.25/0.60 => ( listrelp_list_a_a @ R @ ( cons_list_a @ X3 @ Xs ) @ ( cons_a @ Y @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % listrelp.Cons
% 0.25/0.60 thf(fact_88_listrelp_OCons,axiom,
% 0.25/0.60 ! [R: list_a > list_a > $o,X3: list_a,Y: list_a,Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( R @ X3 @ Y )
% 0.25/0.60 => ( ( listre1221556159list_a @ R @ Xs @ Ys2 )
% 0.25/0.60 => ( listre1221556159list_a @ R @ ( cons_list_a @ X3 @ Xs ) @ ( cons_list_a @ Y @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % listrelp.Cons
% 0.25/0.60 thf(fact_89_listrelp_OCons,axiom,
% 0.25/0.60 ! [R: a > a > $o,X3: a,Y: a,Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( R @ X3 @ Y )
% 0.25/0.60 => ( ( listrelp_a_a @ R @ Xs @ Ys2 )
% 0.25/0.60 => ( listrelp_a_a @ R @ ( cons_a @ X3 @ Xs ) @ ( cons_a @ Y @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % listrelp.Cons
% 0.25/0.60 thf(fact_90_listrelp_ONil,axiom,
% 0.25/0.60 ! [R: a > list_a > $o] : ( listrelp_a_list_a @ R @ nil_a @ nil_list_a ) ).
% 0.25/0.60
% 0.25/0.60 % listrelp.Nil
% 0.25/0.60 thf(fact_91_listrelp_ONil,axiom,
% 0.25/0.60 ! [R: list_a > a > $o] : ( listrelp_list_a_a @ R @ nil_list_a @ nil_a ) ).
% 0.25/0.60
% 0.25/0.60 % listrelp.Nil
% 0.25/0.60 thf(fact_92_listrelp_ONil,axiom,
% 0.25/0.60 ! [R: list_a > list_a > $o] : ( listre1221556159list_a @ R @ nil_list_a @ nil_list_a ) ).
% 0.25/0.60
% 0.25/0.60 % listrelp.Nil
% 0.25/0.60 thf(fact_93_listrelp_ONil,axiom,
% 0.25/0.60 ! [R: a > a > $o] : ( listrelp_a_a @ R @ nil_a @ nil_a ) ).
% 0.25/0.60
% 0.25/0.60 % listrelp.Nil
% 0.25/0.60 thf(fact_94_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.25/0.60 ! [F: a > list_a,A3: a,As2: list_a,Bs2: list_list_a] :
% 0.25/0.60 ( ( map_ta41997947list_a @ F @ ( cons_a @ A3 @ As2 ) @ Bs2 )
% 0.25/0.60 = ( map_ta41997947list_a @ F @ As2 @ ( cons_list_a @ ( F @ A3 ) @ Bs2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % map_tailrec_rev.simps(2)
% 0.25/0.60 thf(fact_95_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.25/0.60 ! [F: list_a > a,A3: list_a,As2: list_list_a,Bs2: list_a] :
% 0.25/0.60 ( ( map_ta2002079599st_a_a @ F @ ( cons_list_a @ A3 @ As2 ) @ Bs2 )
% 0.25/0.60 = ( map_ta2002079599st_a_a @ F @ As2 @ ( cons_a @ ( F @ A3 ) @ Bs2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % map_tailrec_rev.simps(2)
% 0.25/0.60 thf(fact_96_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.25/0.60 ! [F: list_a > list_a,A3: list_a,As2: list_list_a,Bs2: list_list_a] :
% 0.25/0.60 ( ( map_ta982122357list_a @ F @ ( cons_list_a @ A3 @ As2 ) @ Bs2 )
% 0.25/0.60 = ( map_ta982122357list_a @ F @ As2 @ ( cons_list_a @ ( F @ A3 ) @ Bs2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % map_tailrec_rev.simps(2)
% 0.25/0.60 thf(fact_97_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.25/0.60 ! [F: a > a,A3: a,As2: list_a,Bs2: list_a] :
% 0.25/0.60 ( ( map_tailrec_rev_a_a @ F @ ( cons_a @ A3 @ As2 ) @ Bs2 )
% 0.25/0.60 = ( map_tailrec_rev_a_a @ F @ As2 @ ( cons_a @ ( F @ A3 ) @ Bs2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % map_tailrec_rev.simps(2)
% 0.25/0.60 thf(fact_98_map__tailrec__rev_Osimps_I1_J,axiom,
% 0.25/0.60 ! [F: a > a,Bs2: list_a] :
% 0.25/0.60 ( ( map_tailrec_rev_a_a @ F @ nil_a @ Bs2 )
% 0.25/0.60 = Bs2 ) ).
% 0.25/0.60
% 0.25/0.60 % map_tailrec_rev.simps(1)
% 0.25/0.60 thf(fact_99_ord_Olexordp__eq_Ocases,axiom,
% 0.25/0.60 ! [Less: list_a > list_a > $o,A1: list_list_a,A2: list_list_a] :
% 0.25/0.60 ( ( lexordp_eq_list_a @ Less @ A1 @ A2 )
% 0.25/0.60 => ( ( A1 != nil_list_a )
% 0.25/0.60 => ( ! [X: list_a] :
% 0.25/0.60 ( ? [Xs2: list_list_a] :
% 0.25/0.60 ( A1
% 0.25/0.60 = ( cons_list_a @ X @ Xs2 ) )
% 0.25/0.60 => ! [Y3: list_a] :
% 0.25/0.60 ( ? [Ys3: list_list_a] :
% 0.25/0.60 ( A2
% 0.25/0.60 = ( cons_list_a @ Y3 @ Ys3 ) )
% 0.25/0.60 => ~ ( Less @ X @ Y3 ) ) )
% 0.25/0.60 => ~ ! [X: list_a,Y3: list_a,Xs2: list_list_a] :
% 0.25/0.60 ( ( A1
% 0.25/0.60 = ( cons_list_a @ X @ Xs2 ) )
% 0.25/0.60 => ! [Ys3: list_list_a] :
% 0.25/0.60 ( ( A2
% 0.25/0.60 = ( cons_list_a @ Y3 @ Ys3 ) )
% 0.25/0.60 => ( ~ ( Less @ X @ Y3 )
% 0.25/0.60 => ( ~ ( Less @ Y3 @ X )
% 0.25/0.60 => ~ ( lexordp_eq_list_a @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.cases
% 0.25/0.60 thf(fact_100_ord_Olexordp__eq_Ocases,axiom,
% 0.25/0.60 ! [Less: a > a > $o,A1: list_a,A2: list_a] :
% 0.25/0.60 ( ( lexordp_eq_a @ Less @ A1 @ A2 )
% 0.25/0.60 => ( ( A1 != nil_a )
% 0.25/0.60 => ( ! [X: a] :
% 0.25/0.60 ( ? [Xs2: list_a] :
% 0.25/0.60 ( A1
% 0.25/0.60 = ( cons_a @ X @ Xs2 ) )
% 0.25/0.60 => ! [Y3: a] :
% 0.25/0.60 ( ? [Ys3: list_a] :
% 0.25/0.60 ( A2
% 0.25/0.60 = ( cons_a @ Y3 @ Ys3 ) )
% 0.25/0.60 => ~ ( Less @ X @ Y3 ) ) )
% 0.25/0.60 => ~ ! [X: a,Y3: a,Xs2: list_a] :
% 0.25/0.60 ( ( A1
% 0.25/0.60 = ( cons_a @ X @ Xs2 ) )
% 0.25/0.60 => ! [Ys3: list_a] :
% 0.25/0.60 ( ( A2
% 0.25/0.60 = ( cons_a @ Y3 @ Ys3 ) )
% 0.25/0.60 => ( ~ ( Less @ X @ Y3 )
% 0.25/0.60 => ( ~ ( Less @ Y3 @ X )
% 0.25/0.60 => ~ ( lexordp_eq_a @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.cases
% 0.25/0.60 thf(fact_101_ord_Olexordp__eq_Osimps,axiom,
% 0.25/0.60 ( lexordp_eq_list_a
% 0.25/0.60 = ( ^ [Less2: list_a > list_a > $o,A12: list_list_a,A22: list_list_a] :
% 0.25/0.60 ( ? [Ys: list_list_a] :
% 0.25/0.60 ( ( A12 = nil_list_a )
% 0.25/0.60 & ( A22 = Ys ) )
% 0.25/0.60 | ? [X4: list_a,Y2: list_a,Xs3: list_list_a,Ys: list_list_a] :
% 0.25/0.60 ( ( A12
% 0.25/0.60 = ( cons_list_a @ X4 @ Xs3 ) )
% 0.25/0.60 & ( A22
% 0.25/0.60 = ( cons_list_a @ Y2 @ Ys ) )
% 0.25/0.60 & ( Less2 @ X4 @ Y2 ) )
% 0.25/0.60 | ? [X4: list_a,Y2: list_a,Xs3: list_list_a,Ys: list_list_a] :
% 0.25/0.60 ( ( A12
% 0.25/0.60 = ( cons_list_a @ X4 @ Xs3 ) )
% 0.25/0.60 & ( A22
% 0.25/0.60 = ( cons_list_a @ Y2 @ Ys ) )
% 0.25/0.60 & ~ ( Less2 @ X4 @ Y2 )
% 0.25/0.60 & ~ ( Less2 @ Y2 @ X4 )
% 0.25/0.60 & ( lexordp_eq_list_a @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.simps
% 0.25/0.60 thf(fact_102_ord_Olexordp__eq_Osimps,axiom,
% 0.25/0.60 ( lexordp_eq_a
% 0.25/0.60 = ( ^ [Less2: a > a > $o,A12: list_a,A22: list_a] :
% 0.25/0.60 ( ? [Ys: list_a] :
% 0.25/0.60 ( ( A12 = nil_a )
% 0.25/0.60 & ( A22 = Ys ) )
% 0.25/0.60 | ? [X4: a,Y2: a,Xs3: list_a,Ys: list_a] :
% 0.25/0.60 ( ( A12
% 0.25/0.60 = ( cons_a @ X4 @ Xs3 ) )
% 0.25/0.60 & ( A22
% 0.25/0.60 = ( cons_a @ Y2 @ Ys ) )
% 0.25/0.60 & ( Less2 @ X4 @ Y2 ) )
% 0.25/0.60 | ? [X4: a,Y2: a,Xs3: list_a,Ys: list_a] :
% 0.25/0.60 ( ( A12
% 0.25/0.60 = ( cons_a @ X4 @ Xs3 ) )
% 0.25/0.60 & ( A22
% 0.25/0.60 = ( cons_a @ Y2 @ Ys ) )
% 0.25/0.60 & ~ ( Less2 @ X4 @ Y2 )
% 0.25/0.60 & ~ ( Less2 @ Y2 @ X4 )
% 0.25/0.60 & ( lexordp_eq_a @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.simps
% 0.25/0.60 thf(fact_103_ord_Olexordp__eq_Oinducts,axiom,
% 0.25/0.60 ! [Less: list_a > list_a > $o,X12: list_list_a,X23: list_list_a,P: list_list_a > list_list_a > $o] :
% 0.25/0.60 ( ( lexordp_eq_list_a @ Less @ X12 @ X23 )
% 0.25/0.60 => ( ! [X_1: list_list_a] : ( P @ nil_list_a @ X_1 )
% 0.25/0.60 => ( ! [X: list_a,Y3: list_a,Xs2: list_list_a,Ys3: list_list_a] :
% 0.25/0.60 ( ( Less @ X @ Y3 )
% 0.25/0.60 => ( P @ ( cons_list_a @ X @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys3 ) ) )
% 0.25/0.60 => ( ! [X: list_a,Y3: list_a,Xs2: list_list_a,Ys3: list_list_a] :
% 0.25/0.60 ( ~ ( Less @ X @ Y3 )
% 0.25/0.60 => ( ~ ( Less @ Y3 @ X )
% 0.25/0.60 => ( ( lexordp_eq_list_a @ Less @ Xs2 @ Ys3 )
% 0.25/0.60 => ( ( P @ Xs2 @ Ys3 )
% 0.25/0.60 => ( P @ ( cons_list_a @ X @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys3 ) ) ) ) ) )
% 0.25/0.60 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.inducts
% 0.25/0.60 thf(fact_104_ord_Olexordp__eq_Oinducts,axiom,
% 0.25/0.60 ! [Less: a > a > $o,X12: list_a,X23: list_a,P: list_a > list_a > $o] :
% 0.25/0.60 ( ( lexordp_eq_a @ Less @ X12 @ X23 )
% 0.25/0.60 => ( ! [X_1: list_a] : ( P @ nil_a @ X_1 )
% 0.25/0.60 => ( ! [X: a,Y3: a,Xs2: list_a,Ys3: list_a] :
% 0.25/0.60 ( ( Less @ X @ Y3 )
% 0.25/0.60 => ( P @ ( cons_a @ X @ Xs2 ) @ ( cons_a @ Y3 @ Ys3 ) ) )
% 0.25/0.60 => ( ! [X: a,Y3: a,Xs2: list_a,Ys3: list_a] :
% 0.25/0.60 ( ~ ( Less @ X @ Y3 )
% 0.25/0.60 => ( ~ ( Less @ Y3 @ X )
% 0.25/0.60 => ( ( lexordp_eq_a @ Less @ Xs2 @ Ys3 )
% 0.25/0.60 => ( ( P @ Xs2 @ Ys3 )
% 0.25/0.60 => ( P @ ( cons_a @ X @ Xs2 ) @ ( cons_a @ Y3 @ Ys3 ) ) ) ) ) )
% 0.25/0.60 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq.inducts
% 0.25/0.60 thf(fact_105_product__lists_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( product_lists_list_a @ nil_list_list_a )
% 0.25/0.60 = ( cons_list_list_a @ nil_list_a @ nil_list_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % product_lists.simps(1)
% 0.25/0.60 thf(fact_106_product__lists_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( product_lists_a @ nil_list_a )
% 0.25/0.60 = ( cons_list_a @ nil_a @ nil_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % product_lists.simps(1)
% 0.25/0.60 thf(fact_107_subseqs_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( subseqs_list_a @ nil_list_a )
% 0.25/0.60 = ( cons_list_list_a @ nil_list_a @ nil_list_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % subseqs.simps(1)
% 0.25/0.60 thf(fact_108_subseqs_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( subseqs_a @ nil_a )
% 0.25/0.60 = ( cons_list_a @ nil_a @ nil_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % subseqs.simps(1)
% 0.25/0.60 thf(fact_109_lexordp__eq_Ocases,axiom,
% 0.25/0.60 ! [A1: list_nat,A2: list_nat] :
% 0.25/0.60 ( ( ord_lexordp_eq_nat @ A1 @ A2 )
% 0.25/0.60 => ( ( A1 != nil_nat )
% 0.25/0.60 => ( ! [X: nat] :
% 0.25/0.60 ( ? [Xs2: list_nat] :
% 0.25/0.60 ( A1
% 0.25/0.60 = ( cons_nat @ X @ Xs2 ) )
% 0.25/0.60 => ! [Y3: nat] :
% 0.25/0.60 ( ? [Ys3: list_nat] :
% 0.25/0.60 ( A2
% 0.25/0.60 = ( cons_nat @ Y3 @ Ys3 ) )
% 0.25/0.60 => ~ ( ord_less_nat @ X @ Y3 ) ) )
% 0.25/0.60 => ~ ! [X: nat,Y3: nat,Xs2: list_nat] :
% 0.25/0.60 ( ( A1
% 0.25/0.60 = ( cons_nat @ X @ Xs2 ) )
% 0.25/0.60 => ! [Ys3: list_nat] :
% 0.25/0.60 ( ( A2
% 0.25/0.60 = ( cons_nat @ Y3 @ Ys3 ) )
% 0.25/0.60 => ( ~ ( ord_less_nat @ X @ Y3 )
% 0.25/0.60 => ( ~ ( ord_less_nat @ Y3 @ X )
% 0.25/0.60 => ~ ( ord_lexordp_eq_nat @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_eq.cases
% 0.25/0.60 thf(fact_110_lexordp__eq_Osimps,axiom,
% 0.25/0.60 ( ord_lexordp_eq_nat
% 0.25/0.60 = ( ^ [A12: list_nat,A22: list_nat] :
% 0.25/0.60 ( ? [Ys: list_nat] :
% 0.25/0.60 ( ( A12 = nil_nat )
% 0.25/0.60 & ( A22 = Ys ) )
% 0.25/0.60 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 0.25/0.60 ( ( A12
% 0.25/0.60 = ( cons_nat @ X4 @ Xs3 ) )
% 0.25/0.60 & ( A22
% 0.25/0.60 = ( cons_nat @ Y2 @ Ys ) )
% 0.25/0.60 & ( ord_less_nat @ X4 @ Y2 ) )
% 0.25/0.60 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 0.25/0.60 ( ( A12
% 0.25/0.60 = ( cons_nat @ X4 @ Xs3 ) )
% 0.25/0.60 & ( A22
% 0.25/0.60 = ( cons_nat @ Y2 @ Ys ) )
% 0.25/0.60 & ~ ( ord_less_nat @ X4 @ Y2 )
% 0.25/0.60 & ~ ( ord_less_nat @ Y2 @ X4 )
% 0.25/0.60 & ( ord_lexordp_eq_nat @ Xs3 @ Ys ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_eq.simps
% 0.25/0.60 thf(fact_111_lexordp__eq_Oinducts,axiom,
% 0.25/0.60 ! [X12: list_nat,X23: list_nat,P: list_nat > list_nat > $o] :
% 0.25/0.60 ( ( ord_lexordp_eq_nat @ X12 @ X23 )
% 0.25/0.60 => ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 0.25/0.60 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.25/0.60 ( ( ord_less_nat @ X @ Y3 )
% 0.25/0.60 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.25/0.60 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.25/0.60 ( ~ ( ord_less_nat @ X @ Y3 )
% 0.25/0.60 => ( ~ ( ord_less_nat @ Y3 @ X )
% 0.25/0.60 => ( ( ord_lexordp_eq_nat @ Xs2 @ Ys3 )
% 0.25/0.60 => ( ( P @ Xs2 @ Ys3 )
% 0.25/0.60 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) ) ) )
% 0.25/0.60 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_eq.inducts
% 0.25/0.60 thf(fact_112_member__rec_I2_J,axiom,
% 0.25/0.60 ! [Y: list_a] :
% 0.25/0.60 ~ ( member_list_a @ nil_list_a @ Y ) ).
% 0.25/0.60
% 0.25/0.60 % member_rec(2)
% 0.25/0.60 thf(fact_113_member__rec_I2_J,axiom,
% 0.25/0.60 ! [Y: a] :
% 0.25/0.60 ~ ( member_a @ nil_a @ Y ) ).
% 0.25/0.60
% 0.25/0.60 % member_rec(2)
% 0.25/0.60 thf(fact_114_member__rec_I1_J,axiom,
% 0.25/0.60 ! [X3: list_a,Xs: list_list_a,Y: list_a] :
% 0.25/0.60 ( ( member_list_a @ ( cons_list_a @ X3 @ Xs ) @ Y )
% 0.25/0.60 = ( ( X3 = Y )
% 0.25/0.60 | ( member_list_a @ Xs @ Y ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % member_rec(1)
% 0.25/0.60 thf(fact_115_member__rec_I1_J,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a,Y: a] :
% 0.25/0.60 ( ( member_a @ ( cons_a @ X3 @ Xs ) @ Y )
% 0.25/0.60 = ( ( X3 = Y )
% 0.25/0.60 | ( member_a @ Xs @ Y ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % member_rec(1)
% 0.25/0.60 thf(fact_116_splice_Oelims,axiom,
% 0.25/0.60 ! [X3: list_list_a,Xa: list_list_a,Y: list_list_a] :
% 0.25/0.60 ( ( ( splice_list_a @ X3 @ Xa )
% 0.25/0.60 = Y )
% 0.25/0.60 => ( ( ( X3 = nil_list_a )
% 0.25/0.60 => ( Y != Xa ) )
% 0.25/0.60 => ~ ! [X: list_a,Xs2: list_list_a] :
% 0.25/0.60 ( ( X3
% 0.25/0.60 = ( cons_list_a @ X @ Xs2 ) )
% 0.25/0.60 => ( Y
% 0.25/0.60 != ( cons_list_a @ X @ ( splice_list_a @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % splice.elims
% 0.25/0.60 thf(fact_117_splice_Oelims,axiom,
% 0.25/0.60 ! [X3: list_a,Xa: list_a,Y: list_a] :
% 0.25/0.60 ( ( ( splice_a @ X3 @ Xa )
% 0.25/0.60 = Y )
% 0.25/0.60 => ( ( ( X3 = nil_a )
% 0.25/0.60 => ( Y != Xa ) )
% 0.25/0.60 => ~ ! [X: a,Xs2: list_a] :
% 0.25/0.60 ( ( X3
% 0.25/0.60 = ( cons_a @ X @ Xs2 ) )
% 0.25/0.60 => ( Y
% 0.25/0.60 != ( cons_a @ X @ ( splice_a @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % splice.elims
% 0.25/0.60 thf(fact_118_bind__simps_I2_J,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a,F: a > list_a] :
% 0.25/0.60 ( ( bind_a_a @ ( cons_a @ X3 @ Xs ) @ F )
% 0.25/0.60 = ( append_a @ ( F @ X3 ) @ ( bind_a_a @ Xs @ F ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % bind_simps(2)
% 0.25/0.60 thf(fact_119_bind__simps_I2_J,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a,F: a > list_list_a] :
% 0.25/0.60 ( ( bind_a_list_a @ ( cons_a @ X3 @ Xs ) @ F )
% 0.25/0.60 = ( append_list_a @ ( F @ X3 ) @ ( bind_a_list_a @ Xs @ F ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % bind_simps(2)
% 0.25/0.60 thf(fact_120_bind__simps_I2_J,axiom,
% 0.25/0.60 ! [X3: list_a,Xs: list_list_a,F: list_a > list_a] :
% 0.25/0.60 ( ( bind_list_a_a @ ( cons_list_a @ X3 @ Xs ) @ F )
% 0.25/0.60 = ( append_a @ ( F @ X3 ) @ ( bind_list_a_a @ Xs @ F ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % bind_simps(2)
% 0.25/0.60 thf(fact_121_bind__simps_I2_J,axiom,
% 0.25/0.60 ! [X3: list_a,Xs: list_list_a,F: list_a > list_list_a] :
% 0.25/0.60 ( ( bind_list_a_list_a @ ( cons_list_a @ X3 @ Xs ) @ F )
% 0.25/0.60 = ( append_list_a @ ( F @ X3 ) @ ( bind_list_a_list_a @ Xs @ F ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % bind_simps(2)
% 0.25/0.60 thf(fact_122_same__append__eq,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a,Zs2: list_a] :
% 0.25/0.60 ( ( ( append_a @ Xs @ Ys2 )
% 0.25/0.60 = ( append_a @ Xs @ Zs2 ) )
% 0.25/0.60 = ( Ys2 = Zs2 ) ) ).
% 0.25/0.60
% 0.25/0.60 % same_append_eq
% 0.25/0.60 thf(fact_123_same__append__eq,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a,Zs2: list_list_a] :
% 0.25/0.60 ( ( ( append_list_a @ Xs @ Ys2 )
% 0.25/0.60 = ( append_list_a @ Xs @ Zs2 ) )
% 0.25/0.60 = ( Ys2 = Zs2 ) ) ).
% 0.25/0.60
% 0.25/0.60 % same_append_eq
% 0.25/0.60 thf(fact_124_append__same__eq,axiom,
% 0.25/0.60 ! [Ys2: list_a,Xs: list_a,Zs2: list_a] :
% 0.25/0.60 ( ( ( append_a @ Ys2 @ Xs )
% 0.25/0.60 = ( append_a @ Zs2 @ Xs ) )
% 0.25/0.60 = ( Ys2 = Zs2 ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_same_eq
% 0.25/0.60 thf(fact_125_append__same__eq,axiom,
% 0.25/0.60 ! [Ys2: list_list_a,Xs: list_list_a,Zs2: list_list_a] :
% 0.25/0.60 ( ( ( append_list_a @ Ys2 @ Xs )
% 0.25/0.60 = ( append_list_a @ Zs2 @ Xs ) )
% 0.25/0.60 = ( Ys2 = Zs2 ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_same_eq
% 0.25/0.60 thf(fact_126_append__assoc,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a,Zs2: list_a] :
% 0.25/0.60 ( ( append_a @ ( append_a @ Xs @ Ys2 ) @ Zs2 )
% 0.25/0.60 = ( append_a @ Xs @ ( append_a @ Ys2 @ Zs2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_assoc
% 0.25/0.60 thf(fact_127_append__assoc,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a,Zs2: list_list_a] :
% 0.25/0.60 ( ( append_list_a @ ( append_list_a @ Xs @ Ys2 ) @ Zs2 )
% 0.25/0.60 = ( append_list_a @ Xs @ ( append_list_a @ Ys2 @ Zs2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_assoc
% 0.25/0.60 thf(fact_128_append_Oassoc,axiom,
% 0.25/0.60 ! [A3: list_a,B: list_a,C: list_a] :
% 0.25/0.60 ( ( append_a @ ( append_a @ A3 @ B ) @ C )
% 0.25/0.60 = ( append_a @ A3 @ ( append_a @ B @ C ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append.assoc
% 0.25/0.60 thf(fact_129_append_Oassoc,axiom,
% 0.25/0.60 ! [A3: list_list_a,B: list_list_a,C: list_list_a] :
% 0.25/0.60 ( ( append_list_a @ ( append_list_a @ A3 @ B ) @ C )
% 0.25/0.60 = ( append_list_a @ A3 @ ( append_list_a @ B @ C ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append.assoc
% 0.25/0.60 thf(fact_130_append_Oright__neutral,axiom,
% 0.25/0.60 ! [A3: list_list_a] :
% 0.25/0.60 ( ( append_list_a @ A3 @ nil_list_a )
% 0.25/0.60 = A3 ) ).
% 0.25/0.60
% 0.25/0.60 % append.right_neutral
% 0.25/0.60 thf(fact_131_append_Oright__neutral,axiom,
% 0.25/0.60 ! [A3: list_a] :
% 0.25/0.60 ( ( append_a @ A3 @ nil_a )
% 0.25/0.60 = A3 ) ).
% 0.25/0.60
% 0.25/0.60 % append.right_neutral
% 0.25/0.60 thf(fact_132_append__is__Nil__conv,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( ( append_list_a @ Xs @ Ys2 )
% 0.25/0.60 = nil_list_a )
% 0.25/0.60 = ( ( Xs = nil_list_a )
% 0.25/0.60 & ( Ys2 = nil_list_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_is_Nil_conv
% 0.25/0.60 thf(fact_133_append__is__Nil__conv,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( ( append_a @ Xs @ Ys2 )
% 0.25/0.60 = nil_a )
% 0.25/0.60 = ( ( Xs = nil_a )
% 0.25/0.60 & ( Ys2 = nil_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_is_Nil_conv
% 0.25/0.60 thf(fact_134_Nil__is__append__conv,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( nil_list_a
% 0.25/0.60 = ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( ( Xs = nil_list_a )
% 0.25/0.60 & ( Ys2 = nil_list_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Nil_is_append_conv
% 0.25/0.60 thf(fact_135_Nil__is__append__conv,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( nil_a
% 0.25/0.60 = ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( ( Xs = nil_a )
% 0.25/0.60 & ( Ys2 = nil_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Nil_is_append_conv
% 0.25/0.60 thf(fact_136_self__append__conv2,axiom,
% 0.25/0.60 ! [Ys2: list_list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( Ys2
% 0.25/0.60 = ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( Xs = nil_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % self_append_conv2
% 0.25/0.60 thf(fact_137_self__append__conv2,axiom,
% 0.25/0.60 ! [Ys2: list_a,Xs: list_a] :
% 0.25/0.60 ( ( Ys2
% 0.25/0.60 = ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( Xs = nil_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % self_append_conv2
% 0.25/0.60 thf(fact_138_append__self__conv2,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( ( append_list_a @ Xs @ Ys2 )
% 0.25/0.60 = Ys2 )
% 0.25/0.60 = ( Xs = nil_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_self_conv2
% 0.25/0.60 thf(fact_139_append__self__conv2,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( ( append_a @ Xs @ Ys2 )
% 0.25/0.60 = Ys2 )
% 0.25/0.60 = ( Xs = nil_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_self_conv2
% 0.25/0.60 thf(fact_140_self__append__conv,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( Xs
% 0.25/0.60 = ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( Ys2 = nil_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % self_append_conv
% 0.25/0.60 thf(fact_141_self__append__conv,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( Xs
% 0.25/0.60 = ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( Ys2 = nil_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % self_append_conv
% 0.25/0.60 thf(fact_142_append__self__conv,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( ( append_list_a @ Xs @ Ys2 )
% 0.25/0.60 = Xs )
% 0.25/0.60 = ( Ys2 = nil_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_self_conv
% 0.25/0.60 thf(fact_143_append__self__conv,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( ( append_a @ Xs @ Ys2 )
% 0.25/0.60 = Xs )
% 0.25/0.60 = ( Ys2 = nil_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_self_conv
% 0.25/0.60 thf(fact_144_append__Nil2,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( append_list_a @ Xs @ nil_list_a )
% 0.25/0.60 = Xs ) ).
% 0.25/0.60
% 0.25/0.60 % append_Nil2
% 0.25/0.60 thf(fact_145_append__Nil2,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( append_a @ Xs @ nil_a )
% 0.25/0.60 = Xs ) ).
% 0.25/0.60
% 0.25/0.60 % append_Nil2
% 0.25/0.60 thf(fact_146_split__Nil__iff,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( ( splice_list_a @ Xs @ Ys2 )
% 0.25/0.60 = nil_list_a )
% 0.25/0.60 = ( ( Xs = nil_list_a )
% 0.25/0.60 & ( Ys2 = nil_list_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % split_Nil_iff
% 0.25/0.60 thf(fact_147_split__Nil__iff,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( ( splice_a @ Xs @ Ys2 )
% 0.25/0.60 = nil_a )
% 0.25/0.60 = ( ( Xs = nil_a )
% 0.25/0.60 & ( Ys2 = nil_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % split_Nil_iff
% 0.25/0.60 thf(fact_148_splice__Nil2,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( splice_list_a @ Xs @ nil_list_a )
% 0.25/0.60 = Xs ) ).
% 0.25/0.60
% 0.25/0.60 % splice_Nil2
% 0.25/0.60 thf(fact_149_splice__Nil2,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( splice_a @ Xs @ nil_a )
% 0.25/0.60 = Xs ) ).
% 0.25/0.60
% 0.25/0.60 % splice_Nil2
% 0.25/0.60 thf(fact_150_i__append__assoc,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a,F: nat > list_a] :
% 0.25/0.60 ( ( listIn1753026346list_a @ Xs @ ( listIn1753026346list_a @ Ys2 @ F ) )
% 0.25/0.60 = ( listIn1753026346list_a @ ( append_list_a @ Xs @ Ys2 ) @ F ) ) ).
% 0.25/0.60
% 0.25/0.60 % i_append_assoc
% 0.25/0.60 thf(fact_151_i__append__assoc,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a,F: nat > a] :
% 0.25/0.60 ( ( listIn1312259492pend_a @ Xs @ ( listIn1312259492pend_a @ Ys2 @ F ) )
% 0.25/0.60 = ( listIn1312259492pend_a @ ( append_a @ Xs @ Ys2 ) @ F ) ) ).
% 0.25/0.60
% 0.25/0.60 % i_append_assoc
% 0.25/0.60 thf(fact_152_append1__eq__conv,axiom,
% 0.25/0.60 ! [Xs: list_list_a,X3: list_a,Ys2: list_list_a,Y: list_a] :
% 0.25/0.60 ( ( ( append_list_a @ Xs @ ( cons_list_a @ X3 @ nil_list_a ) )
% 0.25/0.60 = ( append_list_a @ Ys2 @ ( cons_list_a @ Y @ nil_list_a ) ) )
% 0.25/0.60 = ( ( Xs = Ys2 )
% 0.25/0.60 & ( X3 = Y ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append1_eq_conv
% 0.25/0.60 thf(fact_153_append1__eq__conv,axiom,
% 0.25/0.60 ! [Xs: list_a,X3: a,Ys2: list_a,Y: a] :
% 0.25/0.60 ( ( ( append_a @ Xs @ ( cons_a @ X3 @ nil_a ) )
% 0.25/0.60 = ( append_a @ Ys2 @ ( cons_a @ Y @ nil_a ) ) )
% 0.25/0.60 = ( ( Xs = Ys2 )
% 0.25/0.60 & ( X3 = Y ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append1_eq_conv
% 0.25/0.60 thf(fact_154_lexordp__eq__simps_I4_J,axiom,
% 0.25/0.60 ! [X3: nat,Xs: list_nat,Y: nat,Ys2: list_nat] :
% 0.25/0.60 ( ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) )
% 0.25/0.60 = ( ( ord_less_nat @ X3 @ Y )
% 0.25/0.60 | ( ~ ( ord_less_nat @ Y @ X3 )
% 0.25/0.60 & ( ord_lexordp_eq_nat @ Xs @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_eq_simps(4)
% 0.25/0.60 thf(fact_155_append__eq__append__conv2,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a,Zs2: list_a,Ts: list_a] :
% 0.25/0.60 ( ( ( append_a @ Xs @ Ys2 )
% 0.25/0.60 = ( append_a @ Zs2 @ Ts ) )
% 0.25/0.60 = ( ? [Us: list_a] :
% 0.25/0.60 ( ( ( Xs
% 0.25/0.60 = ( append_a @ Zs2 @ Us ) )
% 0.25/0.60 & ( ( append_a @ Us @ Ys2 )
% 0.25/0.60 = Ts ) )
% 0.25/0.60 | ( ( ( append_a @ Xs @ Us )
% 0.25/0.60 = Zs2 )
% 0.25/0.60 & ( Ys2
% 0.25/0.60 = ( append_a @ Us @ Ts ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_eq_append_conv2
% 0.25/0.60 thf(fact_156_append__eq__append__conv2,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a,Zs2: list_list_a,Ts: list_list_a] :
% 0.25/0.60 ( ( ( append_list_a @ Xs @ Ys2 )
% 0.25/0.60 = ( append_list_a @ Zs2 @ Ts ) )
% 0.25/0.60 = ( ? [Us: list_list_a] :
% 0.25/0.60 ( ( ( Xs
% 0.25/0.60 = ( append_list_a @ Zs2 @ Us ) )
% 0.25/0.60 & ( ( append_list_a @ Us @ Ys2 )
% 0.25/0.60 = Ts ) )
% 0.25/0.60 | ( ( ( append_list_a @ Xs @ Us )
% 0.25/0.60 = Zs2 )
% 0.25/0.60 & ( Ys2
% 0.25/0.60 = ( append_list_a @ Us @ Ts ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_eq_append_conv2
% 0.25/0.60 thf(fact_157_append__eq__appendI,axiom,
% 0.25/0.60 ! [Xs: list_a,Xs1: list_a,Zs2: list_a,Ys2: list_a,Us2: list_a] :
% 0.25/0.60 ( ( ( append_a @ Xs @ Xs1 )
% 0.25/0.60 = Zs2 )
% 0.25/0.60 => ( ( Ys2
% 0.25/0.60 = ( append_a @ Xs1 @ Us2 ) )
% 0.25/0.60 => ( ( append_a @ Xs @ Ys2 )
% 0.25/0.60 = ( append_a @ Zs2 @ Us2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_eq_appendI
% 0.25/0.60 thf(fact_158_append__eq__appendI,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Xs1: list_list_a,Zs2: list_list_a,Ys2: list_list_a,Us2: list_list_a] :
% 0.25/0.60 ( ( ( append_list_a @ Xs @ Xs1 )
% 0.25/0.60 = Zs2 )
% 0.25/0.60 => ( ( Ys2
% 0.25/0.60 = ( append_list_a @ Xs1 @ Us2 ) )
% 0.25/0.60 => ( ( append_list_a @ Xs @ Ys2 )
% 0.25/0.60 = ( append_list_a @ Zs2 @ Us2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_eq_appendI
% 0.25/0.60 thf(fact_159_append__Cons,axiom,
% 0.25/0.60 ! [X3: list_a,Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( append_list_a @ ( cons_list_a @ X3 @ Xs ) @ Ys2 )
% 0.25/0.60 = ( cons_list_a @ X3 @ ( append_list_a @ Xs @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_Cons
% 0.25/0.60 thf(fact_160_append__Cons,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( append_a @ ( cons_a @ X3 @ Xs ) @ Ys2 )
% 0.25/0.60 = ( cons_a @ X3 @ ( append_a @ Xs @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_Cons
% 0.25/0.60 thf(fact_161_Cons__eq__appendI,axiom,
% 0.25/0.60 ! [X3: list_a,Xs1: list_list_a,Ys2: list_list_a,Xs: list_list_a,Zs2: list_list_a] :
% 0.25/0.60 ( ( ( cons_list_a @ X3 @ Xs1 )
% 0.25/0.60 = Ys2 )
% 0.25/0.60 => ( ( Xs
% 0.25/0.60 = ( append_list_a @ Xs1 @ Zs2 ) )
% 0.25/0.60 => ( ( cons_list_a @ X3 @ Xs )
% 0.25/0.60 = ( append_list_a @ Ys2 @ Zs2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Cons_eq_appendI
% 0.25/0.60 thf(fact_162_Cons__eq__appendI,axiom,
% 0.25/0.60 ! [X3: a,Xs1: list_a,Ys2: list_a,Xs: list_a,Zs2: list_a] :
% 0.25/0.60 ( ( ( cons_a @ X3 @ Xs1 )
% 0.25/0.60 = Ys2 )
% 0.25/0.60 => ( ( Xs
% 0.25/0.60 = ( append_a @ Xs1 @ Zs2 ) )
% 0.25/0.60 => ( ( cons_a @ X3 @ Xs )
% 0.25/0.60 = ( append_a @ Ys2 @ Zs2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Cons_eq_appendI
% 0.25/0.60 thf(fact_163_append_Oleft__neutral,axiom,
% 0.25/0.60 ! [A3: list_list_a] :
% 0.25/0.60 ( ( append_list_a @ nil_list_a @ A3 )
% 0.25/0.60 = A3 ) ).
% 0.25/0.60
% 0.25/0.60 % append.left_neutral
% 0.25/0.60 thf(fact_164_append_Oleft__neutral,axiom,
% 0.25/0.60 ! [A3: list_a] :
% 0.25/0.60 ( ( append_a @ nil_a @ A3 )
% 0.25/0.60 = A3 ) ).
% 0.25/0.60
% 0.25/0.60 % append.left_neutral
% 0.25/0.60 thf(fact_165_append__Nil,axiom,
% 0.25/0.60 ! [Ys2: list_list_a] :
% 0.25/0.60 ( ( append_list_a @ nil_list_a @ Ys2 )
% 0.25/0.60 = Ys2 ) ).
% 0.25/0.60
% 0.25/0.60 % append_Nil
% 0.25/0.60 thf(fact_166_append__Nil,axiom,
% 0.25/0.60 ! [Ys2: list_a] :
% 0.25/0.60 ( ( append_a @ nil_a @ Ys2 )
% 0.25/0.60 = Ys2 ) ).
% 0.25/0.60
% 0.25/0.60 % append_Nil
% 0.25/0.60 thf(fact_167_eq__Nil__appendI,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( Xs = Ys2 )
% 0.25/0.60 => ( Xs
% 0.25/0.60 = ( append_list_a @ nil_list_a @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % eq_Nil_appendI
% 0.25/0.60 thf(fact_168_eq__Nil__appendI,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( Xs = Ys2 )
% 0.25/0.60 => ( Xs
% 0.25/0.60 = ( append_a @ nil_a @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % eq_Nil_appendI
% 0.25/0.60 thf(fact_169_ord_Olexordp__eq__pref,axiom,
% 0.25/0.60 ! [Less: list_a > list_a > $o,U: list_list_a,V: list_list_a] : ( lexordp_eq_list_a @ Less @ U @ ( append_list_a @ U @ V ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq_pref
% 0.25/0.60 thf(fact_170_ord_Olexordp__eq__pref,axiom,
% 0.25/0.60 ! [Less: a > a > $o,U: list_a,V: list_a] : ( lexordp_eq_a @ Less @ U @ ( append_a @ U @ V ) ) ).
% 0.25/0.60
% 0.25/0.60 % ord.lexordp_eq_pref
% 0.25/0.60 thf(fact_171_splice_Osimps_I2_J,axiom,
% 0.25/0.60 ! [X3: list_a,Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( splice_list_a @ ( cons_list_a @ X3 @ Xs ) @ Ys2 )
% 0.25/0.60 = ( cons_list_a @ X3 @ ( splice_list_a @ Ys2 @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % splice.simps(2)
% 0.25/0.60 thf(fact_172_splice_Osimps_I2_J,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( splice_a @ ( cons_a @ X3 @ Xs ) @ Ys2 )
% 0.25/0.60 = ( cons_a @ X3 @ ( splice_a @ Ys2 @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % splice.simps(2)
% 0.25/0.60 thf(fact_173_splice_Osimps_I1_J,axiom,
% 0.25/0.60 ! [Ys2: list_list_a] :
% 0.25/0.60 ( ( splice_list_a @ nil_list_a @ Ys2 )
% 0.25/0.60 = Ys2 ) ).
% 0.25/0.60
% 0.25/0.60 % splice.simps(1)
% 0.25/0.60 thf(fact_174_splice_Osimps_I1_J,axiom,
% 0.25/0.60 ! [Ys2: list_a] :
% 0.25/0.60 ( ( splice_a @ nil_a @ Ys2 )
% 0.25/0.60 = Ys2 ) ).
% 0.25/0.60
% 0.25/0.60 % splice.simps(1)
% 0.25/0.60 thf(fact_175_rev__nonempty__induct,axiom,
% 0.25/0.60 ! [Xs: list_list_a,P: list_list_a > $o] :
% 0.25/0.60 ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ! [X: list_a] : ( P @ ( cons_list_a @ X @ nil_list_a ) )
% 0.25/0.60 => ( ! [X: list_a,Xs2: list_list_a] :
% 0.25/0.60 ( ( Xs2 != nil_list_a )
% 0.25/0.60 => ( ( P @ Xs2 )
% 0.25/0.60 => ( P @ ( append_list_a @ Xs2 @ ( cons_list_a @ X @ nil_list_a ) ) ) ) )
% 0.25/0.60 => ( P @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % rev_nonempty_induct
% 0.25/0.60 thf(fact_176_rev__nonempty__induct,axiom,
% 0.25/0.60 ! [Xs: list_a,P: list_a > $o] :
% 0.25/0.60 ( ( Xs != nil_a )
% 0.25/0.60 => ( ! [X: a] : ( P @ ( cons_a @ X @ nil_a ) )
% 0.25/0.60 => ( ! [X: a,Xs2: list_a] :
% 0.25/0.60 ( ( Xs2 != nil_a )
% 0.25/0.60 => ( ( P @ Xs2 )
% 0.25/0.60 => ( P @ ( append_a @ Xs2 @ ( cons_a @ X @ nil_a ) ) ) ) )
% 0.25/0.60 => ( P @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % rev_nonempty_induct
% 0.25/0.60 thf(fact_177_append__eq__Cons__conv,axiom,
% 0.25/0.60 ! [Ys2: list_list_a,Zs2: list_list_a,X3: list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( ( append_list_a @ Ys2 @ Zs2 )
% 0.25/0.60 = ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = ( ( ( Ys2 = nil_list_a )
% 0.25/0.60 & ( Zs2
% 0.25/0.60 = ( cons_list_a @ X3 @ Xs ) ) )
% 0.25/0.60 | ? [Ys4: list_list_a] :
% 0.25/0.60 ( ( Ys2
% 0.25/0.60 = ( cons_list_a @ X3 @ Ys4 ) )
% 0.25/0.60 & ( ( append_list_a @ Ys4 @ Zs2 )
% 0.25/0.60 = Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_eq_Cons_conv
% 0.25/0.60 thf(fact_178_append__eq__Cons__conv,axiom,
% 0.25/0.60 ! [Ys2: list_a,Zs2: list_a,X3: a,Xs: list_a] :
% 0.25/0.60 ( ( ( append_a @ Ys2 @ Zs2 )
% 0.25/0.60 = ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = ( ( ( Ys2 = nil_a )
% 0.25/0.60 & ( Zs2
% 0.25/0.60 = ( cons_a @ X3 @ Xs ) ) )
% 0.25/0.60 | ? [Ys4: list_a] :
% 0.25/0.60 ( ( Ys2
% 0.25/0.60 = ( cons_a @ X3 @ Ys4 ) )
% 0.25/0.60 & ( ( append_a @ Ys4 @ Zs2 )
% 0.25/0.60 = Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_eq_Cons_conv
% 0.25/0.60 thf(fact_179_Cons__eq__append__conv,axiom,
% 0.25/0.60 ! [X3: list_a,Xs: list_list_a,Ys2: list_list_a,Zs2: list_list_a] :
% 0.25/0.60 ( ( ( cons_list_a @ X3 @ Xs )
% 0.25/0.60 = ( append_list_a @ Ys2 @ Zs2 ) )
% 0.25/0.60 = ( ( ( Ys2 = nil_list_a )
% 0.25/0.60 & ( ( cons_list_a @ X3 @ Xs )
% 0.25/0.60 = Zs2 ) )
% 0.25/0.60 | ? [Ys4: list_list_a] :
% 0.25/0.60 ( ( ( cons_list_a @ X3 @ Ys4 )
% 0.25/0.60 = Ys2 )
% 0.25/0.60 & ( Xs
% 0.25/0.60 = ( append_list_a @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Cons_eq_append_conv
% 0.25/0.60 thf(fact_180_Cons__eq__append__conv,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a,Ys2: list_a,Zs2: list_a] :
% 0.25/0.60 ( ( ( cons_a @ X3 @ Xs )
% 0.25/0.60 = ( append_a @ Ys2 @ Zs2 ) )
% 0.25/0.60 = ( ( ( Ys2 = nil_a )
% 0.25/0.60 & ( ( cons_a @ X3 @ Xs )
% 0.25/0.60 = Zs2 ) )
% 0.25/0.60 | ? [Ys4: list_a] :
% 0.25/0.60 ( ( ( cons_a @ X3 @ Ys4 )
% 0.25/0.60 = Ys2 )
% 0.25/0.60 & ( Xs
% 0.25/0.60 = ( append_a @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Cons_eq_append_conv
% 0.25/0.60 thf(fact_181_rev__exhaust,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( Xs != nil_list_a )
% 0.25/0.60 => ~ ! [Ys3: list_list_a,Y3: list_a] :
% 0.25/0.60 ( Xs
% 0.25/0.60 != ( append_list_a @ Ys3 @ ( cons_list_a @ Y3 @ nil_list_a ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % rev_exhaust
% 0.25/0.60 thf(fact_182_rev__exhaust,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( Xs != nil_a )
% 0.25/0.60 => ~ ! [Ys3: list_a,Y3: a] :
% 0.25/0.60 ( Xs
% 0.25/0.60 != ( append_a @ Ys3 @ ( cons_a @ Y3 @ nil_a ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % rev_exhaust
% 0.25/0.60 thf(fact_183_rev__induct,axiom,
% 0.25/0.60 ! [P: list_list_a > $o,Xs: list_list_a] :
% 0.25/0.60 ( ( P @ nil_list_a )
% 0.25/0.60 => ( ! [X: list_a,Xs2: list_list_a] :
% 0.25/0.60 ( ( P @ Xs2 )
% 0.25/0.60 => ( P @ ( append_list_a @ Xs2 @ ( cons_list_a @ X @ nil_list_a ) ) ) )
% 0.25/0.60 => ( P @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % rev_induct
% 0.25/0.60 thf(fact_184_rev__induct,axiom,
% 0.25/0.60 ! [P: list_a > $o,Xs: list_a] :
% 0.25/0.60 ( ( P @ nil_a )
% 0.25/0.60 => ( ! [X: a,Xs2: list_a] :
% 0.25/0.60 ( ( P @ Xs2 )
% 0.25/0.60 => ( P @ ( append_a @ Xs2 @ ( cons_a @ X @ nil_a ) ) ) )
% 0.25/0.60 => ( P @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % rev_induct
% 0.25/0.60 thf(fact_185_append__eq__Cons,axiom,
% 0.25/0.60 ! [X3: list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( append_list_a @ ( cons_list_a @ X3 @ nil_list_a ) @ Xs )
% 0.25/0.60 = ( cons_list_a @ X3 @ Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_eq_Cons
% 0.25/0.60 thf(fact_186_append__eq__Cons,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a] :
% 0.25/0.60 ( ( append_a @ ( cons_a @ X3 @ nil_a ) @ Xs )
% 0.25/0.60 = ( cons_a @ X3 @ Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_eq_Cons
% 0.25/0.60 thf(fact_187_lexordp__eq_OCons,axiom,
% 0.25/0.60 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 0.25/0.60 ( ( ord_less_nat @ X3 @ Y )
% 0.25/0.60 => ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_eq.Cons
% 0.25/0.60 thf(fact_188_lexordp__eq_OCons__eq,axiom,
% 0.25/0.60 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 0.25/0.60 ( ~ ( ord_less_nat @ X3 @ Y )
% 0.25/0.60 => ( ~ ( ord_less_nat @ Y @ X3 )
% 0.25/0.60 => ( ( ord_lexordp_eq_nat @ Xs @ Ys2 )
% 0.25/0.60 => ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_eq.Cons_eq
% 0.25/0.60 thf(fact_189_maps__simps_I1_J,axiom,
% 0.25/0.60 ! [F: a > list_a,X3: a,Xs: list_a] :
% 0.25/0.60 ( ( maps_a_a @ F @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = ( append_a @ ( F @ X3 ) @ ( maps_a_a @ F @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % maps_simps(1)
% 0.25/0.60 thf(fact_190_maps__simps_I1_J,axiom,
% 0.25/0.60 ! [F: a > list_list_a,X3: a,Xs: list_a] :
% 0.25/0.60 ( ( maps_a_list_a @ F @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = ( append_list_a @ ( F @ X3 ) @ ( maps_a_list_a @ F @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % maps_simps(1)
% 0.25/0.60 thf(fact_191_maps__simps_I1_J,axiom,
% 0.25/0.60 ! [F: list_a > list_a,X3: list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( maps_list_a_a @ F @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = ( append_a @ ( F @ X3 ) @ ( maps_list_a_a @ F @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % maps_simps(1)
% 0.25/0.60 thf(fact_192_maps__simps_I1_J,axiom,
% 0.25/0.60 ! [F: list_a > list_list_a,X3: list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( maps_list_a_list_a @ F @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = ( append_list_a @ ( F @ X3 ) @ ( maps_list_a_list_a @ F @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % maps_simps(1)
% 0.25/0.60 thf(fact_193_concat__eq__append__conv,axiom,
% 0.25/0.60 ! [Xss2: list_list_list_a,Ys2: list_list_a,Zs2: list_list_a] :
% 0.25/0.60 ( ( ( concat_list_a @ Xss2 )
% 0.25/0.60 = ( append_list_a @ Ys2 @ Zs2 ) )
% 0.25/0.60 = ( ( ( Xss2 = nil_list_list_a )
% 0.25/0.60 => ( ( Ys2 = nil_list_a )
% 0.25/0.60 & ( Zs2 = nil_list_a ) ) )
% 0.25/0.60 & ( ( Xss2 != nil_list_list_a )
% 0.25/0.60 => ? [Xss1: list_list_list_a,Xs3: list_list_a,Xs4: list_list_a,Xss22: list_list_list_a] :
% 0.25/0.60 ( ( Xss2
% 0.25/0.60 = ( append_list_list_a @ Xss1 @ ( cons_list_list_a @ ( append_list_a @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.25/0.60 & ( Ys2
% 0.25/0.60 = ( append_list_a @ ( concat_list_a @ Xss1 ) @ Xs3 ) )
% 0.25/0.60 & ( Zs2
% 0.25/0.60 = ( append_list_a @ Xs4 @ ( concat_list_a @ Xss22 ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % concat_eq_append_conv
% 0.25/0.60 thf(fact_194_concat__eq__append__conv,axiom,
% 0.25/0.60 ! [Xss2: list_list_a,Ys2: list_a,Zs2: list_a] :
% 0.25/0.60 ( ( ( concat_a @ Xss2 )
% 0.25/0.60 = ( append_a @ Ys2 @ Zs2 ) )
% 0.25/0.60 = ( ( ( Xss2 = nil_list_a )
% 0.25/0.60 => ( ( Ys2 = nil_a )
% 0.25/0.60 & ( Zs2 = nil_a ) ) )
% 0.25/0.60 & ( ( Xss2 != nil_list_a )
% 0.25/0.60 => ? [Xss1: list_list_a,Xs3: list_a,Xs4: list_a,Xss22: list_list_a] :
% 0.25/0.60 ( ( Xss2
% 0.25/0.60 = ( append_list_a @ Xss1 @ ( cons_list_a @ ( append_a @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.25/0.60 & ( Ys2
% 0.25/0.60 = ( append_a @ ( concat_a @ Xss1 ) @ Xs3 ) )
% 0.25/0.60 & ( Zs2
% 0.25/0.60 = ( append_a @ Xs4 @ ( concat_a @ Xss22 ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % concat_eq_append_conv
% 0.25/0.60 thf(fact_195_rotate1_Osimps_I2_J,axiom,
% 0.25/0.60 ! [X3: list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( rotate1_list_a @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = ( append_list_a @ Xs @ ( cons_list_a @ X3 @ nil_list_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % rotate1.simps(2)
% 0.25/0.60 thf(fact_196_rotate1_Osimps_I2_J,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a] :
% 0.25/0.60 ( ( rotate1_a @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = ( append_a @ Xs @ ( cons_a @ X3 @ nil_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % rotate1.simps(2)
% 0.25/0.60 thf(fact_197_butlast__snoc,axiom,
% 0.25/0.60 ! [Xs: list_list_a,X3: list_a] :
% 0.25/0.60 ( ( butlast_list_a @ ( append_list_a @ Xs @ ( cons_list_a @ X3 @ nil_list_a ) ) )
% 0.25/0.60 = Xs ) ).
% 0.25/0.60
% 0.25/0.60 % butlast_snoc
% 0.25/0.60 thf(fact_198_butlast__snoc,axiom,
% 0.25/0.60 ! [Xs: list_a,X3: a] :
% 0.25/0.60 ( ( butlast_a @ ( append_a @ Xs @ ( cons_a @ X3 @ nil_a ) ) )
% 0.25/0.60 = Xs ) ).
% 0.25/0.60
% 0.25/0.60 % butlast_snoc
% 0.25/0.60 thf(fact_199_last__snoc,axiom,
% 0.25/0.60 ! [Xs: list_list_a,X3: list_a] :
% 0.25/0.60 ( ( last_list_a @ ( append_list_a @ Xs @ ( cons_list_a @ X3 @ nil_list_a ) ) )
% 0.25/0.60 = X3 ) ).
% 0.25/0.60
% 0.25/0.60 % last_snoc
% 0.25/0.60 thf(fact_200_last__snoc,axiom,
% 0.25/0.60 ! [Xs: list_a,X3: a] :
% 0.25/0.60 ( ( last_a @ ( append_a @ Xs @ ( cons_a @ X3 @ nil_a ) ) )
% 0.25/0.60 = X3 ) ).
% 0.25/0.60
% 0.25/0.60 % last_snoc
% 0.25/0.60 thf(fact_201_SuccI,axiom,
% 0.25/0.60 ! [Kl: list_list_a,K: list_a,Kl2: set_list_list_a] :
% 0.25/0.60 ( ( member_list_list_a @ ( append_list_a @ Kl @ ( cons_list_a @ K @ nil_list_a ) ) @ Kl2 )
% 0.25/0.60 => ( member_list_a2 @ K @ ( bNF_Gr1046450207list_a @ Kl2 @ Kl ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % SuccI
% 0.25/0.60 thf(fact_202_SuccI,axiom,
% 0.25/0.60 ! [Kl: list_a,K: a,Kl2: set_list_a] :
% 0.25/0.60 ( ( member_list_a2 @ ( append_a @ Kl @ ( cons_a @ K @ nil_a ) ) @ Kl2 )
% 0.25/0.60 => ( member_a2 @ K @ ( bNF_Greatest_Succ_a @ Kl2 @ Kl ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % SuccI
% 0.25/0.60 thf(fact_203_SuccD,axiom,
% 0.25/0.60 ! [K: list_a,Kl2: set_list_list_a,Kl: list_list_a] :
% 0.25/0.60 ( ( member_list_a2 @ K @ ( bNF_Gr1046450207list_a @ Kl2 @ Kl ) )
% 0.25/0.60 => ( member_list_list_a @ ( append_list_a @ Kl @ ( cons_list_a @ K @ nil_list_a ) ) @ Kl2 ) ) ).
% 0.25/0.60
% 0.25/0.60 % SuccD
% 0.25/0.60 thf(fact_204_SuccD,axiom,
% 0.25/0.60 ! [K: a,Kl2: set_list_a,Kl: list_a] :
% 0.25/0.60 ( ( member_a2 @ K @ ( bNF_Greatest_Succ_a @ Kl2 @ Kl ) )
% 0.25/0.60 => ( member_list_a2 @ ( append_a @ Kl @ ( cons_a @ K @ nil_a ) ) @ Kl2 ) ) ).
% 0.25/0.60
% 0.25/0.60 % SuccD
% 0.25/0.60 thf(fact_205_rotate1__is__Nil__conv,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( ( rotate1_list_a @ Xs )
% 0.25/0.60 = nil_list_a )
% 0.25/0.60 = ( Xs = nil_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % rotate1_is_Nil_conv
% 0.25/0.60 thf(fact_206_rotate1__is__Nil__conv,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( ( rotate1_a @ Xs )
% 0.25/0.60 = nil_a )
% 0.25/0.60 = ( Xs = nil_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % rotate1_is_Nil_conv
% 0.25/0.60 thf(fact_207_last__appendL,axiom,
% 0.25/0.60 ! [Ys2: list_list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( Ys2 = nil_list_a )
% 0.25/0.60 => ( ( last_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( last_list_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_appendL
% 0.25/0.60 thf(fact_208_last__appendL,axiom,
% 0.25/0.60 ! [Ys2: list_a,Xs: list_a] :
% 0.25/0.60 ( ( Ys2 = nil_a )
% 0.25/0.60 => ( ( last_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( last_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_appendL
% 0.25/0.60 thf(fact_209_last__appendR,axiom,
% 0.25/0.60 ! [Ys2: list_list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( Ys2 != nil_list_a )
% 0.25/0.60 => ( ( last_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( last_list_a @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_appendR
% 0.25/0.60 thf(fact_210_last__appendR,axiom,
% 0.25/0.60 ! [Ys2: list_a,Xs: list_a] :
% 0.25/0.60 ( ( Ys2 != nil_a )
% 0.25/0.60 => ( ( last_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( last_a @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_appendR
% 0.25/0.60 thf(fact_211_concat__append,axiom,
% 0.25/0.60 ! [Xs: list_list_list_a,Ys2: list_list_list_a] :
% 0.25/0.60 ( ( concat_list_a @ ( append_list_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( append_list_a @ ( concat_list_a @ Xs ) @ ( concat_list_a @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % concat_append
% 0.25/0.60 thf(fact_212_concat__append,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( concat_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( append_a @ ( concat_a @ Xs ) @ ( concat_a @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % concat_append
% 0.25/0.60 thf(fact_213_append__butlast__last__id,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ( append_list_a @ ( butlast_list_a @ Xs ) @ ( cons_list_a @ ( last_list_a @ Xs ) @ nil_list_a ) )
% 0.25/0.60 = Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_butlast_last_id
% 0.25/0.60 thf(fact_214_append__butlast__last__id,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( Xs != nil_a )
% 0.25/0.60 => ( ( append_a @ ( butlast_a @ Xs ) @ ( cons_a @ ( last_a @ Xs ) @ nil_a ) )
% 0.25/0.60 = Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % append_butlast_last_id
% 0.25/0.60 thf(fact_215_butlast_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( butlast_list_a @ nil_list_a )
% 0.25/0.60 = nil_list_a ) ).
% 0.25/0.60
% 0.25/0.60 % butlast.simps(1)
% 0.25/0.60 thf(fact_216_butlast_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( butlast_a @ nil_a )
% 0.25/0.60 = nil_a ) ).
% 0.25/0.60
% 0.25/0.60 % butlast.simps(1)
% 0.25/0.60 thf(fact_217_snoc__eq__iff__butlast,axiom,
% 0.25/0.60 ! [Xs: list_list_a,X3: list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( ( append_list_a @ Xs @ ( cons_list_a @ X3 @ nil_list_a ) )
% 0.25/0.60 = Ys2 )
% 0.25/0.60 = ( ( Ys2 != nil_list_a )
% 0.25/0.60 & ( ( butlast_list_a @ Ys2 )
% 0.25/0.60 = Xs )
% 0.25/0.60 & ( ( last_list_a @ Ys2 )
% 0.25/0.60 = X3 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % snoc_eq_iff_butlast
% 0.25/0.60 thf(fact_218_snoc__eq__iff__butlast,axiom,
% 0.25/0.60 ! [Xs: list_a,X3: a,Ys2: list_a] :
% 0.25/0.60 ( ( ( append_a @ Xs @ ( cons_a @ X3 @ nil_a ) )
% 0.25/0.60 = Ys2 )
% 0.25/0.60 = ( ( Ys2 != nil_a )
% 0.25/0.60 & ( ( butlast_a @ Ys2 )
% 0.25/0.60 = Xs )
% 0.25/0.60 & ( ( last_a @ Ys2 )
% 0.25/0.60 = X3 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % snoc_eq_iff_butlast
% 0.25/0.60 thf(fact_219_rotate1_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( rotate1_list_a @ nil_list_a )
% 0.25/0.60 = nil_list_a ) ).
% 0.25/0.60
% 0.25/0.60 % rotate1.simps(1)
% 0.25/0.60 thf(fact_220_rotate1_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( rotate1_a @ nil_a )
% 0.25/0.60 = nil_a ) ).
% 0.25/0.60
% 0.25/0.60 % rotate1.simps(1)
% 0.25/0.60 thf(fact_221_last_Osimps,axiom,
% 0.25/0.60 ! [Xs: list_list_a,X3: list_a] :
% 0.25/0.60 ( ( ( Xs = nil_list_a )
% 0.25/0.60 => ( ( last_list_a @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = X3 ) )
% 0.25/0.60 & ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ( last_list_a @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = ( last_list_a @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last.simps
% 0.25/0.60 thf(fact_222_last_Osimps,axiom,
% 0.25/0.60 ! [Xs: list_a,X3: a] :
% 0.25/0.60 ( ( ( Xs = nil_a )
% 0.25/0.60 => ( ( last_a @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = X3 ) )
% 0.25/0.60 & ( ( Xs != nil_a )
% 0.25/0.60 => ( ( last_a @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = ( last_a @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last.simps
% 0.25/0.60 thf(fact_223_last__ConsL,axiom,
% 0.25/0.60 ! [Xs: list_list_a,X3: list_a] :
% 0.25/0.60 ( ( Xs = nil_list_a )
% 0.25/0.60 => ( ( last_list_a @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = X3 ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_ConsL
% 0.25/0.60 thf(fact_224_last__ConsL,axiom,
% 0.25/0.60 ! [Xs: list_a,X3: a] :
% 0.25/0.60 ( ( Xs = nil_a )
% 0.25/0.60 => ( ( last_a @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = X3 ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_ConsL
% 0.25/0.60 thf(fact_225_last__ConsR,axiom,
% 0.25/0.60 ! [Xs: list_list_a,X3: list_a] :
% 0.25/0.60 ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ( last_list_a @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = ( last_list_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_ConsR
% 0.25/0.60 thf(fact_226_last__ConsR,axiom,
% 0.25/0.60 ! [Xs: list_a,X3: a] :
% 0.25/0.60 ( ( Xs != nil_a )
% 0.25/0.60 => ( ( last_a @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = ( last_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_ConsR
% 0.25/0.60 thf(fact_227_last__append,axiom,
% 0.25/0.60 ! [Ys2: list_list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( ( Ys2 = nil_list_a )
% 0.25/0.60 => ( ( last_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( last_list_a @ Xs ) ) )
% 0.25/0.60 & ( ( Ys2 != nil_list_a )
% 0.25/0.60 => ( ( last_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( last_list_a @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_append
% 0.25/0.60 thf(fact_228_last__append,axiom,
% 0.25/0.60 ! [Ys2: list_a,Xs: list_a] :
% 0.25/0.60 ( ( ( Ys2 = nil_a )
% 0.25/0.60 => ( ( last_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( last_a @ Xs ) ) )
% 0.25/0.60 & ( ( Ys2 != nil_a )
% 0.25/0.60 => ( ( last_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( last_a @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_append
% 0.25/0.60 thf(fact_229_longest__common__suffix,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ? [Ss: list_list_a,Xs5: list_list_a,Ys5: list_list_a] :
% 0.25/0.60 ( ( Xs
% 0.25/0.60 = ( append_list_a @ Xs5 @ Ss ) )
% 0.25/0.60 & ( Ys2
% 0.25/0.60 = ( append_list_a @ Ys5 @ Ss ) )
% 0.25/0.60 & ( ( Xs5 = nil_list_a )
% 0.25/0.60 | ( Ys5 = nil_list_a )
% 0.25/0.60 | ( ( last_list_a @ Xs5 )
% 0.25/0.60 != ( last_list_a @ Ys5 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % longest_common_suffix
% 0.25/0.60 thf(fact_230_longest__common__suffix,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ? [Ss: list_a,Xs5: list_a,Ys5: list_a] :
% 0.25/0.60 ( ( Xs
% 0.25/0.60 = ( append_a @ Xs5 @ Ss ) )
% 0.25/0.60 & ( Ys2
% 0.25/0.60 = ( append_a @ Ys5 @ Ss ) )
% 0.25/0.60 & ( ( Xs5 = nil_a )
% 0.25/0.60 | ( Ys5 = nil_a )
% 0.25/0.60 | ( ( last_a @ Xs5 )
% 0.25/0.60 != ( last_a @ Ys5 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % longest_common_suffix
% 0.25/0.60 thf(fact_231_butlast_Osimps_I2_J,axiom,
% 0.25/0.60 ! [Xs: list_list_a,X3: list_a] :
% 0.25/0.60 ( ( ( Xs = nil_list_a )
% 0.25/0.60 => ( ( butlast_list_a @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = nil_list_a ) )
% 0.25/0.60 & ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ( butlast_list_a @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = ( cons_list_a @ X3 @ ( butlast_list_a @ Xs ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % butlast.simps(2)
% 0.25/0.60 thf(fact_232_butlast_Osimps_I2_J,axiom,
% 0.25/0.60 ! [Xs: list_a,X3: a] :
% 0.25/0.60 ( ( ( Xs = nil_a )
% 0.25/0.60 => ( ( butlast_a @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = nil_a ) )
% 0.25/0.60 & ( ( Xs != nil_a )
% 0.25/0.60 => ( ( butlast_a @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = ( cons_a @ X3 @ ( butlast_a @ Xs ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % butlast.simps(2)
% 0.25/0.60 thf(fact_233_concat_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( concat_list_a @ nil_list_list_a )
% 0.25/0.60 = nil_list_a ) ).
% 0.25/0.60
% 0.25/0.60 % concat.simps(1)
% 0.25/0.60 thf(fact_234_concat_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( concat_a @ nil_list_a )
% 0.25/0.60 = nil_a ) ).
% 0.25/0.60
% 0.25/0.60 % concat.simps(1)
% 0.25/0.60 thf(fact_235_concat_Osimps_I2_J,axiom,
% 0.25/0.60 ! [X3: list_list_a,Xs: list_list_list_a] :
% 0.25/0.60 ( ( concat_list_a @ ( cons_list_list_a @ X3 @ Xs ) )
% 0.25/0.60 = ( append_list_a @ X3 @ ( concat_list_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % concat.simps(2)
% 0.25/0.60 thf(fact_236_concat_Osimps_I2_J,axiom,
% 0.25/0.60 ! [X3: list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( concat_a @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 = ( append_a @ X3 @ ( concat_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % concat.simps(2)
% 0.25/0.60 thf(fact_237_butlast__append,axiom,
% 0.25/0.60 ! [Ys2: list_list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( ( Ys2 = nil_list_a )
% 0.25/0.60 => ( ( butlast_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( butlast_list_a @ Xs ) ) )
% 0.25/0.60 & ( ( Ys2 != nil_list_a )
% 0.25/0.60 => ( ( butlast_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( append_list_a @ Xs @ ( butlast_list_a @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % butlast_append
% 0.25/0.60 thf(fact_238_butlast__append,axiom,
% 0.25/0.60 ! [Ys2: list_a,Xs: list_a] :
% 0.25/0.60 ( ( ( Ys2 = nil_a )
% 0.25/0.60 => ( ( butlast_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( butlast_a @ Xs ) ) )
% 0.25/0.60 & ( ( Ys2 != nil_a )
% 0.25/0.60 => ( ( butlast_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( append_a @ Xs @ ( butlast_a @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % butlast_append
% 0.25/0.60 thf(fact_239_maps__simps_I2_J,axiom,
% 0.25/0.60 ! [F: a > list_list_a] :
% 0.25/0.60 ( ( maps_a_list_a @ F @ nil_a )
% 0.25/0.60 = nil_list_a ) ).
% 0.25/0.60
% 0.25/0.60 % maps_simps(2)
% 0.25/0.60 thf(fact_240_maps__simps_I2_J,axiom,
% 0.25/0.60 ! [F: list_a > list_a] :
% 0.25/0.60 ( ( maps_list_a_a @ F @ nil_list_a )
% 0.25/0.60 = nil_a ) ).
% 0.25/0.60
% 0.25/0.60 % maps_simps(2)
% 0.25/0.60 thf(fact_241_maps__simps_I2_J,axiom,
% 0.25/0.60 ! [F: list_a > list_list_a] :
% 0.25/0.60 ( ( maps_list_a_list_a @ F @ nil_list_a )
% 0.25/0.60 = nil_list_a ) ).
% 0.25/0.60
% 0.25/0.60 % maps_simps(2)
% 0.25/0.60 thf(fact_242_maps__simps_I2_J,axiom,
% 0.25/0.60 ! [F: a > list_a] :
% 0.25/0.60 ( ( maps_a_a @ F @ nil_a )
% 0.25/0.60 = nil_a ) ).
% 0.25/0.60
% 0.25/0.60 % maps_simps(2)
% 0.25/0.60 thf(fact_243_concat__eq__appendD,axiom,
% 0.25/0.60 ! [Xss2: list_list_list_a,Ys2: list_list_a,Zs2: list_list_a] :
% 0.25/0.60 ( ( ( concat_list_a @ Xss2 )
% 0.25/0.60 = ( append_list_a @ Ys2 @ Zs2 ) )
% 0.25/0.60 => ( ( Xss2 != nil_list_list_a )
% 0.25/0.60 => ? [Xss12: list_list_list_a,Xs2: list_list_a,Xs5: list_list_a,Xss23: list_list_list_a] :
% 0.25/0.60 ( ( Xss2
% 0.25/0.60 = ( append_list_list_a @ Xss12 @ ( cons_list_list_a @ ( append_list_a @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.25/0.60 & ( Ys2
% 0.25/0.60 = ( append_list_a @ ( concat_list_a @ Xss12 ) @ Xs2 ) )
% 0.25/0.60 & ( Zs2
% 0.25/0.60 = ( append_list_a @ Xs5 @ ( concat_list_a @ Xss23 ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % concat_eq_appendD
% 0.25/0.60 thf(fact_244_concat__eq__appendD,axiom,
% 0.25/0.60 ! [Xss2: list_list_a,Ys2: list_a,Zs2: list_a] :
% 0.25/0.60 ( ( ( concat_a @ Xss2 )
% 0.25/0.60 = ( append_a @ Ys2 @ Zs2 ) )
% 0.25/0.60 => ( ( Xss2 != nil_list_a )
% 0.25/0.60 => ? [Xss12: list_list_a,Xs2: list_a,Xs5: list_a,Xss23: list_list_a] :
% 0.25/0.60 ( ( Xss2
% 0.25/0.60 = ( append_list_a @ Xss12 @ ( cons_list_a @ ( append_a @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.25/0.60 & ( Ys2
% 0.25/0.60 = ( append_a @ ( concat_a @ Xss12 ) @ Xs2 ) )
% 0.25/0.60 & ( Zs2
% 0.25/0.60 = ( append_a @ Xs5 @ ( concat_a @ Xss23 ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % concat_eq_appendD
% 0.25/0.60 thf(fact_245_empty__Shift,axiom,
% 0.25/0.60 ! [Kl2: set_list_list_a,K: list_a] :
% 0.25/0.60 ( ( member_list_list_a @ nil_list_a @ Kl2 )
% 0.25/0.60 => ( ( member_list_a2 @ K @ ( bNF_Gr1046450207list_a @ Kl2 @ nil_list_a ) )
% 0.25/0.60 => ( member_list_list_a @ nil_list_a @ ( bNF_Gr1972240547list_a @ Kl2 @ K ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % empty_Shift
% 0.25/0.60 thf(fact_246_empty__Shift,axiom,
% 0.25/0.60 ! [Kl2: set_list_a,K: a] :
% 0.25/0.60 ( ( member_list_a2 @ nil_a @ Kl2 )
% 0.25/0.60 => ( ( member_a2 @ K @ ( bNF_Greatest_Succ_a @ Kl2 @ nil_a ) )
% 0.25/0.60 => ( member_list_a2 @ nil_a @ ( bNF_Greatest_Shift_a @ Kl2 @ K ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % empty_Shift
% 0.25/0.60 thf(fact_247_Succ__Shift,axiom,
% 0.25/0.60 ! [Kl2: set_list_list_a,K: list_a,Kl: list_list_a] :
% 0.25/0.60 ( ( bNF_Gr1046450207list_a @ ( bNF_Gr1972240547list_a @ Kl2 @ K ) @ Kl )
% 0.25/0.60 = ( bNF_Gr1046450207list_a @ Kl2 @ ( cons_list_a @ K @ Kl ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Succ_Shift
% 0.25/0.60 thf(fact_248_Succ__Shift,axiom,
% 0.25/0.60 ! [Kl2: set_list_a,K: a,Kl: list_a] :
% 0.25/0.60 ( ( bNF_Greatest_Succ_a @ ( bNF_Greatest_Shift_a @ Kl2 @ K ) @ Kl )
% 0.25/0.60 = ( bNF_Greatest_Succ_a @ Kl2 @ ( cons_a @ K @ Kl ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Succ_Shift
% 0.25/0.60 thf(fact_249_concat__conv__foldr,axiom,
% 0.25/0.60 ( concat_list_a
% 0.25/0.60 = ( ^ [Xss3: list_list_list_a] : ( foldr_769741863list_a @ append_list_a @ Xss3 @ nil_list_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % concat_conv_foldr
% 0.25/0.60 thf(fact_250_concat__conv__foldr,axiom,
% 0.25/0.60 ( concat_a
% 0.25/0.60 = ( ^ [Xss3: list_list_a] : ( foldr_list_a_list_a @ append_a @ Xss3 @ nil_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % concat_conv_foldr
% 0.25/0.60 thf(fact_251_foldr__append,axiom,
% 0.25/0.60 ! [F: list_a > list_a > list_a,Xs: list_list_a,Ys2: list_list_a,A3: list_a] :
% 0.25/0.60 ( ( foldr_list_a_list_a @ F @ ( append_list_a @ Xs @ Ys2 ) @ A3 )
% 0.25/0.60 = ( foldr_list_a_list_a @ F @ Xs @ ( foldr_list_a_list_a @ F @ Ys2 @ A3 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % foldr_append
% 0.25/0.60 thf(fact_252_ShiftD,axiom,
% 0.25/0.60 ! [Kl: list_list_a,Kl2: set_list_list_a,K: list_a] :
% 0.25/0.60 ( ( member_list_list_a @ Kl @ ( bNF_Gr1972240547list_a @ Kl2 @ K ) )
% 0.25/0.60 => ( member_list_list_a @ ( cons_list_a @ K @ Kl ) @ Kl2 ) ) ).
% 0.25/0.60
% 0.25/0.60 % ShiftD
% 0.25/0.60 thf(fact_253_ShiftD,axiom,
% 0.25/0.60 ! [Kl: list_a,Kl2: set_list_a,K: a] :
% 0.25/0.60 ( ( member_list_a2 @ Kl @ ( bNF_Greatest_Shift_a @ Kl2 @ K ) )
% 0.25/0.60 => ( member_list_a2 @ ( cons_a @ K @ Kl ) @ Kl2 ) ) ).
% 0.25/0.60
% 0.25/0.60 % ShiftD
% 0.25/0.60 thf(fact_254_list__strict__asc__def,axiom,
% 0.25/0.60 ( list_strict_asc_nat
% 0.25/0.60 = ( list_ord_nat @ ord_less_nat ) ) ).
% 0.25/0.60
% 0.25/0.60 % list_strict_asc_def
% 0.25/0.60 thf(fact_255_lexordp__iff,axiom,
% 0.25/0.60 ( ord_lexordp_nat
% 0.25/0.60 = ( ^ [Xs3: list_nat,Ys: list_nat] :
% 0.25/0.60 ( ? [X4: nat,Vs: list_nat] :
% 0.25/0.60 ( Ys
% 0.25/0.60 = ( append_nat @ Xs3 @ ( cons_nat @ X4 @ Vs ) ) )
% 0.25/0.60 | ? [Us: list_nat,A5: nat,B2: nat,Vs: list_nat,Ws: list_nat] :
% 0.25/0.60 ( ( ord_less_nat @ A5 @ B2 )
% 0.25/0.60 & ( Xs3
% 0.25/0.60 = ( append_nat @ Us @ ( cons_nat @ A5 @ Vs ) ) )
% 0.25/0.60 & ( Ys
% 0.25/0.60 = ( append_nat @ Us @ ( cons_nat @ B2 @ Ws ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_iff
% 0.25/0.60 thf(fact_256_lexordp__append__left__rightI,axiom,
% 0.25/0.60 ! [X3: nat,Y: nat,Us2: list_nat,Xs: list_nat,Ys2: list_nat] :
% 0.25/0.60 ( ( ord_less_nat @ X3 @ Y )
% 0.25/0.60 => ( ord_lexordp_nat @ ( append_nat @ Us2 @ ( cons_nat @ X3 @ Xs ) ) @ ( append_nat @ Us2 @ ( cons_nat @ Y @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_append_left_rightI
% 0.25/0.60 thf(fact_257_lexordp__simps_I3_J,axiom,
% 0.25/0.60 ! [X3: nat,Xs: list_nat,Y: nat,Ys2: list_nat] :
% 0.25/0.60 ( ( ord_lexordp_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) )
% 0.25/0.60 = ( ( ord_less_nat @ X3 @ Y )
% 0.25/0.60 | ( ~ ( ord_less_nat @ Y @ X3 )
% 0.25/0.60 & ( ord_lexordp_nat @ Xs @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_simps(3)
% 0.25/0.60 thf(fact_258_hd__append2,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ( hd_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( hd_list_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % hd_append2
% 0.25/0.60 thf(fact_259_hd__append2,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( Xs != nil_a )
% 0.25/0.60 => ( ( hd_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( hd_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % hd_append2
% 0.25/0.60 thf(fact_260_lexordp__irreflexive,axiom,
% 0.25/0.60 ! [Xs: list_nat] :
% 0.25/0.60 ( ! [X: nat] :
% 0.25/0.60 ~ ( ord_less_nat @ X @ X )
% 0.25/0.60 => ~ ( ord_lexordp_nat @ Xs @ Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_irreflexive
% 0.25/0.60 thf(fact_261_list_Osel_I1_J,axiom,
% 0.25/0.60 ! [X21: list_a,X22: list_list_a] :
% 0.25/0.60 ( ( hd_list_a @ ( cons_list_a @ X21 @ X22 ) )
% 0.25/0.60 = X21 ) ).
% 0.25/0.60
% 0.25/0.60 % list.sel(1)
% 0.25/0.60 thf(fact_262_list_Osel_I1_J,axiom,
% 0.25/0.60 ! [X21: a,X22: list_a] :
% 0.25/0.60 ( ( hd_a @ ( cons_a @ X21 @ X22 ) )
% 0.25/0.60 = X21 ) ).
% 0.25/0.60
% 0.25/0.60 % list.sel(1)
% 0.25/0.60 thf(fact_263_hd__concat,axiom,
% 0.25/0.60 ! [Xs: list_list_list_a] :
% 0.25/0.60 ( ( Xs != nil_list_list_a )
% 0.25/0.60 => ( ( ( hd_list_list_a @ Xs )
% 0.25/0.60 != nil_list_a )
% 0.25/0.60 => ( ( hd_list_a @ ( concat_list_a @ Xs ) )
% 0.25/0.60 = ( hd_list_a @ ( hd_list_list_a @ Xs ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % hd_concat
% 0.25/0.60 thf(fact_264_hd__concat,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ( ( hd_list_a @ Xs )
% 0.25/0.60 != nil_a )
% 0.25/0.60 => ( ( hd_a @ ( concat_a @ Xs ) )
% 0.25/0.60 = ( hd_a @ ( hd_list_a @ Xs ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % hd_concat
% 0.25/0.60 thf(fact_265_hd__append,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( ( Xs = nil_list_a )
% 0.25/0.60 => ( ( hd_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( hd_list_a @ Ys2 ) ) )
% 0.25/0.60 & ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ( hd_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( hd_list_a @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % hd_append
% 0.25/0.60 thf(fact_266_hd__append,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( ( Xs = nil_a )
% 0.25/0.60 => ( ( hd_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( hd_a @ Ys2 ) ) )
% 0.25/0.60 & ( ( Xs != nil_a )
% 0.25/0.60 => ( ( hd_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( hd_a @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % hd_append
% 0.25/0.60 thf(fact_267_longest__common__prefix,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ? [Ps: list_list_a,Xs5: list_list_a,Ys5: list_list_a] :
% 0.25/0.60 ( ( Xs
% 0.25/0.60 = ( append_list_a @ Ps @ Xs5 ) )
% 0.25/0.60 & ( Ys2
% 0.25/0.60 = ( append_list_a @ Ps @ Ys5 ) )
% 0.25/0.60 & ( ( Xs5 = nil_list_a )
% 0.25/0.60 | ( Ys5 = nil_list_a )
% 0.25/0.60 | ( ( hd_list_a @ Xs5 )
% 0.25/0.60 != ( hd_list_a @ Ys5 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % longest_common_prefix
% 0.25/0.60 thf(fact_268_longest__common__prefix,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ? [Ps: list_a,Xs5: list_a,Ys5: list_a] :
% 0.25/0.60 ( ( Xs
% 0.25/0.60 = ( append_a @ Ps @ Xs5 ) )
% 0.25/0.60 & ( Ys2
% 0.25/0.60 = ( append_a @ Ps @ Ys5 ) )
% 0.25/0.60 & ( ( Xs5 = nil_a )
% 0.25/0.60 | ( Ys5 = nil_a )
% 0.25/0.60 | ( ( hd_a @ Xs5 )
% 0.25/0.60 != ( hd_a @ Ys5 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % longest_common_prefix
% 0.25/0.60 thf(fact_269_lexordp_OCons,axiom,
% 0.25/0.60 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 0.25/0.60 ( ( ord_less_nat @ X3 @ Y )
% 0.25/0.60 => ( ord_lexordp_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp.Cons
% 0.25/0.60 thf(fact_270_lexordp_OCons__eq,axiom,
% 0.25/0.60 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 0.25/0.60 ( ~ ( ord_less_nat @ X3 @ Y )
% 0.25/0.60 => ( ~ ( ord_less_nat @ Y @ X3 )
% 0.25/0.60 => ( ( ord_lexordp_nat @ Xs @ Ys2 )
% 0.25/0.60 => ( ord_lexordp_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp.Cons_eq
% 0.25/0.60 thf(fact_271_lexordp__append__leftD,axiom,
% 0.25/0.60 ! [Xs: list_nat,Us2: list_nat,Vs2: list_nat] :
% 0.25/0.60 ( ( ord_lexordp_nat @ ( append_nat @ Xs @ Us2 ) @ ( append_nat @ Xs @ Vs2 ) )
% 0.25/0.60 => ( ! [A: nat] :
% 0.25/0.60 ~ ( ord_less_nat @ A @ A )
% 0.25/0.60 => ( ord_lexordp_nat @ Us2 @ Vs2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_append_leftD
% 0.25/0.60 thf(fact_272_lexordp_Ocases,axiom,
% 0.25/0.60 ! [A1: list_nat,A2: list_nat] :
% 0.25/0.60 ( ( ord_lexordp_nat @ A1 @ A2 )
% 0.25/0.60 => ( ( ( A1 = nil_nat )
% 0.25/0.60 => ! [Y3: nat,Ys3: list_nat] :
% 0.25/0.60 ( A2
% 0.25/0.60 != ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.25/0.60 => ( ! [X: nat] :
% 0.25/0.60 ( ? [Xs2: list_nat] :
% 0.25/0.60 ( A1
% 0.25/0.60 = ( cons_nat @ X @ Xs2 ) )
% 0.25/0.60 => ! [Y3: nat] :
% 0.25/0.60 ( ? [Ys3: list_nat] :
% 0.25/0.60 ( A2
% 0.25/0.60 = ( cons_nat @ Y3 @ Ys3 ) )
% 0.25/0.60 => ~ ( ord_less_nat @ X @ Y3 ) ) )
% 0.25/0.60 => ~ ! [X: nat,Y3: nat,Xs2: list_nat] :
% 0.25/0.60 ( ( A1
% 0.25/0.60 = ( cons_nat @ X @ Xs2 ) )
% 0.25/0.60 => ! [Ys3: list_nat] :
% 0.25/0.60 ( ( A2
% 0.25/0.60 = ( cons_nat @ Y3 @ Ys3 ) )
% 0.25/0.60 => ( ~ ( ord_less_nat @ X @ Y3 )
% 0.25/0.60 => ( ~ ( ord_less_nat @ Y3 @ X )
% 0.25/0.60 => ~ ( ord_lexordp_nat @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp.cases
% 0.25/0.60 thf(fact_273_lexordp_Osimps,axiom,
% 0.25/0.60 ( ord_lexordp_nat
% 0.25/0.60 = ( ^ [A12: list_nat,A22: list_nat] :
% 0.25/0.60 ( ? [Y2: nat,Ys: list_nat] :
% 0.25/0.60 ( ( A12 = nil_nat )
% 0.25/0.60 & ( A22
% 0.25/0.60 = ( cons_nat @ Y2 @ Ys ) ) )
% 0.25/0.60 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 0.25/0.60 ( ( A12
% 0.25/0.60 = ( cons_nat @ X4 @ Xs3 ) )
% 0.25/0.60 & ( A22
% 0.25/0.60 = ( cons_nat @ Y2 @ Ys ) )
% 0.25/0.60 & ( ord_less_nat @ X4 @ Y2 ) )
% 0.25/0.60 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 0.25/0.60 ( ( A12
% 0.25/0.60 = ( cons_nat @ X4 @ Xs3 ) )
% 0.25/0.60 & ( A22
% 0.25/0.60 = ( cons_nat @ Y2 @ Ys ) )
% 0.25/0.60 & ~ ( ord_less_nat @ X4 @ Y2 )
% 0.25/0.60 & ~ ( ord_less_nat @ Y2 @ X4 )
% 0.25/0.60 & ( ord_lexordp_nat @ Xs3 @ Ys ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp.simps
% 0.25/0.60 thf(fact_274_lexordp_Oinducts,axiom,
% 0.25/0.60 ! [X12: list_nat,X23: list_nat,P: list_nat > list_nat > $o] :
% 0.25/0.60 ( ( ord_lexordp_nat @ X12 @ X23 )
% 0.25/0.60 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y3 @ Ys3 ) )
% 0.25/0.60 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.25/0.60 ( ( ord_less_nat @ X @ Y3 )
% 0.25/0.60 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.25/0.60 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.25/0.60 ( ~ ( ord_less_nat @ X @ Y3 )
% 0.25/0.60 => ( ~ ( ord_less_nat @ Y3 @ X )
% 0.25/0.60 => ( ( ord_lexordp_nat @ Xs2 @ Ys3 )
% 0.25/0.60 => ( ( P @ Xs2 @ Ys3 )
% 0.25/0.60 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) ) ) )
% 0.25/0.60 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp.inducts
% 0.25/0.60 thf(fact_275_lexordp__cases,axiom,
% 0.25/0.60 ! [Xs: list_nat,Ys2: list_nat] :
% 0.25/0.60 ( ( ord_lexordp_nat @ Xs @ Ys2 )
% 0.25/0.60 => ( ( ( Xs = nil_nat )
% 0.25/0.60 => ! [Y3: nat,Ys5: list_nat] :
% 0.25/0.60 ( Ys2
% 0.25/0.60 != ( cons_nat @ Y3 @ Ys5 ) ) )
% 0.25/0.60 => ( ! [X: nat] :
% 0.25/0.60 ( ? [Xs5: list_nat] :
% 0.25/0.60 ( Xs
% 0.25/0.60 = ( cons_nat @ X @ Xs5 ) )
% 0.25/0.60 => ! [Y3: nat] :
% 0.25/0.60 ( ? [Ys5: list_nat] :
% 0.25/0.60 ( Ys2
% 0.25/0.60 = ( cons_nat @ Y3 @ Ys5 ) )
% 0.25/0.60 => ~ ( ord_less_nat @ X @ Y3 ) ) )
% 0.25/0.60 => ~ ! [X: nat,Xs5: list_nat] :
% 0.25/0.60 ( ( Xs
% 0.25/0.60 = ( cons_nat @ X @ Xs5 ) )
% 0.25/0.60 => ! [Ys5: list_nat] :
% 0.25/0.60 ( ( Ys2
% 0.25/0.60 = ( cons_nat @ X @ Ys5 ) )
% 0.25/0.60 => ~ ( ord_lexordp_nat @ Xs5 @ Ys5 ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_cases
% 0.25/0.60 thf(fact_276_lexordp__induct,axiom,
% 0.25/0.60 ! [Xs: list_nat,Ys2: list_nat,P: list_nat > list_nat > $o] :
% 0.25/0.60 ( ( ord_lexordp_nat @ Xs @ Ys2 )
% 0.25/0.60 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y3 @ Ys3 ) )
% 0.25/0.60 => ( ! [X: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 0.25/0.60 ( ( ord_less_nat @ X @ Y3 )
% 0.25/0.60 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.25/0.60 => ( ! [X: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.25/0.60 ( ( ord_lexordp_nat @ Xs2 @ Ys3 )
% 0.25/0.60 => ( ( P @ Xs2 @ Ys3 )
% 0.25/0.60 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ X @ Ys3 ) ) ) )
% 0.25/0.60 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % lexordp_induct
% 0.25/0.60 thf(fact_277_distinct__adj__append__iff,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( distinct_adj_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( ( distinct_adj_list_a @ Xs )
% 0.25/0.60 & ( distinct_adj_list_a @ Ys2 )
% 0.25/0.60 & ( ( Xs = nil_list_a )
% 0.25/0.60 | ( Ys2 = nil_list_a )
% 0.25/0.60 | ( ( last_list_a @ Xs )
% 0.25/0.60 != ( hd_list_a @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_append_iff
% 0.25/0.60 thf(fact_278_distinct__adj__append__iff,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( distinct_adj_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( ( distinct_adj_a @ Xs )
% 0.25/0.60 & ( distinct_adj_a @ Ys2 )
% 0.25/0.60 & ( ( Xs = nil_a )
% 0.25/0.60 | ( Ys2 = nil_a )
% 0.25/0.60 | ( ( last_a @ Xs )
% 0.25/0.60 != ( hd_a @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_append_iff
% 0.25/0.60 thf(fact_279_rotate1__hd__tl,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ( rotate1_list_a @ Xs )
% 0.25/0.60 = ( append_list_a @ ( tl_list_a @ Xs ) @ ( cons_list_a @ ( hd_list_a @ Xs ) @ nil_list_a ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % rotate1_hd_tl
% 0.25/0.60 thf(fact_280_rotate1__hd__tl,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( Xs != nil_a )
% 0.25/0.60 => ( ( rotate1_a @ Xs )
% 0.25/0.60 = ( append_a @ ( tl_a @ Xs ) @ ( cons_a @ ( hd_a @ Xs ) @ nil_a ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % rotate1_hd_tl
% 0.25/0.60 thf(fact_281_successively__append__iff,axiom,
% 0.25/0.60 ! [P: list_a > list_a > $o,Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( successively_list_a @ P @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( ( successively_list_a @ P @ Xs )
% 0.25/0.60 & ( successively_list_a @ P @ Ys2 )
% 0.25/0.60 & ( ( Xs = nil_list_a )
% 0.25/0.60 | ( Ys2 = nil_list_a )
% 0.25/0.60 | ( P @ ( last_list_a @ Xs ) @ ( hd_list_a @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively_append_iff
% 0.25/0.60 thf(fact_282_successively__append__iff,axiom,
% 0.25/0.60 ! [P: a > a > $o,Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( successively_a @ P @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( ( successively_a @ P @ Xs )
% 0.25/0.60 & ( successively_a @ P @ Ys2 )
% 0.25/0.60 & ( ( Xs = nil_a )
% 0.25/0.60 | ( Ys2 = nil_a )
% 0.25/0.60 | ( P @ ( last_a @ Xs ) @ ( hd_a @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively_append_iff
% 0.25/0.60 thf(fact_283_distinct__adj__Cons__Cons,axiom,
% 0.25/0.60 ! [X3: list_a,Y: list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( distinct_adj_list_a @ ( cons_list_a @ X3 @ ( cons_list_a @ Y @ Xs ) ) )
% 0.25/0.60 = ( ( X3 != Y )
% 0.25/0.60 & ( distinct_adj_list_a @ ( cons_list_a @ Y @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_Cons_Cons
% 0.25/0.60 thf(fact_284_distinct__adj__Cons__Cons,axiom,
% 0.25/0.60 ! [X3: a,Y: a,Xs: list_a] :
% 0.25/0.60 ( ( distinct_adj_a @ ( cons_a @ X3 @ ( cons_a @ Y @ Xs ) ) )
% 0.25/0.60 = ( ( X3 != Y )
% 0.25/0.60 & ( distinct_adj_a @ ( cons_a @ Y @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_Cons_Cons
% 0.25/0.60 thf(fact_285_tl__append2,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ( tl_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( append_list_a @ ( tl_list_a @ Xs ) @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % tl_append2
% 0.25/0.60 thf(fact_286_tl__append2,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( Xs != nil_a )
% 0.25/0.60 => ( ( tl_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( append_a @ ( tl_a @ Xs ) @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % tl_append2
% 0.25/0.60 thf(fact_287_hd__Cons__tl,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( Xs != nil_list_a )
% 0.25/0.60 => ( ( cons_list_a @ ( hd_list_a @ Xs ) @ ( tl_list_a @ Xs ) )
% 0.25/0.60 = Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % hd_Cons_tl
% 0.25/0.60 thf(fact_288_hd__Cons__tl,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( Xs != nil_a )
% 0.25/0.60 => ( ( cons_a @ ( hd_a @ Xs ) @ ( tl_a @ Xs ) )
% 0.25/0.60 = Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % hd_Cons_tl
% 0.25/0.60 thf(fact_289_list_Ocollapse,axiom,
% 0.25/0.60 ! [List: list_list_a] :
% 0.25/0.60 ( ( List != nil_list_a )
% 0.25/0.60 => ( ( cons_list_a @ ( hd_list_a @ List ) @ ( tl_list_a @ List ) )
% 0.25/0.60 = List ) ) ).
% 0.25/0.60
% 0.25/0.60 % list.collapse
% 0.25/0.60 thf(fact_290_list_Ocollapse,axiom,
% 0.25/0.60 ! [List: list_a] :
% 0.25/0.60 ( ( List != nil_a )
% 0.25/0.60 => ( ( cons_a @ ( hd_a @ List ) @ ( tl_a @ List ) )
% 0.25/0.60 = List ) ) ).
% 0.25/0.60
% 0.25/0.60 % list.collapse
% 0.25/0.60 thf(fact_291_list_Osel_I3_J,axiom,
% 0.25/0.60 ! [X21: list_a,X22: list_list_a] :
% 0.25/0.60 ( ( tl_list_a @ ( cons_list_a @ X21 @ X22 ) )
% 0.25/0.60 = X22 ) ).
% 0.25/0.60
% 0.25/0.60 % list.sel(3)
% 0.25/0.60 thf(fact_292_list_Osel_I3_J,axiom,
% 0.25/0.60 ! [X21: a,X22: list_a] :
% 0.25/0.60 ( ( tl_a @ ( cons_a @ X21 @ X22 ) )
% 0.25/0.60 = X22 ) ).
% 0.25/0.60
% 0.25/0.60 % list.sel(3)
% 0.25/0.60 thf(fact_293_list_Osel_I2_J,axiom,
% 0.25/0.60 ( ( tl_list_a @ nil_list_a )
% 0.25/0.60 = nil_list_a ) ).
% 0.25/0.60
% 0.25/0.60 % list.sel(2)
% 0.25/0.60 thf(fact_294_list_Osel_I2_J,axiom,
% 0.25/0.60 ( ( tl_a @ nil_a )
% 0.25/0.60 = nil_a ) ).
% 0.25/0.60
% 0.25/0.60 % list.sel(2)
% 0.25/0.60 thf(fact_295_successively_Oelims_I3_J,axiom,
% 0.25/0.60 ! [X3: list_a > list_a > $o,Xa: list_list_a] :
% 0.25/0.60 ( ~ ( successively_list_a @ X3 @ Xa )
% 0.25/0.60 => ~ ! [X: list_a,Y3: list_a,Xs2: list_list_a] :
% 0.25/0.60 ( ( Xa
% 0.25/0.60 = ( cons_list_a @ X @ ( cons_list_a @ Y3 @ Xs2 ) ) )
% 0.25/0.60 => ( ( X3 @ X @ Y3 )
% 0.25/0.60 & ( successively_list_a @ X3 @ ( cons_list_a @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively.elims(3)
% 0.25/0.60 thf(fact_296_successively_Oelims_I3_J,axiom,
% 0.25/0.60 ! [X3: a > a > $o,Xa: list_a] :
% 0.25/0.60 ( ~ ( successively_a @ X3 @ Xa )
% 0.25/0.60 => ~ ! [X: a,Y3: a,Xs2: list_a] :
% 0.25/0.60 ( ( Xa
% 0.25/0.60 = ( cons_a @ X @ ( cons_a @ Y3 @ Xs2 ) ) )
% 0.25/0.60 => ( ( X3 @ X @ Y3 )
% 0.25/0.60 & ( successively_a @ X3 @ ( cons_a @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively.elims(3)
% 0.25/0.60 thf(fact_297_successively_Osimps_I3_J,axiom,
% 0.25/0.60 ! [P: list_a > list_a > $o,X3: list_a,Y: list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( successively_list_a @ P @ ( cons_list_a @ X3 @ ( cons_list_a @ Y @ Xs ) ) )
% 0.25/0.60 = ( ( P @ X3 @ Y )
% 0.25/0.60 & ( successively_list_a @ P @ ( cons_list_a @ Y @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively.simps(3)
% 0.25/0.60 thf(fact_298_successively_Osimps_I3_J,axiom,
% 0.25/0.60 ! [P: a > a > $o,X3: a,Y: a,Xs: list_a] :
% 0.25/0.60 ( ( successively_a @ P @ ( cons_a @ X3 @ ( cons_a @ Y @ Xs ) ) )
% 0.25/0.60 = ( ( P @ X3 @ Y )
% 0.25/0.60 & ( successively_a @ P @ ( cons_a @ Y @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively.simps(3)
% 0.25/0.60 thf(fact_299_successively_Osimps_I1_J,axiom,
% 0.25/0.60 ! [P: list_a > list_a > $o] : ( successively_list_a @ P @ nil_list_a ) ).
% 0.25/0.60
% 0.25/0.60 % successively.simps(1)
% 0.25/0.60 thf(fact_300_successively_Osimps_I1_J,axiom,
% 0.25/0.60 ! [P: a > a > $o] : ( successively_a @ P @ nil_a ) ).
% 0.25/0.60
% 0.25/0.60 % successively.simps(1)
% 0.25/0.60 thf(fact_301_distinct__adj__appendD1,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( distinct_adj_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 => ( distinct_adj_list_a @ Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_appendD1
% 0.25/0.60 thf(fact_302_distinct__adj__appendD1,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( distinct_adj_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 => ( distinct_adj_a @ Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_appendD1
% 0.25/0.60 thf(fact_303_distinct__adj__appendD2,axiom,
% 0.25/0.60 ! [Xs: list_list_a,Ys2: list_list_a] :
% 0.25/0.60 ( ( distinct_adj_list_a @ ( append_list_a @ Xs @ Ys2 ) )
% 0.25/0.60 => ( distinct_adj_list_a @ Ys2 ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_appendD2
% 0.25/0.60 thf(fact_304_distinct__adj__appendD2,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( distinct_adj_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 => ( distinct_adj_a @ Ys2 ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_appendD2
% 0.25/0.60 thf(fact_305_distinct__adj__Nil,axiom,
% 0.25/0.60 distinct_adj_list_a @ nil_list_a ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_Nil
% 0.25/0.60 thf(fact_306_distinct__adj__Nil,axiom,
% 0.25/0.60 distinct_adj_a @ nil_a ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_Nil
% 0.25/0.60 thf(fact_307_distinct__adj__ConsD,axiom,
% 0.25/0.60 ! [X3: list_a,Xs: list_list_a] :
% 0.25/0.60 ( ( distinct_adj_list_a @ ( cons_list_a @ X3 @ Xs ) )
% 0.25/0.60 => ( distinct_adj_list_a @ Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_ConsD
% 0.25/0.60 thf(fact_308_distinct__adj__ConsD,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a] :
% 0.25/0.60 ( ( distinct_adj_a @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 => ( distinct_adj_a @ Xs ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_ConsD
% 0.25/0.60 thf(fact_309_butlast__tl,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( butlast_a @ ( tl_a @ Xs ) )
% 0.25/0.60 = ( tl_a @ ( butlast_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % butlast_tl
% 0.25/0.60 thf(fact_310_tl__Nil,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( ( tl_list_a @ Xs )
% 0.25/0.60 = nil_list_a )
% 0.25/0.60 = ( ( Xs = nil_list_a )
% 0.25/0.60 | ? [X4: list_a] :
% 0.25/0.60 ( Xs
% 0.25/0.60 = ( cons_list_a @ X4 @ nil_list_a ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % tl_Nil
% 0.25/0.60 thf(fact_311_tl__Nil,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( ( tl_a @ Xs )
% 0.25/0.60 = nil_a )
% 0.25/0.60 = ( ( Xs = nil_a )
% 0.25/0.60 | ? [X4: a] :
% 0.25/0.60 ( Xs
% 0.25/0.60 = ( cons_a @ X4 @ nil_a ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % tl_Nil
% 0.25/0.60 thf(fact_312_Nil__tl,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( nil_list_a
% 0.25/0.60 = ( tl_list_a @ Xs ) )
% 0.25/0.60 = ( ( Xs = nil_list_a )
% 0.25/0.60 | ? [X4: list_a] :
% 0.25/0.60 ( Xs
% 0.25/0.60 = ( cons_list_a @ X4 @ nil_list_a ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Nil_tl
% 0.25/0.60 thf(fact_313_Nil__tl,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( nil_a
% 0.25/0.60 = ( tl_a @ Xs ) )
% 0.25/0.60 = ( ( Xs = nil_a )
% 0.25/0.60 | ? [X4: a] :
% 0.25/0.60 ( Xs
% 0.25/0.60 = ( cons_a @ X4 @ nil_a ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Nil_tl
% 0.25/0.60 thf(fact_314_list_Oexpand,axiom,
% 0.25/0.60 ! [List: list_list_a,List2: list_list_a] :
% 0.25/0.60 ( ( ( List = nil_list_a )
% 0.25/0.60 = ( List2 = nil_list_a ) )
% 0.25/0.60 => ( ( ( List != nil_list_a )
% 0.25/0.60 => ( ( List2 != nil_list_a )
% 0.25/0.60 => ( ( ( hd_list_a @ List )
% 0.25/0.60 = ( hd_list_a @ List2 ) )
% 0.25/0.60 & ( ( tl_list_a @ List )
% 0.25/0.60 = ( tl_list_a @ List2 ) ) ) ) )
% 0.25/0.60 => ( List = List2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % list.expand
% 0.25/0.60 thf(fact_315_list_Oexpand,axiom,
% 0.25/0.60 ! [List: list_a,List2: list_a] :
% 0.25/0.60 ( ( ( List = nil_a )
% 0.25/0.60 = ( List2 = nil_a ) )
% 0.25/0.60 => ( ( ( List != nil_a )
% 0.25/0.60 => ( ( List2 != nil_a )
% 0.25/0.60 => ( ( ( hd_a @ List )
% 0.25/0.60 = ( hd_a @ List2 ) )
% 0.25/0.60 & ( ( tl_a @ List )
% 0.25/0.60 = ( tl_a @ List2 ) ) ) ) )
% 0.25/0.60 => ( List = List2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % list.expand
% 0.25/0.60 thf(fact_316_last__tl,axiom,
% 0.25/0.60 ! [Xs: list_list_a] :
% 0.25/0.60 ( ( ( Xs = nil_list_a )
% 0.25/0.60 | ( ( tl_list_a @ Xs )
% 0.25/0.60 != nil_list_a ) )
% 0.25/0.60 => ( ( last_list_a @ ( tl_list_a @ Xs ) )
% 0.25/0.60 = ( last_list_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_tl
% 0.25/0.60 thf(fact_317_last__tl,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( ( Xs = nil_a )
% 0.25/0.60 | ( ( tl_a @ Xs )
% 0.25/0.60 != nil_a ) )
% 0.25/0.60 => ( ( last_a @ ( tl_a @ Xs ) )
% 0.25/0.60 = ( last_a @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % last_tl
% 0.25/0.60 thf(fact_318_successively_Osimps_I2_J,axiom,
% 0.25/0.60 ! [P: list_a > list_a > $o,X3: list_a] : ( successively_list_a @ P @ ( cons_list_a @ X3 @ nil_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively.simps(2)
% 0.25/0.60 thf(fact_319_successively_Osimps_I2_J,axiom,
% 0.25/0.60 ! [P: a > a > $o,X3: a] : ( successively_a @ P @ ( cons_a @ X3 @ nil_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively.simps(2)
% 0.25/0.60 thf(fact_320_successively_Oelims_I1_J,axiom,
% 0.25/0.60 ! [X3: list_a > list_a > $o,Xa: list_list_a,Y: $o] :
% 0.25/0.60 ( ( ( successively_list_a @ X3 @ Xa )
% 0.25/0.60 = Y )
% 0.25/0.60 => ( ( ( Xa = nil_list_a )
% 0.25/0.60 => ~ Y )
% 0.25/0.60 => ( ( ? [X: list_a] :
% 0.25/0.60 ( Xa
% 0.25/0.60 = ( cons_list_a @ X @ nil_list_a ) )
% 0.25/0.60 => ~ Y )
% 0.25/0.60 => ~ ! [X: list_a,Y3: list_a,Xs2: list_list_a] :
% 0.25/0.60 ( ( Xa
% 0.25/0.60 = ( cons_list_a @ X @ ( cons_list_a @ Y3 @ Xs2 ) ) )
% 0.25/0.60 => ( Y
% 0.25/0.60 = ( ~ ( ( X3 @ X @ Y3 )
% 0.25/0.60 & ( successively_list_a @ X3 @ ( cons_list_a @ Y3 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively.elims(1)
% 0.25/0.60 thf(fact_321_successively_Oelims_I1_J,axiom,
% 0.25/0.60 ! [X3: a > a > $o,Xa: list_a,Y: $o] :
% 0.25/0.60 ( ( ( successively_a @ X3 @ Xa )
% 0.25/0.60 = Y )
% 0.25/0.60 => ( ( ( Xa = nil_a )
% 0.25/0.60 => ~ Y )
% 0.25/0.60 => ( ( ? [X: a] :
% 0.25/0.60 ( Xa
% 0.25/0.60 = ( cons_a @ X @ nil_a ) )
% 0.25/0.60 => ~ Y )
% 0.25/0.60 => ~ ! [X: a,Y3: a,Xs2: list_a] :
% 0.25/0.60 ( ( Xa
% 0.25/0.60 = ( cons_a @ X @ ( cons_a @ Y3 @ Xs2 ) ) )
% 0.25/0.60 => ( Y
% 0.25/0.60 = ( ~ ( ( X3 @ X @ Y3 )
% 0.25/0.60 & ( successively_a @ X3 @ ( cons_a @ Y3 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively.elims(1)
% 0.25/0.60 thf(fact_322_successively_Oelims_I2_J,axiom,
% 0.25/0.60 ! [X3: list_a > list_a > $o,Xa: list_list_a] :
% 0.25/0.60 ( ( successively_list_a @ X3 @ Xa )
% 0.25/0.60 => ( ( Xa != nil_list_a )
% 0.25/0.60 => ( ! [X: list_a] :
% 0.25/0.60 ( Xa
% 0.25/0.60 != ( cons_list_a @ X @ nil_list_a ) )
% 0.25/0.60 => ~ ! [X: list_a,Y3: list_a,Xs2: list_list_a] :
% 0.25/0.60 ( ( Xa
% 0.25/0.60 = ( cons_list_a @ X @ ( cons_list_a @ Y3 @ Xs2 ) ) )
% 0.25/0.60 => ~ ( ( X3 @ X @ Y3 )
% 0.25/0.60 & ( successively_list_a @ X3 @ ( cons_list_a @ Y3 @ Xs2 ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively.elims(2)
% 0.25/0.60 thf(fact_323_successively_Oelims_I2_J,axiom,
% 0.25/0.60 ! [X3: a > a > $o,Xa: list_a] :
% 0.25/0.60 ( ( successively_a @ X3 @ Xa )
% 0.25/0.60 => ( ( Xa != nil_a )
% 0.25/0.60 => ( ! [X: a] :
% 0.25/0.60 ( Xa
% 0.25/0.60 != ( cons_a @ X @ nil_a ) )
% 0.25/0.60 => ~ ! [X: a,Y3: a,Xs2: list_a] :
% 0.25/0.60 ( ( Xa
% 0.25/0.60 = ( cons_a @ X @ ( cons_a @ Y3 @ Xs2 ) ) )
% 0.25/0.60 => ~ ( ( X3 @ X @ Y3 )
% 0.25/0.60 & ( successively_a @ X3 @ ( cons_a @ Y3 @ Xs2 ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively.elims(2)
% 0.25/0.60 thf(fact_324_distinct__adj__singleton,axiom,
% 0.25/0.60 ! [X3: list_a] : ( distinct_adj_list_a @ ( cons_list_a @ X3 @ nil_list_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_singleton
% 0.25/0.60 thf(fact_325_distinct__adj__singleton,axiom,
% 0.25/0.60 ! [X3: a] : ( distinct_adj_a @ ( cons_a @ X3 @ nil_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_singleton
% 0.25/0.60 thf(fact_326_list_Oexhaust__sel,axiom,
% 0.25/0.60 ! [List: list_a] :
% 0.25/0.60 ( ( List != nil_a )
% 0.25/0.60 => ( List
% 0.25/0.60 = ( cons_a @ ( hd_a @ List ) @ ( tl_a @ List ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % list.exhaust_sel
% 0.25/0.60 thf(fact_327_successively__Cons,axiom,
% 0.25/0.60 ! [P: a > a > $o,X3: a,Xs: list_a] :
% 0.25/0.60 ( ( successively_a @ P @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = ( ( Xs = nil_a )
% 0.25/0.60 | ( ( P @ X3 @ ( hd_a @ Xs ) )
% 0.25/0.60 & ( successively_a @ P @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % successively_Cons
% 0.25/0.60 thf(fact_328_distinct__adj__Cons,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a] :
% 0.25/0.60 ( ( distinct_adj_a @ ( cons_a @ X3 @ Xs ) )
% 0.25/0.60 = ( ( Xs = nil_a )
% 0.25/0.60 | ( ( X3
% 0.25/0.60 != ( hd_a @ Xs ) )
% 0.25/0.60 & ( distinct_adj_a @ Xs ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % distinct_adj_Cons
% 0.25/0.60 thf(fact_329_Cons__in__shuffles__iff,axiom,
% 0.25/0.60 ! [Z: a,Zs2: list_a,Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( member_list_a2 @ ( cons_a @ Z @ Zs2 ) @ ( shuffles_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( ( ( Xs != nil_a )
% 0.25/0.60 & ( ( hd_a @ Xs )
% 0.25/0.60 = Z )
% 0.25/0.60 & ( member_list_a2 @ Zs2 @ ( shuffles_a @ ( tl_a @ Xs ) @ Ys2 ) ) )
% 0.25/0.60 | ( ( Ys2 != nil_a )
% 0.25/0.60 & ( ( hd_a @ Ys2 )
% 0.25/0.60 = Z )
% 0.25/0.60 & ( member_list_a2 @ Zs2 @ ( shuffles_a @ Xs @ ( tl_a @ Ys2 ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Cons_in_shuffles_iff
% 0.25/0.60 thf(fact_330_map2__Cons__not__empty,axiom,
% 0.25/0.60 ! [Xs: list_a,F: a > a > a,Y: a,Ys2: list_a] :
% 0.25/0.60 ( ( Xs != nil_a )
% 0.25/0.60 => ( ( map2_a_a_a @ F @ Xs @ ( cons_a @ Y @ Ys2 ) )
% 0.25/0.60 = ( cons_a @ ( F @ ( hd_a @ Xs ) @ Y ) @ ( map2_a_a_a @ F @ ( tl_a @ Xs ) @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % map2_Cons_not_empty
% 0.25/0.60 thf(fact_331_Nil__in__shuffles,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( member_list_a2 @ nil_a @ ( shuffles_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( ( Xs = nil_a )
% 0.25/0.60 & ( Ys2 = nil_a ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Nil_in_shuffles
% 0.25/0.60 thf(fact_332_shufflesE,axiom,
% 0.25/0.60 ! [Zs2: list_a,Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( member_list_a2 @ Zs2 @ ( shuffles_a @ Xs @ Ys2 ) )
% 0.25/0.60 => ( ( ( Zs2 = Xs )
% 0.25/0.60 => ( Ys2 != nil_a ) )
% 0.25/0.60 => ( ( ( Zs2 = Ys2 )
% 0.25/0.60 => ( Xs != nil_a ) )
% 0.25/0.60 => ( ! [X: a,Xs5: list_a] :
% 0.25/0.60 ( ( Xs
% 0.25/0.60 = ( cons_a @ X @ Xs5 ) )
% 0.25/0.60 => ! [Z2: a,Zs3: list_a] :
% 0.25/0.60 ( ( Zs2
% 0.25/0.60 = ( cons_a @ Z2 @ Zs3 ) )
% 0.25/0.60 => ( ( X = Z2 )
% 0.25/0.60 => ~ ( member_list_a2 @ Zs3 @ ( shuffles_a @ Xs5 @ Ys2 ) ) ) ) )
% 0.25/0.60 => ~ ! [Y3: a,Ys5: list_a] :
% 0.25/0.60 ( ( Ys2
% 0.25/0.60 = ( cons_a @ Y3 @ Ys5 ) )
% 0.25/0.60 => ! [Z2: a,Zs3: list_a] :
% 0.25/0.60 ( ( Zs2
% 0.25/0.60 = ( cons_a @ Z2 @ Zs3 ) )
% 0.25/0.60 => ( ( Y3 = Z2 )
% 0.25/0.60 => ~ ( member_list_a2 @ Zs3 @ ( shuffles_a @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % shufflesE
% 0.25/0.60 thf(fact_333_map2__Cons__Cons,axiom,
% 0.25/0.60 ! [F: a > a > a,X3: a,Xs: list_a,Y: a,Ys2: list_a] :
% 0.25/0.60 ( ( map2_a_a_a @ F @ ( cons_a @ X3 @ Xs ) @ ( cons_a @ Y @ Ys2 ) )
% 0.25/0.60 = ( cons_a @ ( F @ X3 @ Y ) @ ( map2_a_a_a @ F @ Xs @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % map2_Cons_Cons
% 0.25/0.60 thf(fact_334_Cons__in__shuffles__leftI,axiom,
% 0.25/0.60 ! [Zs2: list_a,Xs: list_a,Ys2: list_a,Z: a] :
% 0.25/0.60 ( ( member_list_a2 @ Zs2 @ ( shuffles_a @ Xs @ Ys2 ) )
% 0.25/0.60 => ( member_list_a2 @ ( cons_a @ Z @ Zs2 ) @ ( shuffles_a @ ( cons_a @ Z @ Xs ) @ Ys2 ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Cons_in_shuffles_leftI
% 0.25/0.60 thf(fact_335_Cons__in__shuffles__rightI,axiom,
% 0.25/0.60 ! [Zs2: list_a,Xs: list_a,Ys2: list_a,Z: a] :
% 0.25/0.60 ( ( member_list_a2 @ Zs2 @ ( shuffles_a @ Xs @ Ys2 ) )
% 0.25/0.60 => ( member_list_a2 @ ( cons_a @ Z @ Zs2 ) @ ( shuffles_a @ Xs @ ( cons_a @ Z @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Cons_in_shuffles_rightI
% 0.25/0.60 thf(fact_336_Nil__in__shufflesI,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( Xs = nil_a )
% 0.25/0.60 => ( ( Ys2 = nil_a )
% 0.25/0.60 => ( member_list_a2 @ nil_a @ ( shuffles_a @ Xs @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % Nil_in_shufflesI
% 0.25/0.60 thf(fact_337_map2__Cons__if,axiom,
% 0.25/0.60 ! [Xs: list_a,F: a > a > a,Y: a,Ys2: list_a] :
% 0.25/0.60 ( ( ( Xs = nil_a )
% 0.25/0.60 => ( ( map2_a_a_a @ F @ Xs @ ( cons_a @ Y @ Ys2 ) )
% 0.25/0.60 = nil_a ) )
% 0.25/0.60 & ( ( Xs != nil_a )
% 0.25/0.60 => ( ( map2_a_a_a @ F @ Xs @ ( cons_a @ Y @ Ys2 ) )
% 0.25/0.60 = ( cons_a @ ( F @ ( hd_a @ Xs ) @ Y ) @ ( map2_a_a_a @ F @ ( tl_a @ Xs ) @ Ys2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % map2_Cons_if
% 0.25/0.60 thf(fact_338_remdups__adj__append_H,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a] :
% 0.25/0.60 ( ( ( Xs = nil_a )
% 0.25/0.60 | ( Ys2 = nil_a )
% 0.25/0.60 | ( ( last_a @ Xs )
% 0.25/0.60 != ( hd_a @ Ys2 ) ) )
% 0.25/0.60 => ( ( remdups_adj_a @ ( append_a @ Xs @ Ys2 ) )
% 0.25/0.60 = ( append_a @ ( remdups_adj_a @ Xs ) @ ( remdups_adj_a @ Ys2 ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % remdups_adj_append'
% 0.25/0.60 thf(fact_339_remdups__adj__append,axiom,
% 0.25/0.60 ! [Xs_1: list_a,X3: a,Xs_2: list_a] :
% 0.25/0.60 ( ( remdups_adj_a @ ( append_a @ Xs_1 @ ( cons_a @ X3 @ Xs_2 ) ) )
% 0.25/0.60 = ( append_a @ ( remdups_adj_a @ ( append_a @ Xs_1 @ ( cons_a @ X3 @ nil_a ) ) ) @ ( tl_a @ ( remdups_adj_a @ ( cons_a @ X3 @ Xs_2 ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % remdups_adj_append
% 0.25/0.60 thf(fact_340_remdups__adj__Nil__iff,axiom,
% 0.25/0.60 ! [Xs: list_a] :
% 0.25/0.60 ( ( ( remdups_adj_a @ Xs )
% 0.25/0.60 = nil_a )
% 0.25/0.60 = ( Xs = nil_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % remdups_adj_Nil_iff
% 0.25/0.60 thf(fact_341_remdups__adj__Cons__alt,axiom,
% 0.25/0.60 ! [X3: a,Xs: list_a] :
% 0.25/0.60 ( ( cons_a @ X3 @ ( tl_a @ ( remdups_adj_a @ ( cons_a @ X3 @ Xs ) ) ) )
% 0.25/0.60 = ( remdups_adj_a @ ( cons_a @ X3 @ Xs ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % remdups_adj_Cons_alt
% 0.25/0.60 thf(fact_342_remdups__adj_Oelims,axiom,
% 0.25/0.60 ! [X3: list_a,Y: list_a] :
% 0.25/0.60 ( ( ( remdups_adj_a @ X3 )
% 0.25/0.60 = Y )
% 0.25/0.60 => ( ( ( X3 = nil_a )
% 0.25/0.60 => ( Y != nil_a ) )
% 0.25/0.60 => ( ! [X: a] :
% 0.25/0.60 ( ( X3
% 0.25/0.60 = ( cons_a @ X @ nil_a ) )
% 0.25/0.60 => ( Y
% 0.25/0.60 != ( cons_a @ X @ nil_a ) ) )
% 0.25/0.60 => ~ ! [X: a,Y3: a,Xs2: list_a] :
% 0.25/0.60 ( ( X3
% 0.25/0.60 = ( cons_a @ X @ ( cons_a @ Y3 @ Xs2 ) ) )
% 0.25/0.60 => ~ ( ( ( X = Y3 )
% 0.25/0.60 => ( Y
% 0.25/0.60 = ( remdups_adj_a @ ( cons_a @ X @ Xs2 ) ) ) )
% 0.25/0.60 & ( ( X != Y3 )
% 0.25/0.60 => ( Y
% 0.25/0.60 = ( cons_a @ X @ ( remdups_adj_a @ ( cons_a @ Y3 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % remdups_adj.elims
% 0.25/0.60 thf(fact_343_remdups__adj_Osimps_I2_J,axiom,
% 0.25/0.60 ! [X3: a] :
% 0.25/0.60 ( ( remdups_adj_a @ ( cons_a @ X3 @ nil_a ) )
% 0.25/0.60 = ( cons_a @ X3 @ nil_a ) ) ).
% 0.25/0.60
% 0.25/0.60 % remdups_adj.simps(2)
% 0.25/0.60 thf(fact_344_remdups__adj_Osimps_I1_J,axiom,
% 0.25/0.60 ( ( remdups_adj_a @ nil_a )
% 0.25/0.60 = nil_a ) ).
% 0.25/0.60
% 0.25/0.60 % remdups_adj.simps(1)
% 0.25/0.60 thf(fact_345_remdups__adj_Osimps_I3_J,axiom,
% 0.25/0.60 ! [X3: a,Y: a,Xs: list_a] :
% 0.25/0.60 ( ( ( X3 = Y )
% 0.25/0.60 => ( ( remdups_adj_a @ ( cons_a @ X3 @ ( cons_a @ Y @ Xs ) ) )
% 0.25/0.60 = ( remdups_adj_a @ ( cons_a @ X3 @ Xs ) ) ) )
% 0.25/0.60 & ( ( X3 != Y )
% 0.25/0.60 => ( ( remdups_adj_a @ ( cons_a @ X3 @ ( cons_a @ Y @ Xs ) ) )
% 0.25/0.60 = ( cons_a @ X3 @ ( remdups_adj_a @ ( cons_a @ Y @ Xs ) ) ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % remdups_adj.simps(3)
% 0.25/0.60 thf(fact_346_remdups__adj__append__two,axiom,
% 0.25/0.60 ! [Xs: list_a,X3: a,Y: a] :
% 0.25/0.60 ( ( remdups_adj_a @ ( append_a @ Xs @ ( cons_a @ X3 @ ( cons_a @ Y @ nil_a ) ) ) )
% 0.25/0.60 = ( append_a @ ( remdups_adj_a @ ( append_a @ Xs @ ( cons_a @ X3 @ nil_a ) ) ) @ ( if_list_a @ ( X3 = Y ) @ nil_a @ ( cons_a @ Y @ nil_a ) ) ) ) ).
% 0.25/0.60
% 0.25/0.60 % remdups_adj_append_two
% 0.25/0.60 thf(fact_347_map2__snoc__snoc,axiom,
% 0.25/0.60 ! [Xs: list_a,Ys2: list_a,F: a > a > a,X3: a,Y: a] :
% 0.25/0.60 ( ( ( size_size_list_a @ Xs )
% 0.25/0.60 = ( size_size_list_a @ Ys2 ) )
% 0.25/0.60 => ( ( map2_a_a_a @ F @ ( append_a @ Xs @ ( cons_a @ X3 @ nil_a ) ) @ ( append_a @ Ys2 @ ( cons_a @ Y @ nil_a ) ) )
% 0.25/0.69 = ( append_a @ ( map2_a_a_a @ F @ Xs @ Ys2 ) @ ( cons_a @ ( F @ X3 @ Y ) @ nil_a ) ) ) ) ).
% 0.25/0.69
% 0.25/0.69 % map2_snoc_snoc
% 0.25/0.69 thf(fact_348_length__greater__imp__not__empty,axiom,
% 0.25/0.69 ! [N: nat,Xs: list_a] :
% 0.25/0.69 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.25/0.69 => ( Xs != nil_a ) ) ).
% 0.25/0.69
% 0.25/0.69 % length_greater_imp_not_empty
% 0.25/0.69 thf(fact_349_list__induct2,axiom,
% 0.25/0.69 ! [Xs: list_a,Ys2: list_a,P: list_a > list_a > $o] :
% 0.25/0.69 ( ( ( size_size_list_a @ Xs )
% 0.25/0.69 = ( size_size_list_a @ Ys2 ) )
% 0.25/0.69 => ( ( P @ nil_a @ nil_a )
% 0.25/0.69 => ( ! [X: a,Xs2: list_a,Y3: a,Ys3: list_a] :
% 0.25/0.69 ( ( ( size_size_list_a @ Xs2 )
% 0.25/0.69 = ( size_size_list_a @ Ys3 ) )
% 0.25/0.69 => ( ( P @ Xs2 @ Ys3 )
% 0.25/0.69 => ( P @ ( cons_a @ X @ Xs2 ) @ ( cons_a @ Y3 @ Ys3 ) ) ) )
% 0.25/0.69 => ( P @ Xs @ Ys2 ) ) ) ) ).
% 0.25/0.69
% 0.25/0.69 % list_induct2
% 0.25/0.69 thf(fact_350_list__induct3,axiom,
% 0.25/0.69 ! [Xs: list_a,Ys2: list_a,Zs2: list_a,P: list_a > list_a > list_a > $o] :
% 0.25/0.69 ( ( ( size_size_list_a @ Xs )
% 0.25/0.69 = ( size_size_list_a @ Ys2 ) )
% 0.25/0.69 => ( ( ( size_size_list_a @ Ys2 )
% 0.25/0.69 = ( size_size_list_a @ Zs2 ) )
% 0.25/0.69 => ( ( P @ nil_a @ nil_a @ nil_a )
% 0.25/0.69 => ( ! [X: a,Xs2: list_a,Y3: a,Ys3: list_a,Z2: a,Zs: list_a] :
% 0.25/0.69 ( ( ( size_size_list_a @ Xs2 )
% 0.25/0.69 = ( size_size_list_a @ Ys3 ) )
% 0.25/0.69 => ( ( ( size_size_list_a @ Ys3 )
% 0.25/0.69 = ( size_size_list_a @ Zs ) )
% 0.25/0.69 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.25/0.69 => ( P @ ( cons_a @ X @ Xs2 ) @ ( cons_a @ Y3 @ Ys3 ) @ ( cons_a @ Z2 @ Zs ) ) ) ) )
% 0.25/0.69 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.25/0.69
% 0.25/0.69 % list_induct3
% 0.25/0.69 thf(fact_351_list__induct4,axiom,
% 0.25/0.69 ! [Xs: list_a,Ys2: list_a,Zs2: list_a,Ws2: list_a,P: list_a > list_a > list_a > list_a > $o] :
% 0.25/0.69 ( ( ( size_size_list_a @ Xs )
% 0.25/0.69 = ( size_size_list_a @ Ys2 ) )
% 0.25/0.69 => ( ( ( size_size_list_a @ Ys2 )
% 0.25/0.69 = ( size_size_list_a @ Zs2 ) )
% 0.25/0.69 => ( ( ( size_size_list_a @ Zs2 )
% 0.25/0.69 = ( size_size_list_a @ Ws2 ) )
% 0.25/0.69 => ( ( P @ nil_a @ nil_a @ nil_a @ nil_a )
% 0.25/0.69 => ( ! [X: a,Xs2: list_a,Y3: a,Ys3: list_a,Z2: a,Zs: list_a,W: a,Ws3: list_a] :
% 0.25/0.69 ( ( ( size_size_list_a @ Xs2 )
% 0.25/0.69 = ( size_size_list_a @ Ys3 ) )
% 0.25/0.69 => ( ( ( size_size_list_a @ Ys3 )
% 0.25/0.69 = ( size_size_list_a @ Zs ) )
% 0.25/0.69 => ( ( ( size_size_list_a @ Zs )
% 0.25/0.69 = ( size_size_list_a @ Ws3 ) )
% 0.25/0.69 => ( ( P @ Xs2 @ Ys3 @ Zs @ Ws3 )
% 0.25/0.69 => ( P @ ( cons_a @ X @ Xs2 ) @ ( cons_a @ Y3 @ Ys3 ) @ ( cons_a @ Z2 @ Zs ) @ ( cons_a @ W @ Ws3 ) ) ) ) ) )
% 0.25/0.69 => ( P @ Xs @ Ys2 @ Zs2 @ Ws2 ) ) ) ) ) ) ).
% 0.25/0.69
% 0.25/0.69 % list_induct4
% 0.25/0.69
% 0.25/0.69 % Helper facts (3)
% 0.25/0.69 thf(help_If_3_1_If_001t__List__Olist_Itf__a_J_T,axiom,
% 0.25/0.69 ! [P: $o] :
% 0.25/0.69 ( ( P = $true )
% 0.25/0.69 | ( P = $false ) ) ).
% 0.25/0.69
% 0.25/0.69 thf(help_If_2_1_If_001t__List__Olist_Itf__a_J_T,axiom,
% 0.25/0.69 ! [X3: list_a,Y: list_a] :
% 0.25/0.69 ( ( if_list_a @ $false @ X3 @ Y )
% 0.25/0.69 = Y ) ).
% 0.25/0.69
% 0.25/0.69 thf(help_If_1_1_If_001t__List__Olist_Itf__a_J_T,axiom,
% 0.25/0.69 ! [X3: list_a,Y: list_a] :
% 0.25/0.69 ( ( if_list_a @ $true @ X3 @ Y )
% 0.25/0.69 = X3 ) ).
% 0.25/0.69
% 0.25/0.69 % Conjectures (1)
% 0.25/0.69 thf(conj_0,conjecture,
% 0.25/0.69 ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
% 0.25/0.69 = ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ) ).
% 0.25/0.69
% 0.25/0.69 %------------------------------------------------------------------------------
% 0.25/0.69 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.kUs9ZQ5NR3/cvc5---1.0.5_20057.p...
% 0.25/0.69 (declare-sort $$unsorted 0)
% 0.25/0.69 (declare-sort tptp.list_list_list_a 0)
% 0.25/0.69 (declare-sort tptp.set_list_list_a 0)
% 0.25/0.69 (declare-sort tptp.list_list_a 0)
% 0.25/0.69 (declare-sort tptp.set_list_a 0)
% 0.25/0.69 (declare-sort tptp.list_nat 0)
% 0.25/0.69 (declare-sort tptp.list_a 0)
% 0.25/0.69 (declare-sort tptp.set_a 0)
% 0.25/0.69 (declare-sort tptp.nat 0)
% 0.25/0.69 (declare-sort tptp.a 0)
% 0.25/0.69 (declare-fun tptp.bNF_Gr1972240547list_a (tptp.set_list_list_a tptp.list_a) tptp.set_list_list_a)
% 0.25/0.69 (declare-fun tptp.bNF_Greatest_Shift_a (tptp.set_list_a tptp.a) tptp.set_list_a)
% 0.25/0.69 (declare-fun tptp.bNF_Gr1046450207list_a (tptp.set_list_list_a tptp.list_list_a) tptp.set_list_a)
% 0.25/0.69 (declare-fun tptp.bNF_Greatest_Succ_a (tptp.set_list_a tptp.list_a) tptp.set_a)
% 0.25/0.69 (declare-fun tptp.if_list_a (Bool tptp.list_a tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.list_ord_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 0.25/0.69 (declare-fun tptp.list_strict_asc_nat (tptp.list_nat) Bool)
% 0.25/0.69 (declare-fun tptp.map2_a_a_a ((-> tptp.a tptp.a tptp.a) tptp.list_a tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.listIn1753026346list_a (tptp.list_list_a (-> tptp.nat tptp.list_a) tptp.nat) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.listIn1312259492pend_a (tptp.list_a (-> tptp.nat tptp.a) tptp.nat) tptp.a)
% 0.25/0.69 (declare-fun tptp.append_list_list_a (tptp.list_list_list_a tptp.list_list_list_a) tptp.list_list_list_a)
% 0.25/0.69 (declare-fun tptp.append_list_a (tptp.list_list_a tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 0.25/0.69 (declare-fun tptp.append_a (tptp.list_a tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.bind_list_a_list_a (tptp.list_list_a (-> tptp.list_a tptp.list_list_a)) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.bind_list_a_a (tptp.list_list_a (-> tptp.list_a tptp.list_a)) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.bind_a_list_a (tptp.list_a (-> tptp.a tptp.list_list_a)) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.bind_a_a (tptp.list_a (-> tptp.a tptp.list_a)) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.butlast_list_a (tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.butlast_a (tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.concat_list_a (tptp.list_list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.concat_a (tptp.list_list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.distinct_adj_list_a (tptp.list_list_a) Bool)
% 0.25/0.69 (declare-fun tptp.distinct_adj_a (tptp.list_a) Bool)
% 0.25/0.69 (declare-fun tptp.foldr_769741863list_a ((-> tptp.list_list_a tptp.list_list_a tptp.list_list_a) tptp.list_list_list_a tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.foldr_list_a_list_a ((-> tptp.list_a tptp.list_a tptp.list_a) tptp.list_list_a tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.insert_list_a (tptp.list_a tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.insert_a (tptp.a tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.last_list_a (tptp.list_list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.last_a (tptp.list_a) tptp.a)
% 0.25/0.69 (declare-fun tptp.cons_list_list_a (tptp.list_list_a tptp.list_list_list_a) tptp.list_list_list_a)
% 0.25/0.69 (declare-fun tptp.cons_list_a (tptp.list_a tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 0.25/0.69 (declare-fun tptp.cons_a (tptp.a tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.nil_list_list_a () tptp.list_list_list_a)
% 0.25/0.69 (declare-fun tptp.nil_list_a () tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.nil_nat () tptp.list_nat)
% 0.25/0.69 (declare-fun tptp.nil_a () tptp.list_a)
% 0.25/0.69 (declare-fun tptp.hd_list_list_a (tptp.list_list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.hd_list_a (tptp.list_list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.hd_a (tptp.list_a) tptp.a)
% 0.25/0.69 (declare-fun tptp.tl_list_a (tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.tl_a (tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.list_ex1_list_a ((-> tptp.list_a Bool) tptp.list_list_a) Bool)
% 0.25/0.69 (declare-fun tptp.list_ex1_a ((-> tptp.a Bool) tptp.list_a) Bool)
% 0.25/0.69 (declare-fun tptp.listre1221556159list_a ((-> tptp.list_a tptp.list_a Bool) tptp.list_list_a tptp.list_list_a) Bool)
% 0.25/0.69 (declare-fun tptp.listrelp_list_a_a ((-> tptp.list_a tptp.a Bool) tptp.list_list_a tptp.list_a) Bool)
% 0.25/0.69 (declare-fun tptp.listrelp_a_list_a ((-> tptp.a tptp.list_a Bool) tptp.list_a tptp.list_list_a) Bool)
% 0.25/0.69 (declare-fun tptp.listrelp_a_a ((-> tptp.a tptp.a Bool) tptp.list_a tptp.list_a) Bool)
% 0.25/0.69 (declare-fun tptp.map_ta982122357list_a ((-> tptp.list_a tptp.list_a) tptp.list_list_a tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.map_ta2002079599st_a_a ((-> tptp.list_a tptp.a) tptp.list_list_a tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.map_ta41997947list_a ((-> tptp.a tptp.list_a) tptp.list_a tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.map_tailrec_rev_a_a ((-> tptp.a tptp.a) tptp.list_a tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.maps_list_a_list_a ((-> tptp.list_a tptp.list_list_a) tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.maps_list_a_a ((-> tptp.list_a tptp.list_a) tptp.list_list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.maps_a_list_a ((-> tptp.a tptp.list_list_a) tptp.list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.maps_a_a ((-> tptp.a tptp.list_a) tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.member_list_a (tptp.list_list_a tptp.list_a) Bool)
% 0.25/0.69 (declare-fun tptp.member_a (tptp.list_a tptp.a) Bool)
% 0.25/0.69 (declare-fun tptp.lexordp_eq_list_a ((-> tptp.list_a tptp.list_a Bool) tptp.list_list_a tptp.list_list_a) Bool)
% 0.25/0.69 (declare-fun tptp.lexordp_eq_a ((-> tptp.a tptp.a Bool) tptp.list_a tptp.list_a) Bool)
% 0.25/0.69 (declare-fun tptp.ord_lexordp_nat (tptp.list_nat tptp.list_nat) Bool)
% 0.25/0.69 (declare-fun tptp.ord_lexordp_eq_nat (tptp.list_nat tptp.list_nat) Bool)
% 0.25/0.69 (declare-fun tptp.product_lists_list_a (tptp.list_list_list_a) tptp.list_list_list_a)
% 0.25/0.69 (declare-fun tptp.product_lists_a (tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.remdups_adj_a (tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.rotate1_list_a (tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.rotate1_a (tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.shuffles_a (tptp.list_a tptp.list_a) tptp.set_list_a)
% 0.25/0.69 (declare-fun tptp.splice_list_a (tptp.list_list_a tptp.list_list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.splice_a (tptp.list_a tptp.list_a) tptp.list_a)
% 0.25/0.69 (declare-fun tptp.subseqs_list_a (tptp.list_list_a) tptp.list_list_list_a)
% 0.25/0.69 (declare-fun tptp.subseqs_a (tptp.list_a) tptp.list_list_a)
% 0.25/0.69 (declare-fun tptp.successively_list_a ((-> tptp.list_a tptp.list_a Bool) tptp.list_list_a) Bool)
% 0.25/0.69 (declare-fun tptp.successively_a ((-> tptp.a tptp.a Bool) tptp.list_a) Bool)
% 0.25/0.69 (declare-fun tptp.size_size_list_a (tptp.list_a) tptp.nat)
% 0.25/0.69 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.69 (declare-fun tptp.collect_list_a ((-> tptp.list_a Bool)) tptp.set_list_a)
% 0.25/0.69 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.25/0.69 (declare-fun tptp.member_list_list_a (tptp.list_list_a tptp.set_list_list_a) Bool)
% 0.25/0.69 (declare-fun tptp.member_list_a2 (tptp.list_a tptp.set_list_a) Bool)
% 0.25/0.69 (declare-fun tptp.member_a2 (tptp.a tptp.set_a) Bool)
% 0.25/0.69 (declare-fun tptp.f (tptp.nat) tptp.a)
% 0.25/0.69 (declare-fun tptp.x () tptp.a)
% 0.25/0.69 (declare-fun tptp.xs () tptp.list_a)
% 0.25/0.69 (assert (forall ((F (-> tptp.nat tptp.list_a))) (= (@ (@ tptp.listIn1753026346list_a tptp.nil_list_a) F) F)))
% 0.25/0.69 (assert (forall ((F (-> tptp.nat tptp.a))) (= (@ (@ tptp.listIn1312259492pend_a tptp.nil_a) F) F)))
% 0.25/0.69 (assert (forall ((X21 tptp.list_a) (X22 tptp.list_list_a) (Y21 tptp.list_a) (Y22 tptp.list_list_a)) (= (= (@ (@ tptp.cons_list_a X21) X22) (@ (@ tptp.cons_list_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.69 (assert (forall ((X21 tptp.a) (X22 tptp.list_a) (Y21 tptp.a) (Y22 tptp.list_a)) (= (= (@ (@ tptp.cons_a X21) X22) (@ (@ tptp.cons_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.69 (assert (forall ((X21 tptp.list_a) (X22 tptp.list_list_a)) (not (= tptp.nil_list_a (@ (@ tptp.cons_list_a X21) X22)))))
% 0.25/0.69 (assert (forall ((X21 tptp.a) (X22 tptp.list_a)) (not (= tptp.nil_a (@ (@ tptp.cons_a X21) X22)))))
% 0.25/0.69 (assert (forall ((List tptp.list_list_a) (X21 tptp.list_a) (X22 tptp.list_list_a)) (=> (= List (@ (@ tptp.cons_list_a X21) X22)) (not (= List tptp.nil_list_a)))))
% 0.25/0.69 (assert (forall ((List tptp.list_a) (X21 tptp.a) (X22 tptp.list_a)) (=> (= List (@ (@ tptp.cons_a X21) X22)) (not (= List tptp.nil_a)))))
% 0.25/0.69 (assert (forall ((Y tptp.list_list_a)) (=> (not (= Y tptp.nil_list_a)) (not (forall ((X212 tptp.list_a) (X222 tptp.list_list_a)) (not (= Y (@ (@ tptp.cons_list_a X212) X222))))))))
% 0.25/0.69 (assert (forall ((Y tptp.list_a)) (=> (not (= Y tptp.nil_a)) (not (forall ((X212 tptp.a) (X222 tptp.list_a)) (not (= Y (@ (@ tptp.cons_a X212) X222))))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_list_a Bool)) (List tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X1 tptp.list_a) (X2 tptp.list_list_a)) (=> (@ P X2) (@ P (@ (@ tptp.cons_list_a X1) X2)))) (@ P List)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a Bool)) (List tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X1 tptp.a) (X2 tptp.list_a)) (=> (@ P X2) (@ P (@ (@ tptp.cons_a X1) X2)))) (@ P List)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (= (not (= Xs tptp.nil_list_a)) (exists ((Y2 tptp.list_a) (Ys tptp.list_list_a)) (= Xs (@ (@ tptp.cons_list_a Y2) Ys))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (= (not (= Xs tptp.nil_a)) (exists ((Y2 tptp.a) (Ys tptp.list_a)) (= Xs (@ (@ tptp.cons_a Y2) Ys))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a tptp.list_list_a Bool)) (Xs tptp.list_a) (Ys2 tptp.list_list_a)) (=> (@ (@ P tptp.nil_a) tptp.nil_list_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a)) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) tptp.nil_list_a)) (=> (forall ((Y3 tptp.list_a) (Ys3 tptp.list_list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_list_a Y3) Ys3))) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3)))) (@ (@ P Xs) Ys2)))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_list_a tptp.list_a Bool)) (Xs tptp.list_list_a) (Ys2 tptp.list_a)) (=> (@ (@ P tptp.nil_list_a) tptp.nil_a) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) tptp.nil_a)) (=> (forall ((Y3 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_list_a) (@ (@ tptp.cons_a Y3) Ys3))) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a) (Y3 tptp.a) (Ys3 tptp.list_a)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)))) (@ (@ P Xs) Ys2)))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (@ (@ P tptp.nil_list_a) tptp.nil_list_a) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) tptp.nil_list_a)) (=> (forall ((Y3 tptp.list_a) (Ys3 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) (@ (@ tptp.cons_list_a Y3) Ys3))) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a) (Y3 tptp.list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3)))) (@ (@ P Xs) Ys2)))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ P tptp.nil_a) tptp.nil_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a)) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) tptp.nil_a)) (=> (forall ((Y3 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_a Y3) Ys3))) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys3 tptp.list_a)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)))) (@ (@ P Xs) Ys2)))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (A0 tptp.list_list_a) (A1 tptp.list_list_a)) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Ys3) Xs2) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) Ys3))) (@ (@ P A0) A1)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ P Ys3) Xs2) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) Ys3))) (@ (@ P A0) A1)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_list_a Bool)) (Xs tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (=> (forall ((X tptp.list_a) (Y3 tptp.list_a) (Zs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_list_a X) _let_1)))))) (@ P Xs))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X tptp.a)) (@ P (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (forall ((X tptp.a) (Y3 tptp.a) (Zs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_a X) _let_1)))))) (@ P Xs))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (A0 tptp.list_list_a) (A1 tptp.list_list_a)) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((Xs2 tptp.list_list_a)) (@ (@ P Xs2) tptp.nil_list_a)) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a) (Y3 tptp.list_a) (Ys3 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_list_a X) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((Xs2 tptp.list_a)) (@ (@ P Xs2) tptp.nil_a)) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys3 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_a X) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a)) (not (= (@ (@ tptp.cons_list_a X3) Xs) Xs))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a)) (not (= (@ (@ tptp.cons_a X3) Xs) Xs))))
% 0.25/0.69 (assert (forall ((P (-> (-> tptp.list_a tptp.a) tptp.list_list_a tptp.list_a Bool)) (A0 (-> tptp.list_a tptp.a)) (A1 tptp.list_list_a) (A2 tptp.list_a)) (=> (forall ((F2 (-> tptp.list_a tptp.a)) (X_1 tptp.list_a)) (@ (@ (@ P F2) tptp.nil_list_a) X_1)) (=> (forall ((F2 (-> tptp.list_a tptp.a)) (A tptp.list_a) (As tptp.list_list_a) (Bs tptp.list_a)) (let ((_let_1 (@ P F2))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_a (@ F2 A)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_list_a A) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.69 (assert (forall ((P (-> (-> tptp.a tptp.list_a) tptp.list_a tptp.list_list_a Bool)) (A0 (-> tptp.a tptp.list_a)) (A1 tptp.list_a) (A2 tptp.list_list_a)) (=> (forall ((F2 (-> tptp.a tptp.list_a)) (X_1 tptp.list_list_a)) (@ (@ (@ P F2) tptp.nil_a) X_1)) (=> (forall ((F2 (-> tptp.a tptp.list_a)) (A tptp.a) (As tptp.list_a) (Bs tptp.list_list_a)) (let ((_let_1 (@ P F2))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_list_a (@ F2 A)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_a A) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.69 (assert (forall ((P (-> (-> tptp.list_a tptp.list_a) tptp.list_list_a tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a)) (A1 tptp.list_list_a) (A2 tptp.list_list_a)) (=> (forall ((F2 (-> tptp.list_a tptp.list_a)) (X_1 tptp.list_list_a)) (@ (@ (@ P F2) tptp.nil_list_a) X_1)) (=> (forall ((F2 (-> tptp.list_a tptp.list_a)) (A tptp.list_a) (As tptp.list_list_a) (Bs tptp.list_list_a)) (let ((_let_1 (@ P F2))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_list_a (@ F2 A)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_list_a A) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.69 (assert (forall ((P (-> (-> tptp.a tptp.a) tptp.list_a tptp.list_a Bool)) (A0 (-> tptp.a tptp.a)) (A1 tptp.list_a) (A2 tptp.list_a)) (=> (forall ((F2 (-> tptp.a tptp.a)) (X_1 tptp.list_a)) (@ (@ (@ P F2) tptp.nil_a) X_1)) (=> (forall ((F2 (-> tptp.a tptp.a)) (A tptp.a) (As tptp.list_a) (Bs tptp.list_a)) (let ((_let_1 (@ P F2))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_a (@ F2 A)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_a A) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (P (-> tptp.list_list_a Bool))) (=> (not (= Xs tptp.nil_list_a)) (=> (forall ((X tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (=> (not (= Xs2 tptp.nil_list_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_list_a X) Xs2))))) (@ P Xs))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (P (-> tptp.list_a Bool))) (=> (not (= Xs tptp.nil_a)) (=> (forall ((X tptp.a)) (@ P (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (forall ((X tptp.a) (Xs2 tptp.list_a)) (=> (not (= Xs2 tptp.nil_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_a X) Xs2))))) (@ P Xs))))))
% 0.25/0.69 (assert (forall ((P (-> (-> tptp.list_a tptp.list_a Bool) tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool))) (@ (@ P P2) tptp.nil_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a)) (@ (@ P P2) (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_list_a X) _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.69 (assert (forall ((P (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool))) (@ (@ P P2) tptp.nil_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X tptp.a)) (@ (@ P P2) (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_a X) _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_list_a Bool)) (A0 tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (=> (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Xs2))) (let ((_let_2 (@ tptp.cons_list_a X))) (let ((_let_3 (= X Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a Bool)) (A0 tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X tptp.a)) (@ P (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (let ((_let_2 (@ tptp.cons_a X))) (let ((_let_3 (= X Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.25/0.69 (assert (forall ((P (-> (-> tptp.list_a tptp.list_a Bool) tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool))) (@ (@ P P2) tptp.nil_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Ys3 tptp.list_list_a)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_list_a X) Ys3))))) (@ (@ P A0) A1)))))
% 0.25/0.69 (assert (forall ((P (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool))) (@ (@ P P2) tptp.nil_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X tptp.a) (Ys3 tptp.list_a)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_a X) Ys3))))) (@ (@ P A0) A1)))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_list_a)) (=> (not (= X3 tptp.nil_list_a)) (=> (forall ((X tptp.list_a)) (not (= X3 (@ (@ tptp.cons_list_a X) tptp.nil_list_a)))) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (not (= X3 (@ (@ tptp.cons_list_a X) (@ (@ tptp.cons_list_a Y3) Xs2))))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a)) (=> (not (= X3 tptp.nil_a)) (=> (forall ((X tptp.a)) (not (= X3 (@ (@ tptp.cons_a X) tptp.nil_a)))) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (not (= X3 (@ (@ tptp.cons_a X) (@ (@ tptp.cons_a Y3) Xs2))))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_list_list_a)) (=> (not (= X3 tptp.nil_list_list_a)) (=> (forall ((Xss tptp.list_list_list_a)) (not (= X3 (@ (@ tptp.cons_list_list_a tptp.nil_list_a) Xss)))) (not (forall ((X tptp.list_a) (Xs2 tptp.list_list_a) (Xss tptp.list_list_list_a)) (not (= X3 (@ (@ tptp.cons_list_list_a (@ (@ tptp.cons_list_a X) Xs2)) Xss)))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_list_a)) (=> (not (= X3 tptp.nil_list_a)) (=> (forall ((Xss tptp.list_list_a)) (not (= X3 (@ (@ tptp.cons_list_a tptp.nil_a) Xss)))) (not (forall ((X tptp.a) (Xs2 tptp.list_a) (Xss tptp.list_list_a)) (not (= X3 (@ (@ tptp.cons_list_a (@ (@ tptp.cons_a X) Xs2)) Xss)))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a)) (= (@ (@ tptp.insert_list_a X3) tptp.nil_list_a) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((X3 tptp.a)) (= (@ (@ tptp.insert_a X3) tptp.nil_a) (@ (@ tptp.cons_a X3) tptp.nil_a))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a Bool))) (not (@ (@ tptp.list_ex1_list_a P) tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((P (-> tptp.a Bool))) (not (@ (@ tptp.list_ex1_a P) tptp.nil_a))))
% 0.25/0.69 (assert (forall ((X3 (-> tptp.a tptp.list_a)) (Xa tptp.list_a) (Xb tptp.list_list_a) (Y tptp.list_list_a)) (=> (= (@ (@ (@ tptp.map_ta41997947list_a X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_a) (not (= Y Xb))) (not (forall ((A tptp.a) (As tptp.list_a)) (=> (= Xa (@ (@ tptp.cons_a A) As)) (not (= Y (@ (@ (@ tptp.map_ta41997947list_a X3) As) (@ (@ tptp.cons_list_a (@ X3 A)) Xb)))))))))))
% 0.25/0.69 (assert (forall ((X3 (-> tptp.list_a tptp.a)) (Xa tptp.list_list_a) (Xb tptp.list_a) (Y tptp.list_a)) (=> (= (@ (@ (@ tptp.map_ta2002079599st_a_a X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_list_a) (not (= Y Xb))) (not (forall ((A tptp.list_a) (As tptp.list_list_a)) (=> (= Xa (@ (@ tptp.cons_list_a A) As)) (not (= Y (@ (@ (@ tptp.map_ta2002079599st_a_a X3) As) (@ (@ tptp.cons_a (@ X3 A)) Xb)))))))))))
% 0.25/0.69 (assert (forall ((X3 (-> tptp.list_a tptp.list_a)) (Xa tptp.list_list_a) (Xb tptp.list_list_a) (Y tptp.list_list_a)) (=> (= (@ (@ (@ tptp.map_ta982122357list_a X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_list_a) (not (= Y Xb))) (not (forall ((A tptp.list_a) (As tptp.list_list_a)) (=> (= Xa (@ (@ tptp.cons_list_a A) As)) (not (= Y (@ (@ (@ tptp.map_ta982122357list_a X3) As) (@ (@ tptp.cons_list_a (@ X3 A)) Xb)))))))))))
% 0.25/0.69 (assert (forall ((X3 (-> tptp.a tptp.a)) (Xa tptp.list_a) (Xb tptp.list_a) (Y tptp.list_a)) (=> (= (@ (@ (@ tptp.map_tailrec_rev_a_a X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_a) (not (= Y Xb))) (not (forall ((A tptp.a) (As tptp.list_a)) (=> (= Xa (@ (@ tptp.cons_a A) As)) (not (= Y (@ (@ (@ tptp.map_tailrec_rev_a_a X3) As) (@ (@ tptp.cons_a (@ X3 A)) Xb)))))))))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Xs tptp.list_list_a)) (not (@ (@ (@ tptp.lexordp_eq_list_a Less) (@ (@ tptp.cons_list_a X3) Xs)) tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_eq_a Less) (@ (@ tptp.cons_a X3) Xs)) tptp.nil_a))))
% 0.25/0.69 (assert (forall ((F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.bind_a_list_a tptp.nil_a) F) tptp.nil_list_a)))
% 0.25/0.69 (assert (forall ((F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.bind_list_a_a tptp.nil_list_a) F) tptp.nil_a)))
% 0.25/0.69 (assert (forall ((F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.bind_list_a_list_a tptp.nil_list_a) F) tptp.nil_list_a)))
% 0.25/0.69 (assert (forall ((F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.bind_a_a tptp.nil_a) F) tptp.nil_a)))
% 0.25/0.69 (assert (forall ((R (-> tptp.a tptp.list_a Bool)) (X12 tptp.list_a) (X23 tptp.list_list_a) (P (-> tptp.list_a tptp.list_list_a Bool))) (=> (@ (@ (@ tptp.listrelp_a_list_a R) X12) X23) (=> (@ (@ P tptp.nil_a) tptp.nil_list_a) (=> (forall ((X tptp.a) (Y3 tptp.list_a) (Xs2 tptp.list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ R X) Y3) (=> (@ (@ (@ tptp.listrelp_a_list_a R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3)))))) (@ (@ P X12) X23))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.list_a tptp.a Bool)) (X12 tptp.list_list_a) (X23 tptp.list_a) (P (-> tptp.list_list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.listrelp_list_a_a R) X12) X23) (=> (@ (@ P tptp.nil_list_a) tptp.nil_a) (=> (forall ((X tptp.list_a) (Y3 tptp.a) (Xs2 tptp.list_list_a) (Ys3 tptp.list_a)) (=> (@ (@ R X) Y3) (=> (@ (@ (@ tptp.listrelp_list_a_a R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)))))) (@ (@ P X12) X23))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.list_a tptp.list_a Bool)) (X12 tptp.list_list_a) (X23 tptp.list_list_a) (P (-> tptp.list_list_a tptp.list_list_a Bool))) (=> (@ (@ (@ tptp.listre1221556159list_a R) X12) X23) (=> (@ (@ P tptp.nil_list_a) tptp.nil_list_a) (=> (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ R X) Y3) (=> (@ (@ (@ tptp.listre1221556159list_a R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3)))))) (@ (@ P X12) X23))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.a tptp.a Bool)) (X12 tptp.list_a) (X23 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.listrelp_a_a R) X12) X23) (=> (@ (@ P tptp.nil_a) tptp.nil_a) (=> (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ R X) Y3) (=> (@ (@ (@ tptp.listrelp_a_a R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)))))) (@ (@ P X12) X23))))))
% 0.25/0.69 (assert (= tptp.listrelp_a_list_a (lambda ((R2 (-> tptp.a tptp.list_a Bool)) (A12 tptp.list_a) (A22 tptp.list_list_a)) (or (and (= A12 tptp.nil_a) (= A22 tptp.nil_list_a)) (exists ((X4 tptp.a) (Y2 tptp.list_a) (Xs3 tptp.list_a) (Ys tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_a X4) Xs3)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys)) (@ (@ R2 X4) Y2) (@ (@ (@ tptp.listrelp_a_list_a R2) Xs3) Ys)))))))
% 0.25/0.69 (assert (= tptp.listrelp_list_a_a (lambda ((R2 (-> tptp.list_a tptp.a Bool)) (A12 tptp.list_list_a) (A22 tptp.list_a)) (or (and (= A12 tptp.nil_list_a) (= A22 tptp.nil_a)) (exists ((X4 tptp.list_a) (Y2 tptp.a) (Xs3 tptp.list_list_a) (Ys tptp.list_a)) (and (= A12 (@ (@ tptp.cons_list_a X4) Xs3)) (= A22 (@ (@ tptp.cons_a Y2) Ys)) (@ (@ R2 X4) Y2) (@ (@ (@ tptp.listrelp_list_a_a R2) Xs3) Ys)))))))
% 0.25/0.69 (assert (= tptp.listre1221556159list_a (lambda ((R2 (-> tptp.list_a tptp.list_a Bool)) (A12 tptp.list_list_a) (A22 tptp.list_list_a)) (or (and (= A12 tptp.nil_list_a) (= A22 tptp.nil_list_a)) (exists ((X4 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X4) Xs3)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys)) (@ (@ R2 X4) Y2) (@ (@ (@ tptp.listre1221556159list_a R2) Xs3) Ys)))))))
% 0.25/0.69 (assert (= tptp.listrelp_a_a (lambda ((R2 (-> tptp.a tptp.a Bool)) (A12 tptp.list_a) (A22 tptp.list_a)) (or (and (= A12 tptp.nil_a) (= A22 tptp.nil_a)) (exists ((X4 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X4) Xs3)) (= A22 (@ (@ tptp.cons_a Y2) Ys)) (@ (@ R2 X4) Y2) (@ (@ (@ tptp.listrelp_a_a R2) Xs3) Ys)))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.a tptp.list_a Bool)) (A1 tptp.list_a) (A2 tptp.list_list_a)) (=> (@ (@ (@ tptp.listrelp_a_list_a R) A1) A2) (=> (=> (= A1 tptp.nil_a) (not (= A2 tptp.nil_list_a))) (not (forall ((X tptp.a) (Y3 tptp.list_a) (Xs2 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X) Xs2)) (forall ((Ys3 tptp.list_list_a)) (=> (= A2 (@ (@ tptp.cons_list_a Y3) Ys3)) (=> (@ (@ R X) Y3) (not (@ (@ (@ tptp.listrelp_a_list_a R) Xs2) Ys3))))))))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.list_a tptp.a Bool)) (A1 tptp.list_list_a) (A2 tptp.list_a)) (=> (@ (@ (@ tptp.listrelp_list_a_a R) A1) A2) (=> (=> (= A1 tptp.nil_list_a) (not (= A2 tptp.nil_a))) (not (forall ((X tptp.list_a) (Y3 tptp.a) (Xs2 tptp.list_list_a)) (=> (= A1 (@ (@ tptp.cons_list_a X) Xs2)) (forall ((Ys3 tptp.list_a)) (=> (= A2 (@ (@ tptp.cons_a Y3) Ys3)) (=> (@ (@ R X) Y3) (not (@ (@ (@ tptp.listrelp_list_a_a R) Xs2) Ys3))))))))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a) (A2 tptp.list_list_a)) (=> (@ (@ (@ tptp.listre1221556159list_a R) A1) A2) (=> (=> (= A1 tptp.nil_list_a) (not (= A2 tptp.nil_list_a))) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (=> (= A1 (@ (@ tptp.cons_list_a X) Xs2)) (forall ((Ys3 tptp.list_list_a)) (=> (= A2 (@ (@ tptp.cons_list_a Y3) Ys3)) (=> (@ (@ R X) Y3) (not (@ (@ (@ tptp.listre1221556159list_a R) Xs2) Ys3))))))))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.a tptp.a Bool)) (A1 tptp.list_a) (A2 tptp.list_a)) (=> (@ (@ (@ tptp.listrelp_a_a R) A1) A2) (=> (=> (= A1 tptp.nil_a) (not (= A2 tptp.nil_a))) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X) Xs2)) (forall ((Ys3 tptp.list_a)) (=> (= A2 (@ (@ tptp.cons_a Y3) Ys3)) (=> (@ (@ R X) Y3) (not (@ (@ (@ tptp.listrelp_a_a R) Xs2) Ys3))))))))))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Xs tptp.list_list_a) (Y tptp.list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_eq_list_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.cons_list_a Y) Ys2)) (or (@ (@ Less X3) Y) (and (not (@ (@ Less Y) X3)) (@ (@ _let_1 Xs) Ys2)))))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2)) (or (@ (@ Less X3) Y) (and (not (@ (@ Less Y) X3)) (@ (@ _let_1 Xs) Ys2)))))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a)) (= (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs) tptp.nil_list_a) (= Xs tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (= (@ (@ (@ tptp.lexordp_eq_a Less) Xs) tptp.nil_a) (= Xs tptp.nil_a))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Ys2 tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) tptp.nil_list_a) Ys2)))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Ys2 tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) tptp.nil_a) Ys2)))
% 0.25/0.69 (assert (= tptp.lexordp_eq_a tptp.lexordp_eq_a))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) Xs) Xs)))
% 0.25/0.69 (assert (forall ((A3 tptp.list_a) (P (-> tptp.list_a Bool))) (= (@ (@ tptp.member_list_a2 A3) (@ tptp.collect_list_a P)) (@ P A3))))
% 0.25/0.69 (assert (forall ((A3 tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a2 A3) (@ tptp.collect_a P)) (@ P A3))))
% 0.25/0.69 (assert (forall ((A4 tptp.set_list_a)) (= (@ tptp.collect_list_a (lambda ((X4 tptp.list_a)) (@ (@ tptp.member_list_a2 X4) A4))) A4)))
% 0.25/0.69 (assert (forall ((A4 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (@ (@ tptp.member_a2 X4) A4))) A4)))
% 0.25/0.69 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (@ (@ Less X3) Y) (@ (@ (@ tptp.lexordp_eq_list_a Less) (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.cons_list_a Y) Ys2)))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ Less X3) Y) (@ (@ (@ tptp.lexordp_eq_a Less) (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2)))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_eq_list_a Less))) (=> (not (@ (@ Less X3) Y)) (=> (not (@ (@ Less Y) X3)) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.cons_list_a Y) Ys2))))))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a Less))) (=> (not (@ (@ Less X3) Y)) (=> (not (@ (@ Less Y) X3)) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2))))))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Ys2 tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) tptp.nil_list_a) Ys2)))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (Ys2 tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) tptp.nil_a) Ys2)))
% 0.25/0.69 (assert (forall ((R (-> tptp.a tptp.list_a Bool)) (X3 tptp.a) (Y tptp.list_a) (Xs tptp.list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.listrelp_a_list_a R))) (=> (@ (@ R X3) Y) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_list_a Y) Ys2)))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.list_a tptp.a Bool)) (X3 tptp.list_a) (Y tptp.a) (Xs tptp.list_list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.listrelp_list_a_a R))) (=> (@ (@ R X3) Y) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2)))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.listre1221556159list_a R))) (=> (@ (@ R X3) Y) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.cons_list_a Y) Ys2)))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.listrelp_a_a R))) (=> (@ (@ R X3) Y) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2)))))))
% 0.25/0.69 (assert (forall ((R (-> tptp.a tptp.list_a Bool))) (@ (@ (@ tptp.listrelp_a_list_a R) tptp.nil_a) tptp.nil_list_a)))
% 0.25/0.69 (assert (forall ((R (-> tptp.list_a tptp.a Bool))) (@ (@ (@ tptp.listrelp_list_a_a R) tptp.nil_list_a) tptp.nil_a)))
% 0.25/0.69 (assert (forall ((R (-> tptp.list_a tptp.list_a Bool))) (@ (@ (@ tptp.listre1221556159list_a R) tptp.nil_list_a) tptp.nil_list_a)))
% 0.25/0.69 (assert (forall ((R (-> tptp.a tptp.a Bool))) (@ (@ (@ tptp.listrelp_a_a R) tptp.nil_a) tptp.nil_a)))
% 0.25/0.69 (assert (forall ((F (-> tptp.a tptp.list_a)) (A3 tptp.a) (As2 tptp.list_a) (Bs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.map_ta41997947list_a F))) (= (@ (@ _let_1 (@ (@ tptp.cons_a A3) As2)) Bs2) (@ (@ _let_1 As2) (@ (@ tptp.cons_list_a (@ F A3)) Bs2))))))
% 0.25/0.69 (assert (forall ((F (-> tptp.list_a tptp.a)) (A3 tptp.list_a) (As2 tptp.list_list_a) (Bs2 tptp.list_a)) (let ((_let_1 (@ tptp.map_ta2002079599st_a_a F))) (= (@ (@ _let_1 (@ (@ tptp.cons_list_a A3) As2)) Bs2) (@ (@ _let_1 As2) (@ (@ tptp.cons_a (@ F A3)) Bs2))))))
% 0.25/0.69 (assert (forall ((F (-> tptp.list_a tptp.list_a)) (A3 tptp.list_a) (As2 tptp.list_list_a) (Bs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.map_ta982122357list_a F))) (= (@ (@ _let_1 (@ (@ tptp.cons_list_a A3) As2)) Bs2) (@ (@ _let_1 As2) (@ (@ tptp.cons_list_a (@ F A3)) Bs2))))))
% 0.25/0.69 (assert (forall ((F (-> tptp.a tptp.a)) (A3 tptp.a) (As2 tptp.list_a) (Bs2 tptp.list_a)) (let ((_let_1 (@ tptp.map_tailrec_rev_a_a F))) (= (@ (@ _let_1 (@ (@ tptp.cons_a A3) As2)) Bs2) (@ (@ _let_1 As2) (@ (@ tptp.cons_a (@ F A3)) Bs2))))))
% 0.25/0.69 (assert (forall ((F (-> tptp.a tptp.a)) (Bs2 tptp.list_a)) (= (@ (@ (@ tptp.map_tailrec_rev_a_a F) tptp.nil_a) Bs2) Bs2)))
% 0.25/0.69 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a) (A2 tptp.list_list_a)) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) A1) A2) (=> (not (= A1 tptp.nil_list_a)) (=> (forall ((X tptp.list_a)) (=> (exists ((Xs2 tptp.list_list_a)) (= A1 (@ (@ tptp.cons_list_a X) Xs2))) (forall ((Y3 tptp.list_a)) (=> (exists ((Ys3 tptp.list_list_a)) (= A2 (@ (@ tptp.cons_list_a Y3) Ys3))) (not (@ (@ Less X) Y3)))))) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (=> (= A1 (@ (@ tptp.cons_list_a X) Xs2)) (forall ((Ys3 tptp.list_list_a)) (=> (= A2 (@ (@ tptp.cons_list_a Y3) Ys3)) (=> (not (@ (@ Less X) Y3)) (=> (not (@ (@ Less Y3) X)) (not (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs2) Ys3))))))))))))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (A1 tptp.list_a) (A2 tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_eq_a Less) A1) A2) (=> (not (= A1 tptp.nil_a)) (=> (forall ((X tptp.a)) (=> (exists ((Xs2 tptp.list_a)) (= A1 (@ (@ tptp.cons_a X) Xs2))) (forall ((Y3 tptp.a)) (=> (exists ((Ys3 tptp.list_a)) (= A2 (@ (@ tptp.cons_a Y3) Ys3))) (not (@ (@ Less X) Y3)))))) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X) Xs2)) (forall ((Ys3 tptp.list_a)) (=> (= A2 (@ (@ tptp.cons_a Y3) Ys3)) (=> (not (@ (@ Less X) Y3)) (=> (not (@ (@ Less Y3) X)) (not (@ (@ (@ tptp.lexordp_eq_a Less) Xs2) Ys3))))))))))))))
% 0.25/0.69 (assert (= tptp.lexordp_eq_list_a (lambda ((Less2 (-> tptp.list_a tptp.list_a Bool)) (A12 tptp.list_list_a) (A22 tptp.list_list_a)) (or (exists ((Ys tptp.list_list_a)) (and (= A12 tptp.nil_list_a) (= A22 Ys))) (exists ((X4 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X4) Xs3)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys)) (@ (@ Less2 X4) Y2))) (exists ((X4 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X4) Xs3)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys)) (not (@ (@ Less2 X4) Y2)) (not (@ (@ Less2 Y2) X4)) (@ (@ (@ tptp.lexordp_eq_list_a Less2) Xs3) Ys)))))))
% 0.25/0.69 (assert (= tptp.lexordp_eq_a (lambda ((Less2 (-> tptp.a tptp.a Bool)) (A12 tptp.list_a) (A22 tptp.list_a)) (or (exists ((Ys tptp.list_a)) (and (= A12 tptp.nil_a) (= A22 Ys))) (exists ((X4 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X4) Xs3)) (= A22 (@ (@ tptp.cons_a Y2) Ys)) (@ (@ Less2 X4) Y2))) (exists ((X4 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X4) Xs3)) (= A22 (@ (@ tptp.cons_a Y2) Ys)) (not (@ (@ Less2 X4) Y2)) (not (@ (@ Less2 Y2) X4)) (@ (@ (@ tptp.lexordp_eq_a Less2) Xs3) Ys)))))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X12 tptp.list_list_a) (X23 tptp.list_list_a) (P (-> tptp.list_list_a tptp.list_list_a Bool))) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) X12) X23) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ Less X) Y3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3)))) (=> (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (not (@ (@ Less X) Y3)) (=> (not (@ (@ Less Y3) X)) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3))))))) (@ (@ P X12) X23)))))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (X12 tptp.list_a) (X23 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.lexordp_eq_a Less) X12) X23) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ Less X) Y3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)))) (=> (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys3 tptp.list_a)) (=> (not (@ (@ Less X) Y3)) (=> (not (@ (@ Less Y3) X)) (=> (@ (@ (@ tptp.lexordp_eq_a Less) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3))))))) (@ (@ P X12) X23)))))))
% 0.25/0.69 (assert (= (@ tptp.product_lists_list_a tptp.nil_list_list_a) (@ (@ tptp.cons_list_list_a tptp.nil_list_a) tptp.nil_list_list_a)))
% 0.25/0.69 (assert (= (@ tptp.product_lists_a tptp.nil_list_a) (@ (@ tptp.cons_list_a tptp.nil_a) tptp.nil_list_a)))
% 0.25/0.69 (assert (= (@ tptp.subseqs_list_a tptp.nil_list_a) (@ (@ tptp.cons_list_list_a tptp.nil_list_a) tptp.nil_list_list_a)))
% 0.25/0.69 (assert (= (@ tptp.subseqs_a tptp.nil_a) (@ (@ tptp.cons_list_a tptp.nil_a) tptp.nil_list_a)))
% 0.25/0.69 (assert (forall ((A1 tptp.list_nat) (A2 tptp.list_nat)) (=> (@ (@ tptp.ord_lexordp_eq_nat A1) A2) (=> (not (= A1 tptp.nil_nat)) (=> (forall ((X tptp.nat)) (=> (exists ((Xs2 tptp.list_nat)) (= A1 (@ (@ tptp.cons_nat X) Xs2))) (forall ((Y3 tptp.nat)) (=> (exists ((Ys3 tptp.list_nat)) (= A2 (@ (@ tptp.cons_nat Y3) Ys3))) (not (@ (@ tptp.ord_less_nat X) Y3)))))) (not (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= A1 (@ (@ tptp.cons_nat X) Xs2)) (forall ((Ys3 tptp.list_nat)) (=> (= A2 (@ (@ tptp.cons_nat Y3) Ys3)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (=> (not (@ (@ tptp.ord_less_nat Y3) X)) (not (@ (@ tptp.ord_lexordp_eq_nat Xs2) Ys3))))))))))))))
% 0.25/0.69 (assert (= tptp.ord_lexordp_eq_nat (lambda ((A12 tptp.list_nat) (A22 tptp.list_nat)) (or (exists ((Ys tptp.list_nat)) (and (= A12 tptp.nil_nat) (= A22 Ys))) (exists ((X4 tptp.nat) (Y2 tptp.nat) (Xs3 tptp.list_nat) (Ys tptp.list_nat)) (and (= A12 (@ (@ tptp.cons_nat X4) Xs3)) (= A22 (@ (@ tptp.cons_nat Y2) Ys)) (@ (@ tptp.ord_less_nat X4) Y2))) (exists ((X4 tptp.nat) (Y2 tptp.nat) (Xs3 tptp.list_nat) (Ys tptp.list_nat)) (and (= A12 (@ (@ tptp.cons_nat X4) Xs3)) (= A22 (@ (@ tptp.cons_nat Y2) Ys)) (not (@ (@ tptp.ord_less_nat X4) Y2)) (not (@ (@ tptp.ord_less_nat Y2) X4)) (@ (@ tptp.ord_lexordp_eq_nat Xs3) Ys)))))))
% 0.25/0.69 (assert (forall ((X12 tptp.list_nat) (X23 tptp.list_nat) (P (-> tptp.list_nat tptp.list_nat Bool))) (=> (@ (@ tptp.ord_lexordp_eq_nat X12) X23) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P tptp.nil_nat) X_1)) (=> (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat X) Y3) (@ (@ P (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (=> (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (=> (not (@ (@ tptp.ord_less_nat Y3) X)) (=> (@ (@ tptp.ord_lexordp_eq_nat Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3))))))) (@ (@ P X12) X23)))))))
% 0.25/0.69 (assert (forall ((Y tptp.list_a)) (not (@ (@ tptp.member_list_a tptp.nil_list_a) Y))))
% 0.25/0.69 (assert (forall ((Y tptp.a)) (not (@ (@ tptp.member_a tptp.nil_a) Y))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (Y tptp.list_a)) (= (@ (@ tptp.member_list_a (@ (@ tptp.cons_list_a X3) Xs)) Y) (or (= X3 Y) (@ (@ tptp.member_list_a Xs) Y)))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a) (Y tptp.a)) (= (@ (@ tptp.member_a (@ (@ tptp.cons_a X3) Xs)) Y) (or (= X3 Y) (@ (@ tptp.member_a Xs) Y)))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_list_a) (Xa tptp.list_list_a) (Y tptp.list_list_a)) (=> (= (@ (@ tptp.splice_list_a X3) Xa) Y) (=> (=> (= X3 tptp.nil_list_a) (not (= Y Xa))) (not (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X))) (=> (= X3 (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice_list_a Xa) Xs2))))))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xa tptp.list_a) (Y tptp.list_a)) (=> (= (@ (@ tptp.splice_a X3) Xa) Y) (=> (=> (= X3 tptp.nil_a) (not (= Y Xa))) (not (forall ((X tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (=> (= X3 (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice_a Xa) Xs2))))))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a) (F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.bind_a_a (@ (@ tptp.cons_a X3) Xs)) F) (@ (@ tptp.append_a (@ F X3)) (@ (@ tptp.bind_a_a Xs) F)))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a) (F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.bind_a_list_a (@ (@ tptp.cons_a X3) Xs)) F) (@ (@ tptp.append_list_a (@ F X3)) (@ (@ tptp.bind_a_list_a Xs) F)))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.bind_list_a_a (@ (@ tptp.cons_list_a X3) Xs)) F) (@ (@ tptp.append_a (@ F X3)) (@ (@ tptp.bind_list_a_a Xs) F)))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.bind_list_a_list_a (@ (@ tptp.cons_list_a X3) Xs)) F) (@ (@ tptp.append_list_a (@ F X3)) (@ (@ tptp.bind_list_a_list_a Xs) F)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs2)) (= Ys2 Zs2)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs2)) (= Ys2 Zs2)))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_a) (Xs tptp.list_a) (Zs2 tptp.list_a)) (= (= (@ (@ tptp.append_a Ys2) Xs) (@ (@ tptp.append_a Zs2) Xs)) (= Ys2 Zs2))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a) (Zs2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Ys2) Xs) (@ (@ tptp.append_list_a Zs2) Xs)) (= Ys2 Zs2))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (@ (@ tptp.append_a (@ _let_1 Ys2)) Zs2) (@ _let_1 (@ (@ tptp.append_a Ys2) Zs2))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (= (@ (@ tptp.append_list_a (@ _let_1 Ys2)) Zs2) (@ _let_1 (@ (@ tptp.append_list_a Ys2) Zs2))))))
% 0.25/0.69 (assert (forall ((A3 tptp.list_a) (B tptp.list_a) (C tptp.list_a)) (let ((_let_1 (@ tptp.append_a A3))) (= (@ (@ tptp.append_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_a B) C))))))
% 0.25/0.69 (assert (forall ((A3 tptp.list_list_a) (B tptp.list_list_a) (C tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a A3))) (= (@ (@ tptp.append_list_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_list_a B) C))))))
% 0.25/0.69 (assert (forall ((A3 tptp.list_list_a)) (= (@ (@ tptp.append_list_a A3) tptp.nil_list_a) A3)))
% 0.25/0.69 (assert (forall ((A3 tptp.list_a)) (= (@ (@ tptp.append_a A3) tptp.nil_a) A3)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys2) tptp.nil_list_a) (and (= Xs tptp.nil_list_a) (= Ys2 tptp.nil_list_a)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) tptp.nil_a) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= tptp.nil_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (and (= Xs tptp.nil_list_a) (= Ys2 tptp.nil_list_a)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= tptp.nil_a (@ (@ tptp.append_a Xs) Ys2)) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a)) (= (= Ys2 (@ (@ tptp.append_list_a Xs) Ys2)) (= Xs tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (= (= Ys2 (@ (@ tptp.append_a Xs) Ys2)) (= Xs tptp.nil_a))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys2) Ys2) (= Xs tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) Ys2) (= Xs tptp.nil_a))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= Xs (@ (@ tptp.append_list_a Xs) Ys2)) (= Ys2 tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= Xs (@ (@ tptp.append_a Xs) Ys2)) (= Ys2 tptp.nil_a))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys2) Xs) (= Ys2 tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) Xs) (= Ys2 tptp.nil_a))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (= (@ (@ tptp.append_list_a Xs) tptp.nil_list_a) Xs)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (= (@ (@ tptp.append_a Xs) tptp.nil_a) Xs)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= (@ (@ tptp.splice_list_a Xs) Ys2) tptp.nil_list_a) (and (= Xs tptp.nil_list_a) (= Ys2 tptp.nil_list_a)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.splice_a Xs) Ys2) tptp.nil_a) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (= (@ (@ tptp.splice_list_a Xs) tptp.nil_list_a) Xs)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (= (@ (@ tptp.splice_a Xs) tptp.nil_a) Xs)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (F (-> tptp.nat tptp.list_a))) (= (@ (@ tptp.listIn1753026346list_a Xs) (@ (@ tptp.listIn1753026346list_a Ys2) F)) (@ (@ tptp.listIn1753026346list_a (@ (@ tptp.append_list_a Xs) Ys2)) F))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (F (-> tptp.nat tptp.a))) (= (@ (@ tptp.listIn1312259492pend_a Xs) (@ (@ tptp.listIn1312259492pend_a Ys2) F)) (@ (@ tptp.listIn1312259492pend_a (@ (@ tptp.append_a Xs) Ys2)) F))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (X3 tptp.list_a) (Ys2 tptp.list_list_a) (Y tptp.list_a)) (= (= (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a)) (@ (@ tptp.append_list_a Ys2) (@ (@ tptp.cons_list_a Y) tptp.nil_list_a))) (and (= Xs Ys2) (= X3 Y)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (X3 tptp.a) (Ys2 tptp.list_a) (Y tptp.a)) (= (= (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X3) tptp.nil_a)) (@ (@ tptp.append_a Ys2) (@ (@ tptp.cons_a Y) tptp.nil_a))) (and (= Xs Ys2) (= X3 Y)))))
% 0.25/0.69 (assert (forall ((X3 tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys2 tptp.list_nat)) (= (@ (@ tptp.ord_lexordp_eq_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)) (or (@ (@ tptp.ord_less_nat X3) Y) (and (not (@ (@ tptp.ord_less_nat Y) X3)) (@ (@ tptp.ord_lexordp_eq_nat Xs) Ys2))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a) (Ts tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) (@ (@ tptp.append_a Zs2) Ts)) (exists ((Us tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us))) (or (and (= Xs (@ (@ tptp.append_a Zs2) Us)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append_a Xs) Us) Zs2) (= Ys2 (@ _let_1 Ts)))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a) (Ts tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys2) (@ (@ tptp.append_list_a Zs2) Ts)) (exists ((Us tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Us))) (or (and (= Xs (@ (@ tptp.append_list_a Zs2) Us)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append_list_a Xs) Us) Zs2) (= Ys2 (@ _let_1 Ts)))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Xs1 tptp.list_a) (Zs2 tptp.list_a) (Ys2 tptp.list_a) (Us2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys2 (@ (@ tptp.append_a Xs1) Us2)) (= (@ _let_1 Ys2) (@ (@ tptp.append_a Zs2) Us2)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Xs1 tptp.list_list_a) (Zs2 tptp.list_list_a) (Ys2 tptp.list_list_a) (Us2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys2 (@ (@ tptp.append_list_a Xs1) Us2)) (= (@ _let_1 Ys2) (@ (@ tptp.append_list_a Zs2) Us2)))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (= (@ (@ tptp.append_list_a (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.append_list_a Xs) Ys2))))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ (@ tptp.append_a (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.append_a Xs) Ys2))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs1 tptp.list_list_a) (Ys2 tptp.list_list_a) (Xs tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs (@ (@ tptp.append_list_a Xs1) Zs2)) (= (@ _let_1 Xs) (@ (@ tptp.append_list_a Ys2) Zs2)))))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs1 tptp.list_a) (Ys2 tptp.list_a) (Xs tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs (@ (@ tptp.append_a Xs1) Zs2)) (= (@ _let_1 Xs) (@ (@ tptp.append_a Ys2) Zs2)))))))
% 0.25/0.69 (assert (forall ((A3 tptp.list_list_a)) (= (@ (@ tptp.append_list_a tptp.nil_list_a) A3) A3)))
% 0.25/0.69 (assert (forall ((A3 tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) A3) A3)))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_list_a)) (= (@ (@ tptp.append_list_a tptp.nil_list_a) Ys2) Ys2)))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) Ys2) Ys2)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (= Xs Ys2) (= Xs (@ (@ tptp.append_list_a tptp.nil_list_a) Ys2)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (= Xs Ys2) (= Xs (@ (@ tptp.append_a tptp.nil_a) Ys2)))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (U tptp.list_list_a) (V tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) U) (@ (@ tptp.append_list_a U) V))))
% 0.25/0.69 (assert (forall ((Less (-> tptp.a tptp.a Bool)) (U tptp.list_a) (V tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) U) (@ (@ tptp.append_a U) V))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (= (@ (@ tptp.splice_list_a (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.splice_list_a Ys2) Xs))))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ (@ tptp.splice_a (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.splice_a Ys2) Xs))))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_list_a)) (= (@ (@ tptp.splice_list_a tptp.nil_list_a) Ys2) Ys2)))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_a)) (= (@ (@ tptp.splice_a tptp.nil_a) Ys2) Ys2)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (P (-> tptp.list_list_a Bool))) (=> (not (= Xs tptp.nil_list_a)) (=> (forall ((X tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (=> (not (= Xs2 tptp.nil_list_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_list_a Xs2) (@ (@ tptp.cons_list_a X) tptp.nil_list_a)))))) (@ P Xs))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (P (-> tptp.list_a Bool))) (=> (not (= Xs tptp.nil_a)) (=> (forall ((X tptp.a)) (@ P (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (forall ((X tptp.a) (Xs2 tptp.list_a)) (=> (not (= Xs2 tptp.nil_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_a Xs2) (@ (@ tptp.cons_a X) tptp.nil_a)))))) (@ P Xs))))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a) (X3 tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a X3) Xs))) (= (= (@ (@ tptp.append_list_a Ys2) Zs2) _let_1) (or (and (= Ys2 tptp.nil_list_a) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_list_a)) (and (= Ys2 (@ (@ tptp.cons_list_a X3) Ys4)) (= (@ (@ tptp.append_list_a Ys4) Zs2) Xs))))))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_a) (Zs2 tptp.list_a) (X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a X3) Xs))) (= (= (@ (@ tptp.append_a Ys2) Zs2) _let_1) (or (and (= Ys2 tptp.nil_a) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_a)) (and (= Ys2 (@ (@ tptp.cons_a X3) Ys4)) (= (@ (@ tptp.append_a Ys4) Zs2) Xs))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a X3) Xs))) (= (= _let_1 (@ (@ tptp.append_list_a Ys2) Zs2)) (or (and (= Ys2 tptp.nil_list_a) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_list_a)) (and (= (@ (@ tptp.cons_list_a X3) Ys4) Ys2) (= Xs (@ (@ tptp.append_list_a Ys4) Zs2)))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a X3) Xs))) (= (= _let_1 (@ (@ tptp.append_a Ys2) Zs2)) (or (and (= Ys2 tptp.nil_a) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_a)) (and (= (@ (@ tptp.cons_a X3) Ys4) Ys2) (= Xs (@ (@ tptp.append_a Ys4) Zs2)))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (not (forall ((Ys3 tptp.list_list_a) (Y3 tptp.list_a)) (not (= Xs (@ (@ tptp.append_list_a Ys3) (@ (@ tptp.cons_list_a Y3) tptp.nil_list_a)))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (not (forall ((Ys3 tptp.list_a) (Y3 tptp.a)) (not (= Xs (@ (@ tptp.append_a Ys3) (@ (@ tptp.cons_a Y3) tptp.nil_a)))))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_list_a Bool)) (Xs tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_list_a Xs2) (@ (@ tptp.cons_list_a X) tptp.nil_list_a))))) (@ P Xs)))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_a Xs2) (@ (@ tptp.cons_a X) tptp.nil_a))))) (@ P Xs)))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (= (@ (@ tptp.append_list_a (@ _let_1 tptp.nil_list_a)) Xs) (@ _let_1 Xs)))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ (@ tptp.append_a (@ _let_1 tptp.nil_a)) Xs) (@ _let_1 Xs)))))
% 0.25/0.69 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (@ (@ tptp.ord_lexordp_eq_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)))))
% 0.25/0.69 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (=> (not (@ (@ tptp.ord_less_nat Y) X3)) (=> (@ (@ tptp.ord_lexordp_eq_nat Xs) Ys2) (@ (@ tptp.ord_lexordp_eq_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)))))))
% 0.25/0.69 (assert (forall ((F (-> tptp.a tptp.list_a)) (X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.maps_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs))))))
% 0.25/0.69 (assert (forall ((F (-> tptp.a tptp.list_list_a)) (X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.maps_a_list_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.append_list_a (@ F X3)) (@ _let_1 Xs))))))
% 0.25/0.69 (assert (forall ((F (-> tptp.list_a tptp.list_a)) (X3 tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.maps_list_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs))))))
% 0.25/0.69 (assert (forall ((F (-> tptp.list_a tptp.list_list_a)) (X3 tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.maps_list_a_list_a F))) (= (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.append_list_a (@ F X3)) (@ _let_1 Xs))))))
% 0.25/0.69 (assert (forall ((Xss2 tptp.list_list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (= Xss2 tptp.nil_list_list_a))) (= (= (@ tptp.concat_list_a Xss2) (@ (@ tptp.append_list_a Ys2) Zs2)) (and (=> _let_1 (and (= Ys2 tptp.nil_list_a) (= Zs2 tptp.nil_list_a))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_list_a) (Xs3 tptp.list_list_a) (Xs4 tptp.list_list_a) (Xss22 tptp.list_list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_list_a Xss1) (@ (@ tptp.cons_list_list_a (@ (@ tptp.append_list_a Xs3) Xs4)) Xss22))) (= Ys2 (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xss1)) Xs3)) (= Zs2 (@ (@ tptp.append_list_a Xs4) (@ tptp.concat_list_a Xss22)))))))))))
% 0.25/0.69 (assert (forall ((Xss2 tptp.list_list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (= Xss2 tptp.nil_list_a))) (= (= (@ tptp.concat_a Xss2) (@ (@ tptp.append_a Ys2) Zs2)) (and (=> _let_1 (and (= Ys2 tptp.nil_a) (= Zs2 tptp.nil_a))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_a) (Xs3 tptp.list_a) (Xs4 tptp.list_a) (Xss22 tptp.list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_a Xss1) (@ (@ tptp.cons_list_a (@ (@ tptp.append_a Xs3) Xs4)) Xss22))) (= Ys2 (@ (@ tptp.append_a (@ tptp.concat_a Xss1)) Xs3)) (= Zs2 (@ (@ tptp.append_a Xs4) (@ tptp.concat_a Xss22)))))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (= (@ tptp.rotate1_list_a (@ _let_1 Xs)) (@ (@ tptp.append_list_a Xs) (@ _let_1 tptp.nil_list_a))))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ tptp.rotate1_a (@ _let_1 Xs)) (@ (@ tptp.append_a Xs) (@ _let_1 tptp.nil_a))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (= (@ tptp.butlast_list_a (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a))) Xs)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (X3 tptp.a)) (= (@ tptp.butlast_a (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X3) tptp.nil_a))) Xs)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (= (@ tptp.last_list_a (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a))) X3)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (X3 tptp.a)) (= (@ tptp.last_a (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X3) tptp.nil_a))) X3)))
% 0.25/0.69 (assert (forall ((Kl tptp.list_list_a) (K tptp.list_a) (Kl2 tptp.set_list_list_a)) (=> (@ (@ tptp.member_list_list_a (@ (@ tptp.append_list_a Kl) (@ (@ tptp.cons_list_a K) tptp.nil_list_a))) Kl2) (@ (@ tptp.member_list_a2 K) (@ (@ tptp.bNF_Gr1046450207list_a Kl2) Kl)))))
% 0.25/0.69 (assert (forall ((Kl tptp.list_a) (K tptp.a) (Kl2 tptp.set_list_a)) (=> (@ (@ tptp.member_list_a2 (@ (@ tptp.append_a Kl) (@ (@ tptp.cons_a K) tptp.nil_a))) Kl2) (@ (@ tptp.member_a2 K) (@ (@ tptp.bNF_Greatest_Succ_a Kl2) Kl)))))
% 0.25/0.69 (assert (forall ((K tptp.list_a) (Kl2 tptp.set_list_list_a) (Kl tptp.list_list_a)) (=> (@ (@ tptp.member_list_a2 K) (@ (@ tptp.bNF_Gr1046450207list_a Kl2) Kl)) (@ (@ tptp.member_list_list_a (@ (@ tptp.append_list_a Kl) (@ (@ tptp.cons_list_a K) tptp.nil_list_a))) Kl2))))
% 0.25/0.69 (assert (forall ((K tptp.a) (Kl2 tptp.set_list_a) (Kl tptp.list_a)) (=> (@ (@ tptp.member_a2 K) (@ (@ tptp.bNF_Greatest_Succ_a Kl2) Kl)) (@ (@ tptp.member_list_a2 (@ (@ tptp.append_a Kl) (@ (@ tptp.cons_a K) tptp.nil_a))) Kl2))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (= (= (@ tptp.rotate1_list_a Xs) tptp.nil_list_a) (= Xs tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (= (= (@ tptp.rotate1_a Xs) tptp.nil_a) (= Xs tptp.nil_a))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a)) (=> (= Ys2 tptp.nil_list_a) (= (@ tptp.last_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ tptp.last_list_a Xs)))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (=> (= Ys2 tptp.nil_a) (= (@ tptp.last_a (@ (@ tptp.append_a Xs) Ys2)) (@ tptp.last_a Xs)))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a)) (=> (not (= Ys2 tptp.nil_list_a)) (= (@ tptp.last_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ tptp.last_list_a Ys2)))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (=> (not (= Ys2 tptp.nil_a)) (= (@ tptp.last_a (@ (@ tptp.append_a Xs) Ys2)) (@ tptp.last_a Ys2)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_list_a) (Ys2 tptp.list_list_list_a)) (= (@ tptp.concat_list_a (@ (@ tptp.append_list_list_a Xs) Ys2)) (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xs)) (@ tptp.concat_list_a Ys2)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (@ tptp.concat_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ (@ tptp.append_a (@ tptp.concat_a Xs)) (@ tptp.concat_a Ys2)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ (@ tptp.append_list_a (@ tptp.butlast_list_a Xs)) (@ (@ tptp.cons_list_a (@ tptp.last_list_a Xs)) tptp.nil_list_a)) Xs))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ (@ tptp.append_a (@ tptp.butlast_a Xs)) (@ (@ tptp.cons_a (@ tptp.last_a Xs)) tptp.nil_a)) Xs))))
% 0.25/0.69 (assert (= (@ tptp.butlast_list_a tptp.nil_list_a) tptp.nil_list_a))
% 0.25/0.69 (assert (= (@ tptp.butlast_a tptp.nil_a) tptp.nil_a))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (X3 tptp.list_a) (Ys2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a)) Ys2) (and (not (= Ys2 tptp.nil_list_a)) (= (@ tptp.butlast_list_a Ys2) Xs) (= (@ tptp.last_list_a Ys2) X3)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (X3 tptp.a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X3) tptp.nil_a)) Ys2) (and (not (= Ys2 tptp.nil_a)) (= (@ tptp.butlast_a Ys2) Xs) (= (@ tptp.last_a Ys2) X3)))))
% 0.25/0.69 (assert (= (@ tptp.rotate1_list_a tptp.nil_list_a) tptp.nil_list_a))
% 0.25/0.69 (assert (= (@ tptp.rotate1_a tptp.nil_a) tptp.nil_a))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (let ((_let_1 (@ tptp.last_list_a (@ (@ tptp.cons_list_a X3) Xs)))) (let ((_let_2 (= Xs tptp.nil_list_a))) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ tptp.last_list_a Xs))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.last_a (@ (@ tptp.cons_a X3) Xs)))) (let ((_let_2 (= Xs tptp.nil_a))) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ tptp.last_a Xs))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (=> (= Xs tptp.nil_list_a) (= (@ tptp.last_list_a (@ (@ tptp.cons_list_a X3) Xs)) X3))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (X3 tptp.a)) (=> (= Xs tptp.nil_a) (= (@ tptp.last_a (@ (@ tptp.cons_a X3) Xs)) X3))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ tptp.last_list_a (@ (@ tptp.cons_list_a X3) Xs)) (@ tptp.last_list_a Xs)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (X3 tptp.a)) (=> (not (= Xs tptp.nil_a)) (= (@ tptp.last_a (@ (@ tptp.cons_a X3) Xs)) (@ tptp.last_a Xs)))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.last_list_a (@ (@ tptp.append_list_a Xs) Ys2)))) (let ((_let_2 (= Ys2 tptp.nil_list_a))) (and (=> _let_2 (= _let_1 (@ tptp.last_list_a Xs))) (=> (not _let_2) (= _let_1 (@ tptp.last_list_a Ys2))))))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.last_a (@ (@ tptp.append_a Xs) Ys2)))) (let ((_let_2 (= Ys2 tptp.nil_a))) (and (=> _let_2 (= _let_1 (@ tptp.last_a Xs))) (=> (not _let_2) (= _let_1 (@ tptp.last_a Ys2))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (exists ((Ss tptp.list_list_a) (Xs5 tptp.list_list_a) (Ys5 tptp.list_list_a)) (and (= Xs (@ (@ tptp.append_list_a Xs5) Ss)) (= Ys2 (@ (@ tptp.append_list_a Ys5) Ss)) (or (= Xs5 tptp.nil_list_a) (= Ys5 tptp.nil_list_a) (not (= (@ tptp.last_list_a Xs5) (@ tptp.last_list_a Ys5))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (exists ((Ss tptp.list_a) (Xs5 tptp.list_a) (Ys5 tptp.list_a)) (and (= Xs (@ (@ tptp.append_a Xs5) Ss)) (= Ys2 (@ (@ tptp.append_a Ys5) Ss)) (or (= Xs5 tptp.nil_a) (= Ys5 tptp.nil_a) (not (= (@ tptp.last_a Xs5) (@ tptp.last_a Ys5))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (let ((_let_2 (@ tptp.butlast_list_a (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_list_a))) (and (=> _let_3 (= _let_2 tptp.nil_list_a)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_a Xs))))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.cons_a X3))) (let ((_let_2 (@ tptp.butlast_a (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_a))) (and (=> _let_3 (= _let_2 tptp.nil_a)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_a Xs))))))))))
% 0.25/0.69 (assert (= (@ tptp.concat_list_a tptp.nil_list_list_a) tptp.nil_list_a))
% 0.25/0.69 (assert (= (@ tptp.concat_a tptp.nil_list_a) tptp.nil_a))
% 0.25/0.69 (assert (forall ((X3 tptp.list_list_a) (Xs tptp.list_list_list_a)) (= (@ tptp.concat_list_a (@ (@ tptp.cons_list_list_a X3) Xs)) (@ (@ tptp.append_list_a X3) (@ tptp.concat_list_a Xs)))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a)) (= (@ tptp.concat_a (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.append_a X3) (@ tptp.concat_a Xs)))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (let ((_let_2 (@ tptp.butlast_list_a (@ _let_1 Ys2)))) (let ((_let_3 (= Ys2 tptp.nil_list_a))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_list_a Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_a Ys2))))))))))
% 0.25/0.69 (assert (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (let ((_let_2 (@ tptp.butlast_a (@ _let_1 Ys2)))) (let ((_let_3 (= Ys2 tptp.nil_a))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_a Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_a Ys2))))))))))
% 0.25/0.69 (assert (forall ((F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.maps_a_list_a F) tptp.nil_a) tptp.nil_list_a)))
% 0.25/0.69 (assert (forall ((F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.maps_list_a_a F) tptp.nil_list_a) tptp.nil_a)))
% 0.25/0.69 (assert (forall ((F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.maps_list_a_list_a F) tptp.nil_list_a) tptp.nil_list_a)))
% 0.25/0.69 (assert (forall ((F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.maps_a_a F) tptp.nil_a) tptp.nil_a)))
% 0.25/0.69 (assert (forall ((Xss2 tptp.list_list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a)) (=> (= (@ tptp.concat_list_a Xss2) (@ (@ tptp.append_list_a Ys2) Zs2)) (=> (not (= Xss2 tptp.nil_list_list_a)) (exists ((Xss12 tptp.list_list_list_a) (Xs2 tptp.list_list_a) (Xs5 tptp.list_list_a) (Xss23 tptp.list_list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_list_a Xss12) (@ (@ tptp.cons_list_list_a (@ (@ tptp.append_list_a Xs2) Xs5)) Xss23))) (= Ys2 (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xss12)) Xs2)) (= Zs2 (@ (@ tptp.append_list_a Xs5) (@ tptp.concat_list_a Xss23)))))))))
% 0.25/0.69 (assert (forall ((Xss2 tptp.list_list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a)) (=> (= (@ tptp.concat_a Xss2) (@ (@ tptp.append_a Ys2) Zs2)) (=> (not (= Xss2 tptp.nil_list_a)) (exists ((Xss12 tptp.list_list_a) (Xs2 tptp.list_a) (Xs5 tptp.list_a) (Xss23 tptp.list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_a Xss12) (@ (@ tptp.cons_list_a (@ (@ tptp.append_a Xs2) Xs5)) Xss23))) (= Ys2 (@ (@ tptp.append_a (@ tptp.concat_a Xss12)) Xs2)) (= Zs2 (@ (@ tptp.append_a Xs5) (@ tptp.concat_a Xss23)))))))))
% 0.25/0.69 (assert (forall ((Kl2 tptp.set_list_list_a) (K tptp.list_a)) (let ((_let_1 (@ tptp.member_list_list_a tptp.nil_list_a))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member_list_a2 K) (@ (@ tptp.bNF_Gr1046450207list_a Kl2) tptp.nil_list_a)) (@ _let_1 (@ (@ tptp.bNF_Gr1972240547list_a Kl2) K)))))))
% 0.25/0.69 (assert (forall ((Kl2 tptp.set_list_a) (K tptp.a)) (let ((_let_1 (@ tptp.member_list_a2 tptp.nil_a))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member_a2 K) (@ (@ tptp.bNF_Greatest_Succ_a Kl2) tptp.nil_a)) (@ _let_1 (@ (@ tptp.bNF_Greatest_Shift_a Kl2) K)))))))
% 0.25/0.69 (assert (forall ((Kl2 tptp.set_list_list_a) (K tptp.list_a) (Kl tptp.list_list_a)) (= (@ (@ tptp.bNF_Gr1046450207list_a (@ (@ tptp.bNF_Gr1972240547list_a Kl2) K)) Kl) (@ (@ tptp.bNF_Gr1046450207list_a Kl2) (@ (@ tptp.cons_list_a K) Kl)))))
% 0.25/0.69 (assert (forall ((Kl2 tptp.set_list_a) (K tptp.a) (Kl tptp.list_a)) (= (@ (@ tptp.bNF_Greatest_Succ_a (@ (@ tptp.bNF_Greatest_Shift_a Kl2) K)) Kl) (@ (@ tptp.bNF_Greatest_Succ_a Kl2) (@ (@ tptp.cons_a K) Kl)))))
% 0.25/0.69 (assert (= tptp.concat_list_a (lambda ((Xss3 tptp.list_list_list_a)) (@ (@ (@ tptp.foldr_769741863list_a tptp.append_list_a) Xss3) tptp.nil_list_a))))
% 0.25/0.69 (assert (= tptp.concat_a (lambda ((Xss3 tptp.list_list_a)) (@ (@ (@ tptp.foldr_list_a_list_a tptp.append_a) Xss3) tptp.nil_a))))
% 0.25/0.69 (assert (forall ((F (-> tptp.list_a tptp.list_a tptp.list_a)) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (A3 tptp.list_a)) (let ((_let_1 (@ tptp.foldr_list_a_list_a F))) (= (@ (@ _let_1 (@ (@ tptp.append_list_a Xs) Ys2)) A3) (@ (@ _let_1 Xs) (@ (@ _let_1 Ys2) A3))))))
% 0.25/0.69 (assert (forall ((Kl tptp.list_list_a) (Kl2 tptp.set_list_list_a) (K tptp.list_a)) (=> (@ (@ tptp.member_list_list_a Kl) (@ (@ tptp.bNF_Gr1972240547list_a Kl2) K)) (@ (@ tptp.member_list_list_a (@ (@ tptp.cons_list_a K) Kl)) Kl2))))
% 0.25/0.69 (assert (forall ((Kl tptp.list_a) (Kl2 tptp.set_list_a) (K tptp.a)) (=> (@ (@ tptp.member_list_a2 Kl) (@ (@ tptp.bNF_Greatest_Shift_a Kl2) K)) (@ (@ tptp.member_list_a2 (@ (@ tptp.cons_a K) Kl)) Kl2))))
% 0.25/0.69 (assert (= tptp.list_strict_asc_nat (@ tptp.list_ord_nat tptp.ord_less_nat)))
% 0.25/0.69 (assert (= tptp.ord_lexordp_nat (lambda ((Xs3 tptp.list_nat) (Ys tptp.list_nat)) (or (exists ((X4 tptp.nat) (Vs tptp.list_nat)) (= Ys (@ (@ tptp.append_nat Xs3) (@ (@ tptp.cons_nat X4) Vs)))) (exists ((Us tptp.list_nat) (A5 tptp.nat) (B2 tptp.nat) (Vs tptp.list_nat) (Ws tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Us))) (and (@ (@ tptp.ord_less_nat A5) B2) (= Xs3 (@ _let_1 (@ (@ tptp.cons_nat A5) Vs))) (= Ys (@ _let_1 (@ (@ tptp.cons_nat B2) Ws))))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Us2 tptp.list_nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Us2))) (=> (@ (@ tptp.ord_less_nat X3) Y) (@ (@ tptp.ord_lexordp_nat (@ _let_1 (@ (@ tptp.cons_nat X3) Xs))) (@ _let_1 (@ (@ tptp.cons_nat Y) Ys2)))))))
% 0.25/0.69 (assert (forall ((X3 tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys2 tptp.list_nat)) (= (@ (@ tptp.ord_lexordp_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)) (or (@ (@ tptp.ord_less_nat X3) Y) (and (not (@ (@ tptp.ord_less_nat Y) X3)) (@ (@ tptp.ord_lexordp_nat Xs) Ys2))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ tptp.hd_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ tptp.hd_list_a Xs)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ tptp.hd_a (@ (@ tptp.append_a Xs) Ys2)) (@ tptp.hd_a Xs)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_nat)) (=> (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))) (not (@ (@ tptp.ord_lexordp_nat Xs) Xs)))))
% 0.25/0.69 (assert (forall ((X21 tptp.list_a) (X22 tptp.list_list_a)) (= (@ tptp.hd_list_a (@ (@ tptp.cons_list_a X21) X22)) X21)))
% 0.25/0.69 (assert (forall ((X21 tptp.a) (X22 tptp.list_a)) (= (@ tptp.hd_a (@ (@ tptp.cons_a X21) X22)) X21)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_list_a)) (let ((_let_1 (@ tptp.hd_list_list_a Xs))) (=> (not (= Xs tptp.nil_list_list_a)) (=> (not (= _let_1 tptp.nil_list_a)) (= (@ tptp.hd_list_a (@ tptp.concat_list_a Xs)) (@ tptp.hd_list_a _let_1)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.hd_list_a Xs))) (=> (not (= Xs tptp.nil_list_a)) (=> (not (= _let_1 tptp.nil_a)) (= (@ tptp.hd_a (@ tptp.concat_a Xs)) (@ tptp.hd_a _let_1)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.hd_list_a (@ (@ tptp.append_list_a Xs) Ys2)))) (let ((_let_2 (= Xs tptp.nil_list_a))) (and (=> _let_2 (= _let_1 (@ tptp.hd_list_a Ys2))) (=> (not _let_2) (= _let_1 (@ tptp.hd_list_a Xs))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.hd_a (@ (@ tptp.append_a Xs) Ys2)))) (let ((_let_2 (= Xs tptp.nil_a))) (and (=> _let_2 (= _let_1 (@ tptp.hd_a Ys2))) (=> (not _let_2) (= _let_1 (@ tptp.hd_a Xs))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (exists ((Ps tptp.list_list_a) (Xs5 tptp.list_list_a) (Ys5 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Ps))) (and (= Xs (@ _let_1 Xs5)) (= Ys2 (@ _let_1 Ys5)) (or (= Xs5 tptp.nil_list_a) (= Ys5 tptp.nil_list_a) (not (= (@ tptp.hd_list_a Xs5) (@ tptp.hd_list_a Ys5)))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (exists ((Ps tptp.list_a) (Xs5 tptp.list_a) (Ys5 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Ps))) (and (= Xs (@ _let_1 Xs5)) (= Ys2 (@ _let_1 Ys5)) (or (= Xs5 tptp.nil_a) (= Ys5 tptp.nil_a) (not (= (@ tptp.hd_a Xs5) (@ tptp.hd_a Ys5)))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (@ (@ tptp.ord_lexordp_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)))))
% 0.25/0.69 (assert (forall ((X3 tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (=> (not (@ (@ tptp.ord_less_nat Y) X3)) (=> (@ (@ tptp.ord_lexordp_nat Xs) Ys2) (@ (@ tptp.ord_lexordp_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_nat) (Us2 tptp.list_nat) (Vs2 tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Xs))) (=> (@ (@ tptp.ord_lexordp_nat (@ _let_1 Us2)) (@ _let_1 Vs2)) (=> (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (@ (@ tptp.ord_lexordp_nat Us2) Vs2))))))
% 0.25/0.69 (assert (forall ((A1 tptp.list_nat) (A2 tptp.list_nat)) (=> (@ (@ tptp.ord_lexordp_nat A1) A2) (=> (=> (= A1 tptp.nil_nat) (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (not (= A2 (@ (@ tptp.cons_nat Y3) Ys3))))) (=> (forall ((X tptp.nat)) (=> (exists ((Xs2 tptp.list_nat)) (= A1 (@ (@ tptp.cons_nat X) Xs2))) (forall ((Y3 tptp.nat)) (=> (exists ((Ys3 tptp.list_nat)) (= A2 (@ (@ tptp.cons_nat Y3) Ys3))) (not (@ (@ tptp.ord_less_nat X) Y3)))))) (not (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= A1 (@ (@ tptp.cons_nat X) Xs2)) (forall ((Ys3 tptp.list_nat)) (=> (= A2 (@ (@ tptp.cons_nat Y3) Ys3)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (=> (not (@ (@ tptp.ord_less_nat Y3) X)) (not (@ (@ tptp.ord_lexordp_nat Xs2) Ys3))))))))))))))
% 0.25/0.69 (assert (= tptp.ord_lexordp_nat (lambda ((A12 tptp.list_nat) (A22 tptp.list_nat)) (or (exists ((Y2 tptp.nat) (Ys tptp.list_nat)) (and (= A12 tptp.nil_nat) (= A22 (@ (@ tptp.cons_nat Y2) Ys)))) (exists ((X4 tptp.nat) (Y2 tptp.nat) (Xs3 tptp.list_nat) (Ys tptp.list_nat)) (and (= A12 (@ (@ tptp.cons_nat X4) Xs3)) (= A22 (@ (@ tptp.cons_nat Y2) Ys)) (@ (@ tptp.ord_less_nat X4) Y2))) (exists ((X4 tptp.nat) (Y2 tptp.nat) (Xs3 tptp.list_nat) (Ys tptp.list_nat)) (and (= A12 (@ (@ tptp.cons_nat X4) Xs3)) (= A22 (@ (@ tptp.cons_nat Y2) Ys)) (not (@ (@ tptp.ord_less_nat X4) Y2)) (not (@ (@ tptp.ord_less_nat Y2) X4)) (@ (@ tptp.ord_lexordp_nat Xs3) Ys)))))))
% 0.25/0.69 (assert (forall ((X12 tptp.list_nat) (X23 tptp.list_nat) (P (-> tptp.list_nat tptp.list_nat Bool))) (=> (@ (@ tptp.ord_lexordp_nat X12) X23) (=> (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_nat Y3) Ys3))) (=> (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat X) Y3) (@ (@ P (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (=> (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (=> (not (@ (@ tptp.ord_less_nat Y3) X)) (=> (@ (@ tptp.ord_lexordp_nat Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3))))))) (@ (@ P X12) X23)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_lexordp_nat Xs) Ys2) (=> (=> (= Xs tptp.nil_nat) (forall ((Y3 tptp.nat) (Ys5 tptp.list_nat)) (not (= Ys2 (@ (@ tptp.cons_nat Y3) Ys5))))) (=> (forall ((X tptp.nat)) (=> (exists ((Xs5 tptp.list_nat)) (= Xs (@ (@ tptp.cons_nat X) Xs5))) (forall ((Y3 tptp.nat)) (=> (exists ((Ys5 tptp.list_nat)) (= Ys2 (@ (@ tptp.cons_nat Y3) Ys5))) (not (@ (@ tptp.ord_less_nat X) Y3)))))) (not (forall ((X tptp.nat) (Xs5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X) Xs5)) (forall ((Ys5 tptp.list_nat)) (=> (= Ys2 (@ (@ tptp.cons_nat X) Ys5)) (not (@ (@ tptp.ord_lexordp_nat Xs5) Ys5))))))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat) (P (-> tptp.list_nat tptp.list_nat Bool))) (=> (@ (@ tptp.ord_lexordp_nat Xs) Ys2) (=> (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_nat Y3) Ys3))) (=> (forall ((X tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat X) Y3) (@ (@ P (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (=> (forall ((X tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X))) (=> (@ (@ tptp.ord_lexordp_nat Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ _let_1 Xs2)) (@ _let_1 Ys3)))))) (@ (@ P Xs) Ys2)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (@ tptp.distinct_adj_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (and (@ tptp.distinct_adj_list_a Xs) (@ tptp.distinct_adj_list_a Ys2) (or (= Xs tptp.nil_list_a) (= Ys2 tptp.nil_list_a) (not (= (@ tptp.last_list_a Xs) (@ tptp.hd_list_a Ys2))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (@ tptp.distinct_adj_a (@ (@ tptp.append_a Xs) Ys2)) (and (@ tptp.distinct_adj_a Xs) (@ tptp.distinct_adj_a Ys2) (or (= Xs tptp.nil_a) (= Ys2 tptp.nil_a) (not (= (@ tptp.last_a Xs) (@ tptp.hd_a Ys2))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ tptp.rotate1_list_a Xs) (@ (@ tptp.append_list_a (@ tptp.tl_list_a Xs)) (@ (@ tptp.cons_list_a (@ tptp.hd_list_a Xs)) tptp.nil_list_a))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ tptp.rotate1_a Xs) (@ (@ tptp.append_a (@ tptp.tl_a Xs)) (@ (@ tptp.cons_a (@ tptp.hd_a Xs)) tptp.nil_a))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.successively_list_a P))) (= (@ _let_1 (@ (@ tptp.append_list_a Xs) Ys2)) (and (@ _let_1 Xs) (@ _let_1 Ys2) (or (= Xs tptp.nil_list_a) (= Ys2 tptp.nil_list_a) (@ (@ P (@ tptp.last_list_a Xs)) (@ tptp.hd_list_a Ys2))))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.a tptp.a Bool)) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.successively_a P))) (= (@ _let_1 (@ (@ tptp.append_a Xs) Ys2)) (and (@ _let_1 Xs) (@ _let_1 Ys2) (or (= Xs tptp.nil_a) (= Ys2 tptp.nil_a) (@ (@ P (@ tptp.last_a Xs)) (@ tptp.hd_a Ys2))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y) Xs))) (= (@ tptp.distinct_adj_list_a (@ (@ tptp.cons_list_a X3) _let_1)) (and (not (= X3 Y)) (@ tptp.distinct_adj_list_a _let_1))))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Y tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y) Xs))) (= (@ tptp.distinct_adj_a (@ (@ tptp.cons_a X3) _let_1)) (and (not (= X3 Y)) (@ tptp.distinct_adj_a _let_1))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ tptp.tl_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ (@ tptp.append_list_a (@ tptp.tl_list_a Xs)) Ys2)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ tptp.tl_a (@ (@ tptp.append_a Xs) Ys2)) (@ (@ tptp.append_a (@ tptp.tl_a Xs)) Ys2)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ (@ tptp.cons_list_a (@ tptp.hd_list_a Xs)) (@ tptp.tl_list_a Xs)) Xs))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ (@ tptp.cons_a (@ tptp.hd_a Xs)) (@ tptp.tl_a Xs)) Xs))))
% 0.25/0.69 (assert (forall ((List tptp.list_list_a)) (=> (not (= List tptp.nil_list_a)) (= (@ (@ tptp.cons_list_a (@ tptp.hd_list_a List)) (@ tptp.tl_list_a List)) List))))
% 0.25/0.69 (assert (forall ((List tptp.list_a)) (=> (not (= List tptp.nil_a)) (= (@ (@ tptp.cons_a (@ tptp.hd_a List)) (@ tptp.tl_a List)) List))))
% 0.25/0.69 (assert (forall ((X21 tptp.list_a) (X22 tptp.list_list_a)) (= (@ tptp.tl_list_a (@ (@ tptp.cons_list_a X21) X22)) X22)))
% 0.25/0.69 (assert (forall ((X21 tptp.a) (X22 tptp.list_a)) (= (@ tptp.tl_a (@ (@ tptp.cons_a X21) X22)) X22)))
% 0.25/0.69 (assert (= (@ tptp.tl_list_a tptp.nil_list_a) tptp.nil_list_a))
% 0.25/0.69 (assert (= (@ tptp.tl_a tptp.nil_a) tptp.nil_a))
% 0.25/0.69 (assert (forall ((X3 (-> tptp.list_a tptp.list_a Bool)) (Xa tptp.list_list_a)) (=> (not (@ (@ tptp.successively_list_a X3) Xa)) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_list_a X) _let_1)) (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_list_a X3) _let_1)))))))))
% 0.25/0.69 (assert (forall ((X3 (-> tptp.a tptp.a Bool)) (Xa tptp.list_a)) (=> (not (@ (@ tptp.successively_a X3) Xa)) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_a X) _let_1)) (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_a X3) _let_1)))))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y) Xs))) (let ((_let_2 (@ tptp.successively_list_a P))) (= (@ _let_2 (@ (@ tptp.cons_list_a X3) _let_1)) (and (@ (@ P X3) Y) (@ _let_2 _let_1)))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Y tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y) Xs))) (let ((_let_2 (@ tptp.successively_a P))) (= (@ _let_2 (@ (@ tptp.cons_a X3) _let_1)) (and (@ (@ P X3) Y) (@ _let_2 _let_1)))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a tptp.list_a Bool))) (@ (@ tptp.successively_list_a P) tptp.nil_list_a)))
% 0.25/0.69 (assert (forall ((P (-> tptp.a tptp.a Bool))) (@ (@ tptp.successively_a P) tptp.nil_a)))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (@ tptp.distinct_adj_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ tptp.distinct_adj_list_a Xs))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ tptp.distinct_adj_a (@ (@ tptp.append_a Xs) Ys2)) (@ tptp.distinct_adj_a Xs))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (@ tptp.distinct_adj_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ tptp.distinct_adj_list_a Ys2))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ tptp.distinct_adj_a (@ (@ tptp.append_a Xs) Ys2)) (@ tptp.distinct_adj_a Ys2))))
% 0.25/0.69 (assert (@ tptp.distinct_adj_list_a tptp.nil_list_a))
% 0.25/0.69 (assert (@ tptp.distinct_adj_a tptp.nil_a))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Xs tptp.list_list_a)) (=> (@ tptp.distinct_adj_list_a (@ (@ tptp.cons_list_a X3) Xs)) (@ tptp.distinct_adj_list_a Xs))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a)) (=> (@ tptp.distinct_adj_a (@ (@ tptp.cons_a X3) Xs)) (@ tptp.distinct_adj_a Xs))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (= (@ tptp.butlast_a (@ tptp.tl_a Xs)) (@ tptp.tl_a (@ tptp.butlast_a Xs)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (= (= (@ tptp.tl_list_a Xs) tptp.nil_list_a) (or (= Xs tptp.nil_list_a) (exists ((X4 tptp.list_a)) (= Xs (@ (@ tptp.cons_list_a X4) tptp.nil_list_a)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (= (= (@ tptp.tl_a Xs) tptp.nil_a) (or (= Xs tptp.nil_a) (exists ((X4 tptp.a)) (= Xs (@ (@ tptp.cons_a X4) tptp.nil_a)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (= (= tptp.nil_list_a (@ tptp.tl_list_a Xs)) (or (= Xs tptp.nil_list_a) (exists ((X4 tptp.list_a)) (= Xs (@ (@ tptp.cons_list_a X4) tptp.nil_list_a)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (= (= tptp.nil_a (@ tptp.tl_a Xs)) (or (= Xs tptp.nil_a) (exists ((X4 tptp.a)) (= Xs (@ (@ tptp.cons_a X4) tptp.nil_a)))))))
% 0.25/0.69 (assert (forall ((List tptp.list_list_a) (List2 tptp.list_list_a)) (let ((_let_1 (= List2 tptp.nil_list_a))) (let ((_let_2 (= List tptp.nil_list_a))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (and (= (@ tptp.hd_list_a List) (@ tptp.hd_list_a List2)) (= (@ tptp.tl_list_a List) (@ tptp.tl_list_a List2))))) (= List List2)))))))
% 0.25/0.69 (assert (forall ((List tptp.list_a) (List2 tptp.list_a)) (let ((_let_1 (= List2 tptp.nil_a))) (let ((_let_2 (= List tptp.nil_a))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (and (= (@ tptp.hd_a List) (@ tptp.hd_a List2)) (= (@ tptp.tl_a List) (@ tptp.tl_a List2))))) (= List List2)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.tl_list_a Xs))) (=> (or (= Xs tptp.nil_list_a) (not (= _let_1 tptp.nil_list_a))) (= (@ tptp.last_list_a _let_1) (@ tptp.last_list_a Xs))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (let ((_let_1 (@ tptp.tl_a Xs))) (=> (or (= Xs tptp.nil_a) (not (= _let_1 tptp.nil_a))) (= (@ tptp.last_a _let_1) (@ tptp.last_a Xs))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a)) (@ (@ tptp.successively_list_a P) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((P (-> tptp.a tptp.a Bool)) (X3 tptp.a)) (@ (@ tptp.successively_a P) (@ (@ tptp.cons_a X3) tptp.nil_a))))
% 0.25/0.69 (assert (forall ((X3 (-> tptp.list_a tptp.list_a Bool)) (Xa tptp.list_list_a) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ (@ tptp.successively_list_a X3) Xa) Y) (=> (=> (= Xa tptp.nil_list_a) _let_1) (=> (=> (exists ((X tptp.list_a)) (= Xa (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) _let_1) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_list_a X) _let_1)) (= Y (not (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_list_a X3) _let_1))))))))))))))
% 0.25/0.69 (assert (forall ((X3 (-> tptp.a tptp.a Bool)) (Xa tptp.list_a) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ (@ tptp.successively_a X3) Xa) Y) (=> (=> (= Xa tptp.nil_a) _let_1) (=> (=> (exists ((X tptp.a)) (= Xa (@ (@ tptp.cons_a X) tptp.nil_a))) _let_1) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_a X) _let_1)) (= Y (not (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_a X3) _let_1))))))))))))))
% 0.25/0.69 (assert (forall ((X3 (-> tptp.list_a tptp.list_a Bool)) (Xa tptp.list_list_a)) (=> (@ (@ tptp.successively_list_a X3) Xa) (=> (not (= Xa tptp.nil_list_a)) (=> (forall ((X tptp.list_a)) (not (= Xa (@ (@ tptp.cons_list_a X) tptp.nil_list_a)))) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_list_a X) _let_1)) (not (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_list_a X3) _let_1))))))))))))
% 0.25/0.69 (assert (forall ((X3 (-> tptp.a tptp.a Bool)) (Xa tptp.list_a)) (=> (@ (@ tptp.successively_a X3) Xa) (=> (not (= Xa tptp.nil_a)) (=> (forall ((X tptp.a)) (not (= Xa (@ (@ tptp.cons_a X) tptp.nil_a)))) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_a X) _let_1)) (not (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_a X3) _let_1))))))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a)) (@ tptp.distinct_adj_list_a (@ (@ tptp.cons_list_a X3) tptp.nil_list_a))))
% 0.25/0.69 (assert (forall ((X3 tptp.a)) (@ tptp.distinct_adj_a (@ (@ tptp.cons_a X3) tptp.nil_a))))
% 0.25/0.69 (assert (forall ((List tptp.list_a)) (=> (not (= List tptp.nil_a)) (= List (@ (@ tptp.cons_a (@ tptp.hd_a List)) (@ tptp.tl_a List))))))
% 0.25/0.69 (assert (forall ((P (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.successively_a P))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (or (= Xs tptp.nil_a) (and (@ (@ P X3) (@ tptp.hd_a Xs)) (@ _let_1 Xs)))))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a)) (= (@ tptp.distinct_adj_a (@ (@ tptp.cons_a X3) Xs)) (or (= Xs tptp.nil_a) (and (not (= X3 (@ tptp.hd_a Xs))) (@ tptp.distinct_adj_a Xs))))))
% 0.25/0.69 (assert (forall ((Z tptp.a) (Zs2 tptp.list_a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.shuffles_a Xs))) (let ((_let_2 (@ tptp.member_list_a2 Zs2))) (= (@ (@ tptp.member_list_a2 (@ (@ tptp.cons_a Z) Zs2)) (@ _let_1 Ys2)) (or (and (not (= Xs tptp.nil_a)) (= (@ tptp.hd_a Xs) Z) (@ _let_2 (@ (@ tptp.shuffles_a (@ tptp.tl_a Xs)) Ys2))) (and (not (= Ys2 tptp.nil_a)) (= (@ tptp.hd_a Ys2) Z) (@ _let_2 (@ _let_1 (@ tptp.tl_a Ys2))))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (F (-> tptp.a tptp.a tptp.a)) (Y tptp.a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.map2_a_a_a F))) (=> (not (= Xs tptp.nil_a)) (= (@ (@ _let_1 Xs) (@ (@ tptp.cons_a Y) Ys2)) (@ (@ tptp.cons_a (@ (@ F (@ tptp.hd_a Xs)) Y)) (@ (@ _let_1 (@ tptp.tl_a Xs)) Ys2)))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (@ (@ tptp.member_list_a2 tptp.nil_a) (@ (@ tptp.shuffles_a Xs) Ys2)) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))))
% 0.25/0.69 (assert (forall ((Zs2 tptp.list_a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ tptp.member_list_a2 Zs2) (@ (@ tptp.shuffles_a Xs) Ys2)) (=> (=> (= Zs2 Xs) (not (= Ys2 tptp.nil_a))) (=> (=> (= Zs2 Ys2) (not (= Xs tptp.nil_a))) (=> (forall ((X tptp.a) (Xs5 tptp.list_a)) (=> (= Xs (@ (@ tptp.cons_a X) Xs5)) (forall ((Z2 tptp.a) (Zs3 tptp.list_a)) (=> (= Zs2 (@ (@ tptp.cons_a Z2) Zs3)) (=> (= X Z2) (not (@ (@ tptp.member_list_a2 Zs3) (@ (@ tptp.shuffles_a Xs5) Ys2)))))))) (not (forall ((Y3 tptp.a) (Ys5 tptp.list_a)) (=> (= Ys2 (@ (@ tptp.cons_a Y3) Ys5)) (forall ((Z2 tptp.a) (Zs3 tptp.list_a)) (=> (= Zs2 (@ (@ tptp.cons_a Z2) Zs3)) (=> (= Y3 Z2) (not (@ (@ tptp.member_list_a2 Zs3) (@ (@ tptp.shuffles_a Xs) Ys5)))))))))))))))
% 0.25/0.69 (assert (forall ((F (-> tptp.a tptp.a tptp.a)) (X3 tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.map2_a_a_a F))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2)) (@ (@ tptp.cons_a (@ (@ F X3) Y)) (@ (@ _let_1 Xs) Ys2))))))
% 0.25/0.69 (assert (forall ((Zs2 tptp.list_a) (Xs tptp.list_a) (Ys2 tptp.list_a) (Z tptp.a)) (let ((_let_1 (@ tptp.cons_a Z))) (=> (@ (@ tptp.member_list_a2 Zs2) (@ (@ tptp.shuffles_a Xs) Ys2)) (@ (@ tptp.member_list_a2 (@ _let_1 Zs2)) (@ (@ tptp.shuffles_a (@ _let_1 Xs)) Ys2))))))
% 0.25/0.69 (assert (forall ((Zs2 tptp.list_a) (Xs tptp.list_a) (Ys2 tptp.list_a) (Z tptp.a)) (let ((_let_1 (@ tptp.cons_a Z))) (let ((_let_2 (@ tptp.shuffles_a Xs))) (=> (@ (@ tptp.member_list_a2 Zs2) (@ _let_2 Ys2)) (@ (@ tptp.member_list_a2 (@ _let_1 Zs2)) (@ _let_2 (@ _let_1 Ys2))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (= Xs tptp.nil_a) (=> (= Ys2 tptp.nil_a) (@ (@ tptp.member_list_a2 tptp.nil_a) (@ (@ tptp.shuffles_a Xs) Ys2))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (F (-> tptp.a tptp.a tptp.a)) (Y tptp.a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.map2_a_a_a F))) (let ((_let_2 (@ (@ _let_1 Xs) (@ (@ tptp.cons_a Y) Ys2)))) (let ((_let_3 (= Xs tptp.nil_a))) (and (=> _let_3 (= _let_2 tptp.nil_a)) (=> (not _let_3) (= _let_2 (@ (@ tptp.cons_a (@ (@ F (@ tptp.hd_a Xs)) Y)) (@ (@ _let_1 (@ tptp.tl_a Xs)) Ys2))))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (or (= Xs tptp.nil_a) (= Ys2 tptp.nil_a) (not (= (@ tptp.last_a Xs) (@ tptp.hd_a Ys2)))) (= (@ tptp.remdups_adj_a (@ (@ tptp.append_a Xs) Ys2)) (@ (@ tptp.append_a (@ tptp.remdups_adj_a Xs)) (@ tptp.remdups_adj_a Ys2))))))
% 0.25/0.69 (assert (forall ((Xs_1 tptp.list_a) (X3 tptp.a) (Xs_2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (let ((_let_2 (@ _let_1 Xs_2))) (let ((_let_3 (@ tptp.append_a Xs_1))) (= (@ tptp.remdups_adj_a (@ _let_3 _let_2)) (@ (@ tptp.append_a (@ tptp.remdups_adj_a (@ _let_3 (@ _let_1 tptp.nil_a)))) (@ tptp.tl_a (@ tptp.remdups_adj_a _let_2)))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a)) (= (= (@ tptp.remdups_adj_a Xs) tptp.nil_a) (= Xs tptp.nil_a))))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (let ((_let_2 (@ tptp.remdups_adj_a (@ _let_1 Xs)))) (= (@ _let_1 (@ tptp.tl_a _let_2)) _let_2)))))
% 0.25/0.69 (assert (forall ((X3 tptp.list_a) (Y tptp.list_a)) (=> (= (@ tptp.remdups_adj_a X3) Y) (=> (=> (= X3 tptp.nil_a) (not (= Y tptp.nil_a))) (=> (forall ((X tptp.a)) (let ((_let_1 (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (= X3 _let_1) (not (= Y _let_1))))) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (let ((_let_2 (@ tptp.cons_a X))) (let ((_let_3 (= X Y3))) (=> (= X3 (@ _let_2 _let_1)) (not (and (=> _let_3 (= Y (@ tptp.remdups_adj_a (@ _let_2 Xs2)))) (=> (not _let_3) (= Y (@ _let_2 (@ tptp.remdups_adj_a _let_1)))))))))))))))))
% 0.25/0.69 (assert (forall ((X3 tptp.a)) (let ((_let_1 (@ (@ tptp.cons_a X3) tptp.nil_a))) (= (@ tptp.remdups_adj_a _let_1) _let_1))))
% 0.25/0.69 (assert (= (@ tptp.remdups_adj_a tptp.nil_a) tptp.nil_a))
% 0.25/0.69 (assert (forall ((X3 tptp.a) (Y tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y) Xs))) (let ((_let_2 (@ tptp.cons_a X3))) (let ((_let_3 (@ tptp.remdups_adj_a (@ _let_2 _let_1)))) (let ((_let_4 (= X3 Y))) (and (=> _let_4 (= _let_3 (@ tptp.remdups_adj_a (@ _let_2 Xs)))) (=> (not _let_4) (= _let_3 (@ _let_2 (@ tptp.remdups_adj_a _let_1)))))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (X3 tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.cons_a Y) tptp.nil_a))) (let ((_let_2 (@ tptp.cons_a X3))) (let ((_let_3 (@ tptp.append_a Xs))) (= (@ tptp.remdups_adj_a (@ _let_3 (@ _let_2 _let_1))) (@ (@ tptp.append_a (@ tptp.remdups_adj_a (@ _let_3 (@ _let_2 tptp.nil_a)))) (@ (@ (@ tptp.if_list_a (= X3 Y)) tptp.nil_a) _let_1))))))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (F (-> tptp.a tptp.a tptp.a)) (X3 tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.map2_a_a_a F))) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys2)) (= (@ (@ _let_1 (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X3) tptp.nil_a))) (@ (@ tptp.append_a Ys2) (@ (@ tptp.cons_a Y) tptp.nil_a))) (@ (@ tptp.append_a (@ (@ _let_1 Xs) Ys2)) (@ (@ tptp.cons_a (@ (@ F X3) Y)) tptp.nil_a)))))))
% 0.25/0.69 (assert (forall ((N tptp.nat) (Xs tptp.list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (not (= Xs tptp.nil_a)))))
% 0.25/0.69 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys2)) (=> (@ (@ P tptp.nil_a) tptp.nil_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys3 tptp.list_a)) (=> (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3))))) (@ (@ P Xs) Ys2))))))
% 0.87/1.10 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a) (P (-> tptp.list_a tptp.list_a tptp.list_a Bool))) (let ((_let_1 (@ tptp.size_size_list_a Ys2))) (=> (= (@ tptp.size_size_list_a Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_a Zs2)) (=> (@ (@ (@ P tptp.nil_a) tptp.nil_a) tptp.nil_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys3 tptp.list_a) (Z2 tptp.a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.size_size_list_a Ys3))) (=> (= (@ tptp.size_size_list_a Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_a Zs)) (=> (@ (@ (@ P Xs2) Ys3) Zs) (@ (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)) (@ (@ tptp.cons_a Z2) Zs))))))) (@ (@ (@ P Xs) Ys2) Zs2))))))))
% 0.87/1.10 (assert (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a) (Ws2 tptp.list_a) (P (-> tptp.list_a tptp.list_a tptp.list_a tptp.list_a Bool))) (let ((_let_1 (@ tptp.size_size_list_a Zs2))) (let ((_let_2 (@ tptp.size_size_list_a Ys2))) (=> (= (@ tptp.size_size_list_a Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_a Ws2)) (=> (@ (@ (@ (@ P tptp.nil_a) tptp.nil_a) tptp.nil_a) tptp.nil_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys3 tptp.list_a) (Z2 tptp.a) (Zs tptp.list_a) (W tptp.a) (Ws3 tptp.list_a)) (let ((_let_1 (@ tptp.size_size_list_a Zs))) (let ((_let_2 (@ tptp.size_size_list_a Ys3))) (=> (= (@ tptp.size_size_list_a Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_a Ws3)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs) Ws3) (@ (@ (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)) (@ (@ tptp.cons_a Z2) Zs)) (@ (@ tptp.cons_a W) Ws3))))))))) (@ (@ (@ (@ P Xs) Ys2) Zs2) Ws2))))))))))
% 0.87/1.10 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 0.87/1.10 (assert (forall ((X3 tptp.list_a) (Y tptp.list_a)) (= (@ (@ (@ tptp.if_list_a false) X3) Y) Y)))
% 0.87/1.10 (assert (forall ((X3 tptp.list_a) (Y tptp.list_a)) (= (@ (@ (@ tptp.if_list_a true) X3) Y) X3)))
% 0.87/1.10 (assert (let ((_let_1 (@ tptp.cons_a tptp.x))) (not (= (@ (@ tptp.listIn1312259492pend_a (@ _let_1 tptp.xs)) tptp.f) (@ (@ tptp.listIn1312259492pend_a (@ _let_1 tptp.nil_a)) (@ (@ tptp.listIn1312259492pend_a tptp.xs) tptp.f))))))
% 0.87/1.10 (set-info :filename cvc5---1.0.5_20057)
% 0.87/1.10 (check-sat-assuming ( true ))
% 0.87/1.10 ------- get file name : TPTP file name is ITP100^1
% 0.87/1.10 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20057.smt2...
% 0.87/1.10 --- Run --ho-elim --full-saturate-quant at 10...
% 0.87/1.10 % SZS status Theorem for ITP100^1
% 0.87/1.10 % SZS output start Proof for ITP100^1
% 0.87/1.10 (
% 0.87/1.10 (let ((_let_1 (@ (@ tptp.listIn1312259492pend_a tptp.xs) tptp.f))) (let ((_let_2 (@ tptp.cons_a tptp.x))) (let ((_let_3 (@ (@ tptp.listIn1312259492pend_a (@ _let_2 tptp.xs)) tptp.f))) (let ((_let_4 (not (= _let_3 (@ (@ tptp.listIn1312259492pend_a (@ _let_2 tptp.nil_a)) _let_1))))) (let ((_let_5 (= tptp.ord_lexordp_nat (lambda ((Xs3 tptp.list_nat) (Ys tptp.list_nat)) (or (exists ((X4 tptp.nat) (Vs tptp.list_nat)) (= Ys (@ (@ tptp.append_nat Xs3) (@ (@ tptp.cons_nat X4) Vs)))) (exists ((Us tptp.list_nat) (A5 tptp.nat) (B2 tptp.nat) (Vs tptp.list_nat) (Ws tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Us))) (and (@ (@ tptp.ord_less_nat A5) B2) (= Xs3 (@ _let_1 (@ (@ tptp.cons_nat A5) Vs))) (= Ys (@ _let_1 (@ (@ tptp.cons_nat B2) Ws))))))))))) (let ((_let_6 (= tptp.list_strict_asc_nat (@ tptp.list_ord_nat tptp.ord_less_nat)))) (let ((_let_7 (@ tptp.concat_a tptp.nil_list_a))) (let ((_let_8 (= _let_7 tptp.nil_a))) (let ((_let_9 (@ tptp.concat_list_a tptp.nil_list_list_a))) (let ((_let_10 (= _let_9 tptp.nil_list_a))) (let ((_let_11 (forall ((X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ (@ tptp.append_a (@ _let_1 tptp.nil_a)) Xs) (@ _let_1 Xs)))))) (let ((_let_12 (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (F (-> tptp.nat tptp.a))) (= (@ (@ tptp.listIn1312259492pend_a Xs) (@ (@ tptp.listIn1312259492pend_a Ys2) F)) (@ (@ tptp.listIn1312259492pend_a (@ (@ tptp.append_a Xs) Ys2)) F))))) (let ((_let_13 (@ (@ tptp.cons_list_a tptp.nil_a) tptp.nil_list_a))) (let ((_let_14 (@ (@ tptp.cons_list_list_a tptp.nil_list_a) tptp.nil_list_list_a))) (let ((_let_15 (ho_54 k_53 tptp.x))) (let ((_let_16 (ho_37 _let_15 tptp.xs))) (let ((_let_17 (ho_37 _let_15 (ho_28 k_31 (ho_30 k_29 tptp.nil_list_list_a))))) (let ((_let_18 (ho_94 (ho_93 k_92 _let_17) (ho_94 (ho_93 k_92 tptp.xs) k_201)))) (let ((_let_19 (= _let_18 (ho_94 (ho_93 k_92 _let_16) k_201)))) (let ((_let_20 (ho_37 (ho_33 k_32 _let_17) tptp.xs))) (let ((_let_21 (= _let_18 (ho_94 (ho_93 k_92 _let_20) k_201)))) (let ((_let_22 (= _let_16 _let_20))) (let ((_let_23 (SYMM (ASSUME :args (_let_10))))) (let ((_let_24 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_6)) (EQ_RESOLVE (SYMM (ASSUME :args (_let_8))) (MACRO_SR_EQ_INTRO _let_23 :args ((= tptp.nil_a _let_7) SB_DEFAULT SBA_FIXPOINT))) _let_23))) (let ((_let_25 (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (BOUND_VARIABLE_18719 |u_(-> tptp.nat tptp.a)|)) (= (ho_94 (ho_93 k_92 (ho_37 (ho_33 k_32 Xs) Ys2)) BOUND_VARIABLE_18719) (ho_94 (ho_93 k_92 Xs) (ho_94 (ho_93 k_92 Ys2) BOUND_VARIABLE_18719)))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_12)) (PREPROCESS :args ((= _let_12 _let_25)))))) (let ((_let_27 (forall ((X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (ho_54 k_53 X3))) (= (ho_37 (ho_33 k_32 (ho_37 _let_1 (ho_28 k_31 (ho_30 k_29 tptp.nil_list_list_a)))) Xs) (ho_37 _let_1 Xs)))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO _let_24 :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ _let_1 Xs) (@ (@ tptp.append_a (@ _let_1 (@ tptp.concat_a (@ tptp.concat_list_a tptp.nil_list_list_a)))) Xs)))) _let_27))))))) (let ((_let_29 (and _let_21 _let_22))) (let ((_let_30 (ASSUME :args (_let_22)))) (let ((_let_31 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_29)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_30 _let_31) (SCOPE (TRANS (SYMM (SYMM _let_31)) (CONG (CONG (REFL :args (k_92)) (SYMM _let_30) :args (APPLY_UF ho_93)) (REFL :args (k_201)) :args (APPLY_UF ho_94))) :args (_let_22 _let_21))) :args (_let_21 _let_22))) :args (true _let_29)) :args ((or _let_19 (not _let_21) (not _let_22)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.x tptp.xs QUANTIFIERS_INST_E_MATCHING ((ho_37 (ho_54 k_53 X3) Xs)))) :args (_let_27)))) _let_28 :args (_let_22 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_26 :args (_let_17 tptp.xs k_201 QUANTIFIERS_INST_E_MATCHING ((ho_94 (ho_93 k_92 Xs) (ho_94 (ho_93 k_92 Ys2) BOUND_VARIABLE_18719))))) :args (_let_25)))) _let_26 :args (_let_21 false _let_25)) (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_24 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (= _let_3 (@ (@ tptp.listIn1312259492pend_a (@ _let_2 (@ tptp.concat_a _let_9))) _let_1))) (not _let_19)))))) :args (false false _let_22 false _let_21 true _let_19)) :args ((forall ((F (-> tptp.nat tptp.list_a))) (= (@ (@ tptp.listIn1753026346list_a tptp.nil_list_a) F) F)) (forall ((F (-> tptp.nat tptp.a))) (= (@ (@ tptp.listIn1312259492pend_a tptp.nil_a) F) F)) (forall ((X21 tptp.list_a) (X22 tptp.list_list_a) (Y21 tptp.list_a) (Y22 tptp.list_list_a)) (= (= (@ (@ tptp.cons_list_a X21) X22) (@ (@ tptp.cons_list_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((X21 tptp.a) (X22 tptp.list_a) (Y21 tptp.a) (Y22 tptp.list_a)) (= (= (@ (@ tptp.cons_a X21) X22) (@ (@ tptp.cons_a Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((X21 tptp.list_a) (X22 tptp.list_list_a)) (not (= tptp.nil_list_a (@ (@ tptp.cons_list_a X21) X22)))) (forall ((X21 tptp.a) (X22 tptp.list_a)) (not (= tptp.nil_a (@ (@ tptp.cons_a X21) X22)))) (forall ((List tptp.list_list_a) (X21 tptp.list_a) (X22 tptp.list_list_a)) (=> (= List (@ (@ tptp.cons_list_a X21) X22)) (not (= List tptp.nil_list_a)))) (forall ((List tptp.list_a) (X21 tptp.a) (X22 tptp.list_a)) (=> (= List (@ (@ tptp.cons_a X21) X22)) (not (= List tptp.nil_a)))) (forall ((Y tptp.list_list_a)) (=> (not (= Y tptp.nil_list_a)) (not (forall ((X212 tptp.list_a) (X222 tptp.list_list_a)) (not (= Y (@ (@ tptp.cons_list_a X212) X222))))))) (forall ((Y tptp.list_a)) (=> (not (= Y tptp.nil_a)) (not (forall ((X212 tptp.a) (X222 tptp.list_a)) (not (= Y (@ (@ tptp.cons_a X212) X222))))))) (forall ((P (-> tptp.list_list_a Bool)) (List tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X1 tptp.list_a) (X2 tptp.list_list_a)) (=> (@ P X2) (@ P (@ (@ tptp.cons_list_a X1) X2)))) (@ P List)))) (forall ((P (-> tptp.list_a Bool)) (List tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X1 tptp.a) (X2 tptp.list_a)) (=> (@ P X2) (@ P (@ (@ tptp.cons_a X1) X2)))) (@ P List)))) (forall ((Xs tptp.list_list_a)) (= (not (= Xs tptp.nil_list_a)) (exists ((Y2 tptp.list_a) (Ys tptp.list_list_a)) (= Xs (@ (@ tptp.cons_list_a Y2) Ys))))) (forall ((Xs tptp.list_a)) (= (not (= Xs tptp.nil_a)) (exists ((Y2 tptp.a) (Ys tptp.list_a)) (= Xs (@ (@ tptp.cons_a Y2) Ys))))) (forall ((P (-> tptp.list_a tptp.list_list_a Bool)) (Xs tptp.list_a) (Ys2 tptp.list_list_a)) (=> (@ (@ P tptp.nil_a) tptp.nil_list_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a)) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) tptp.nil_list_a)) (=> (forall ((Y3 tptp.list_a) (Ys3 tptp.list_list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_list_a Y3) Ys3))) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3)))) (@ (@ P Xs) Ys2)))))) (forall ((P (-> tptp.list_list_a tptp.list_a Bool)) (Xs tptp.list_list_a) (Ys2 tptp.list_a)) (=> (@ (@ P tptp.nil_list_a) tptp.nil_a) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) tptp.nil_a)) (=> (forall ((Y3 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_list_a) (@ (@ tptp.cons_a Y3) Ys3))) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a) (Y3 tptp.a) (Ys3 tptp.list_a)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)))) (@ (@ P Xs) Ys2)))))) (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (@ (@ P tptp.nil_list_a) tptp.nil_list_a) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) tptp.nil_list_a)) (=> (forall ((Y3 tptp.list_a) (Ys3 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) (@ (@ tptp.cons_list_a Y3) Ys3))) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a) (Y3 tptp.list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3)))) (@ (@ P Xs) Ys2)))))) (forall ((P (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ P tptp.nil_a) tptp.nil_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a)) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) tptp.nil_a)) (=> (forall ((Y3 tptp.a) (Ys3 tptp.list_a)) (@ (@ P tptp.nil_a) (@ (@ tptp.cons_a Y3) Ys3))) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys3 tptp.list_a)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)))) (@ (@ P Xs) Ys2)))))) (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (A0 tptp.list_list_a) (A1 tptp.list_list_a)) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ P Ys3) Xs2) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) Ys3))) (@ (@ P A0) A1)))) (forall ((P (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ P Ys3) Xs2) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) Ys3))) (@ (@ P A0) A1)))) (forall ((P (-> tptp.list_list_a Bool)) (Xs tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (=> (forall ((X tptp.list_a) (Y3 tptp.list_a) (Zs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_list_a X) _let_1)))))) (@ P Xs))))) (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X tptp.a)) (@ P (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (forall ((X tptp.a) (Y3 tptp.a) (Zs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_a X) _let_1)))))) (@ P Xs))))) (forall ((P (-> tptp.list_list_a tptp.list_list_a Bool)) (A0 tptp.list_list_a) (A1 tptp.list_list_a)) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((Xs2 tptp.list_list_a)) (@ (@ P Xs2) tptp.nil_list_a)) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a) (Y3 tptp.list_a) (Ys3 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_list_a X) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_a tptp.list_a Bool)) (A0 tptp.list_a) (A1 tptp.list_a)) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((Xs2 tptp.list_a)) (@ (@ P Xs2) tptp.nil_a)) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys3 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_a X) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a)) (not (= (@ (@ tptp.cons_list_a X3) Xs) Xs))) (forall ((X3 tptp.a) (Xs tptp.list_a)) (not (= (@ (@ tptp.cons_a X3) Xs) Xs))) (forall ((P (-> (-> tptp.list_a tptp.a) tptp.list_list_a tptp.list_a Bool)) (A0 (-> tptp.list_a tptp.a)) (A1 tptp.list_list_a) (A2 tptp.list_a)) (=> (forall ((F2 (-> tptp.list_a tptp.a)) (X_1 tptp.list_a)) (@ (@ (@ P F2) tptp.nil_list_a) X_1)) (=> (forall ((F2 (-> tptp.list_a tptp.a)) (A tptp.list_a) (As tptp.list_list_a) (Bs tptp.list_a)) (let ((_let_1 (@ P F2))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_a (@ F2 A)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_list_a A) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.a tptp.list_a) tptp.list_a tptp.list_list_a Bool)) (A0 (-> tptp.a tptp.list_a)) (A1 tptp.list_a) (A2 tptp.list_list_a)) (=> (forall ((F2 (-> tptp.a tptp.list_a)) (X_1 tptp.list_list_a)) (@ (@ (@ P F2) tptp.nil_a) X_1)) (=> (forall ((F2 (-> tptp.a tptp.list_a)) (A tptp.a) (As tptp.list_a) (Bs tptp.list_list_a)) (let ((_let_1 (@ P F2))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_list_a (@ F2 A)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_a A) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.list_a tptp.list_a) tptp.list_list_a tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a)) (A1 tptp.list_list_a) (A2 tptp.list_list_a)) (=> (forall ((F2 (-> tptp.list_a tptp.list_a)) (X_1 tptp.list_list_a)) (@ (@ (@ P F2) tptp.nil_list_a) X_1)) (=> (forall ((F2 (-> tptp.list_a tptp.list_a)) (A tptp.list_a) (As tptp.list_list_a) (Bs tptp.list_list_a)) (let ((_let_1 (@ P F2))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_list_a (@ F2 A)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_list_a A) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.a tptp.a) tptp.list_a tptp.list_a Bool)) (A0 (-> tptp.a tptp.a)) (A1 tptp.list_a) (A2 tptp.list_a)) (=> (forall ((F2 (-> tptp.a tptp.a)) (X_1 tptp.list_a)) (@ (@ (@ P F2) tptp.nil_a) X_1)) (=> (forall ((F2 (-> tptp.a tptp.a)) (A tptp.a) (As tptp.list_a) (Bs tptp.list_a)) (let ((_let_1 (@ P F2))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_a (@ F2 A)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_a A) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((Xs tptp.list_list_a) (P (-> tptp.list_list_a Bool))) (=> (not (= Xs tptp.nil_list_a)) (=> (forall ((X tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (=> (not (= Xs2 tptp.nil_list_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_list_a X) Xs2))))) (@ P Xs))))) (forall ((Xs tptp.list_a) (P (-> tptp.list_a Bool))) (=> (not (= Xs tptp.nil_a)) (=> (forall ((X tptp.a)) (@ P (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (forall ((X tptp.a) (Xs2 tptp.list_a)) (=> (not (= Xs2 tptp.nil_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_a X) Xs2))))) (@ P Xs))))) (forall ((P (-> (-> tptp.list_a tptp.list_a Bool) tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool))) (@ (@ P P2) tptp.nil_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a)) (@ (@ P P2) (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_list_a X) _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool))) (@ (@ P P2) tptp.nil_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X tptp.a)) (@ (@ P P2) (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_a X) _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_list_a Bool)) (A0 tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (=> (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Xs2))) (let ((_let_2 (@ tptp.cons_list_a X))) (let ((_let_3 (= X Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))) (forall ((P (-> tptp.list_a Bool)) (A0 tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X tptp.a)) (@ P (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (let ((_let_2 (@ tptp.cons_a X))) (let ((_let_3 (= X Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))) (forall ((P (-> (-> tptp.list_a tptp.list_a Bool) tptp.list_list_a Bool)) (A0 (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool))) (@ (@ P P2) tptp.nil_list_a)) (=> (forall ((P2 (-> tptp.list_a tptp.list_a Bool)) (X tptp.list_a) (Ys3 tptp.list_list_a)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_list_a X) Ys3))))) (@ (@ P A0) A1)))) (forall ((P (-> (-> tptp.a tptp.a Bool) tptp.list_a Bool)) (A0 (-> tptp.a tptp.a Bool)) (A1 tptp.list_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool))) (@ (@ P P2) tptp.nil_a)) (=> (forall ((P2 (-> tptp.a tptp.a Bool)) (X tptp.a) (Ys3 tptp.list_a)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_a X) Ys3))))) (@ (@ P A0) A1)))) (forall ((X3 tptp.list_list_a)) (=> (not (= X3 tptp.nil_list_a)) (=> (forall ((X tptp.list_a)) (not (= X3 (@ (@ tptp.cons_list_a X) tptp.nil_list_a)))) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (not (= X3 (@ (@ tptp.cons_list_a X) (@ (@ tptp.cons_list_a Y3) Xs2))))))))) (forall ((X3 tptp.list_a)) (=> (not (= X3 tptp.nil_a)) (=> (forall ((X tptp.a)) (not (= X3 (@ (@ tptp.cons_a X) tptp.nil_a)))) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (not (= X3 (@ (@ tptp.cons_a X) (@ (@ tptp.cons_a Y3) Xs2))))))))) (forall ((X3 tptp.list_list_list_a)) (=> (not (= X3 tptp.nil_list_list_a)) (=> (forall ((Xss tptp.list_list_list_a)) (not (= X3 (@ (@ tptp.cons_list_list_a tptp.nil_list_a) Xss)))) (not (forall ((X tptp.list_a) (Xs2 tptp.list_list_a) (Xss tptp.list_list_list_a)) (not (= X3 (@ (@ tptp.cons_list_list_a (@ (@ tptp.cons_list_a X) Xs2)) Xss)))))))) (forall ((X3 tptp.list_list_a)) (=> (not (= X3 tptp.nil_list_a)) (=> (forall ((Xss tptp.list_list_a)) (not (= X3 (@ (@ tptp.cons_list_a tptp.nil_a) Xss)))) (not (forall ((X tptp.a) (Xs2 tptp.list_a) (Xss tptp.list_list_a)) (not (= X3 (@ (@ tptp.cons_list_a (@ (@ tptp.cons_a X) Xs2)) Xss)))))))) (forall ((X3 tptp.list_a)) (= (@ (@ tptp.insert_list_a X3) tptp.nil_list_a) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a))) (forall ((X3 tptp.a)) (= (@ (@ tptp.insert_a X3) tptp.nil_a) (@ (@ tptp.cons_a X3) tptp.nil_a))) (forall ((P (-> tptp.list_a Bool))) (not (@ (@ tptp.list_ex1_list_a P) tptp.nil_list_a))) (forall ((P (-> tptp.a Bool))) (not (@ (@ tptp.list_ex1_a P) tptp.nil_a))) (forall ((X3 (-> tptp.a tptp.list_a)) (Xa tptp.list_a) (Xb tptp.list_list_a) (Y tptp.list_list_a)) (=> (= (@ (@ (@ tptp.map_ta41997947list_a X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_a) (not (= Y Xb))) (not (forall ((A tptp.a) (As tptp.list_a)) (=> (= Xa (@ (@ tptp.cons_a A) As)) (not (= Y (@ (@ (@ tptp.map_ta41997947list_a X3) As) (@ (@ tptp.cons_list_a (@ X3 A)) Xb)))))))))) (forall ((X3 (-> tptp.list_a tptp.a)) (Xa tptp.list_list_a) (Xb tptp.list_a) (Y tptp.list_a)) (=> (= (@ (@ (@ tptp.map_ta2002079599st_a_a X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_list_a) (not (= Y Xb))) (not (forall ((A tptp.list_a) (As tptp.list_list_a)) (=> (= Xa (@ (@ tptp.cons_list_a A) As)) (not (= Y (@ (@ (@ tptp.map_ta2002079599st_a_a X3) As) (@ (@ tptp.cons_a (@ X3 A)) Xb)))))))))) (forall ((X3 (-> tptp.list_a tptp.list_a)) (Xa tptp.list_list_a) (Xb tptp.list_list_a) (Y tptp.list_list_a)) (=> (= (@ (@ (@ tptp.map_ta982122357list_a X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_list_a) (not (= Y Xb))) (not (forall ((A tptp.list_a) (As tptp.list_list_a)) (=> (= Xa (@ (@ tptp.cons_list_a A) As)) (not (= Y (@ (@ (@ tptp.map_ta982122357list_a X3) As) (@ (@ tptp.cons_list_a (@ X3 A)) Xb)))))))))) (forall ((X3 (-> tptp.a tptp.a)) (Xa tptp.list_a) (Xb tptp.list_a) (Y tptp.list_a)) (=> (= (@ (@ (@ tptp.map_tailrec_rev_a_a X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_a) (not (= Y Xb))) (not (forall ((A tptp.a) (As tptp.list_a)) (=> (= Xa (@ (@ tptp.cons_a A) As)) (not (= Y (@ (@ (@ tptp.map_tailrec_rev_a_a X3) As) (@ (@ tptp.cons_a (@ X3 A)) Xb)))))))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Xs tptp.list_list_a)) (not (@ (@ (@ tptp.lexordp_eq_list_a Less) (@ (@ tptp.cons_list_a X3) Xs)) tptp.nil_list_a))) (forall ((Less (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Xs tptp.list_a)) (not (@ (@ (@ tptp.lexordp_eq_a Less) (@ (@ tptp.cons_a X3) Xs)) tptp.nil_a))) (forall ((F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.bind_a_list_a tptp.nil_a) F) tptp.nil_list_a)) (forall ((F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.bind_list_a_a tptp.nil_list_a) F) tptp.nil_a)) (forall ((F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.bind_list_a_list_a tptp.nil_list_a) F) tptp.nil_list_a)) (forall ((F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.bind_a_a tptp.nil_a) F) tptp.nil_a)) (forall ((R (-> tptp.a tptp.list_a Bool)) (X12 tptp.list_a) (X23 tptp.list_list_a) (P (-> tptp.list_a tptp.list_list_a Bool))) (=> (@ (@ (@ tptp.listrelp_a_list_a R) X12) X23) (=> (@ (@ P tptp.nil_a) tptp.nil_list_a) (=> (forall ((X tptp.a) (Y3 tptp.list_a) (Xs2 tptp.list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ R X) Y3) (=> (@ (@ (@ tptp.listrelp_a_list_a R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3)))))) (@ (@ P X12) X23))))) (forall ((R (-> tptp.list_a tptp.a Bool)) (X12 tptp.list_list_a) (X23 tptp.list_a) (P (-> tptp.list_list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.listrelp_list_a_a R) X12) X23) (=> (@ (@ P tptp.nil_list_a) tptp.nil_a) (=> (forall ((X tptp.list_a) (Y3 tptp.a) (Xs2 tptp.list_list_a) (Ys3 tptp.list_a)) (=> (@ (@ R X) Y3) (=> (@ (@ (@ tptp.listrelp_list_a_a R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)))))) (@ (@ P X12) X23))))) (forall ((R (-> tptp.list_a tptp.list_a Bool)) (X12 tptp.list_list_a) (X23 tptp.list_list_a) (P (-> tptp.list_list_a tptp.list_list_a Bool))) (=> (@ (@ (@ tptp.listre1221556159list_a R) X12) X23) (=> (@ (@ P tptp.nil_list_a) tptp.nil_list_a) (=> (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ R X) Y3) (=> (@ (@ (@ tptp.listre1221556159list_a R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3)))))) (@ (@ P X12) X23))))) (forall ((R (-> tptp.a tptp.a Bool)) (X12 tptp.list_a) (X23 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.listrelp_a_a R) X12) X23) (=> (@ (@ P tptp.nil_a) tptp.nil_a) (=> (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ R X) Y3) (=> (@ (@ (@ tptp.listrelp_a_a R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)))))) (@ (@ P X12) X23))))) (= tptp.listrelp_a_list_a (lambda ((R2 (-> tptp.a tptp.list_a Bool)) (A12 tptp.list_a) (A22 tptp.list_list_a)) (or (and (= A12 tptp.nil_a) (= A22 tptp.nil_list_a)) (exists ((X4 tptp.a) (Y2 tptp.list_a) (Xs3 tptp.list_a) (Ys tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_a X4) Xs3)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys)) (@ (@ R2 X4) Y2) (@ (@ (@ tptp.listrelp_a_list_a R2) Xs3) Ys)))))) (= tptp.listrelp_list_a_a (lambda ((R2 (-> tptp.list_a tptp.a Bool)) (A12 tptp.list_list_a) (A22 tptp.list_a)) (or (and (= A12 tptp.nil_list_a) (= A22 tptp.nil_a)) (exists ((X4 tptp.list_a) (Y2 tptp.a) (Xs3 tptp.list_list_a) (Ys tptp.list_a)) (and (= A12 (@ (@ tptp.cons_list_a X4) Xs3)) (= A22 (@ (@ tptp.cons_a Y2) Ys)) (@ (@ R2 X4) Y2) (@ (@ (@ tptp.listrelp_list_a_a R2) Xs3) Ys)))))) (= tptp.listre1221556159list_a (lambda ((R2 (-> tptp.list_a tptp.list_a Bool)) (A12 tptp.list_list_a) (A22 tptp.list_list_a)) (or (and (= A12 tptp.nil_list_a) (= A22 tptp.nil_list_a)) (exists ((X4 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X4) Xs3)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys)) (@ (@ R2 X4) Y2) (@ (@ (@ tptp.listre1221556159list_a R2) Xs3) Ys)))))) (= tptp.listrelp_a_a (lambda ((R2 (-> tptp.a tptp.a Bool)) (A12 tptp.list_a) (A22 tptp.list_a)) (or (and (= A12 tptp.nil_a) (= A22 tptp.nil_a)) (exists ((X4 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X4) Xs3)) (= A22 (@ (@ tptp.cons_a Y2) Ys)) (@ (@ R2 X4) Y2) (@ (@ (@ tptp.listrelp_a_a R2) Xs3) Ys)))))) (forall ((R (-> tptp.a tptp.list_a Bool)) (A1 tptp.list_a) (A2 tptp.list_list_a)) (=> (@ (@ (@ tptp.listrelp_a_list_a R) A1) A2) (=> (=> (= A1 tptp.nil_a) (not (= A2 tptp.nil_list_a))) (not (forall ((X tptp.a) (Y3 tptp.list_a) (Xs2 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X) Xs2)) (forall ((Ys3 tptp.list_list_a)) (=> (= A2 (@ (@ tptp.cons_list_a Y3) Ys3)) (=> (@ (@ R X) Y3) (not (@ (@ (@ tptp.listrelp_a_list_a R) Xs2) Ys3))))))))))) (forall ((R (-> tptp.list_a tptp.a Bool)) (A1 tptp.list_list_a) (A2 tptp.list_a)) (=> (@ (@ (@ tptp.listrelp_list_a_a R) A1) A2) (=> (=> (= A1 tptp.nil_list_a) (not (= A2 tptp.nil_a))) (not (forall ((X tptp.list_a) (Y3 tptp.a) (Xs2 tptp.list_list_a)) (=> (= A1 (@ (@ tptp.cons_list_a X) Xs2)) (forall ((Ys3 tptp.list_a)) (=> (= A2 (@ (@ tptp.cons_a Y3) Ys3)) (=> (@ (@ R X) Y3) (not (@ (@ (@ tptp.listrelp_list_a_a R) Xs2) Ys3))))))))))) (forall ((R (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a) (A2 tptp.list_list_a)) (=> (@ (@ (@ tptp.listre1221556159list_a R) A1) A2) (=> (=> (= A1 tptp.nil_list_a) (not (= A2 tptp.nil_list_a))) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (=> (= A1 (@ (@ tptp.cons_list_a X) Xs2)) (forall ((Ys3 tptp.list_list_a)) (=> (= A2 (@ (@ tptp.cons_list_a Y3) Ys3)) (=> (@ (@ R X) Y3) (not (@ (@ (@ tptp.listre1221556159list_a R) Xs2) Ys3))))))))))) (forall ((R (-> tptp.a tptp.a Bool)) (A1 tptp.list_a) (A2 tptp.list_a)) (=> (@ (@ (@ tptp.listrelp_a_a R) A1) A2) (=> (=> (= A1 tptp.nil_a) (not (= A2 tptp.nil_a))) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X) Xs2)) (forall ((Ys3 tptp.list_a)) (=> (= A2 (@ (@ tptp.cons_a Y3) Ys3)) (=> (@ (@ R X) Y3) (not (@ (@ (@ tptp.listrelp_a_a R) Xs2) Ys3))))))))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Xs tptp.list_list_a) (Y tptp.list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_eq_list_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.cons_list_a Y) Ys2)) (or (@ (@ Less X3) Y) (and (not (@ (@ Less Y) X3)) (@ (@ _let_1 Xs) Ys2)))))) (forall ((Less (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2)) (or (@ (@ Less X3) Y) (and (not (@ (@ Less Y) X3)) (@ (@ _let_1 Xs) Ys2)))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a)) (= (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs) tptp.nil_list_a) (= Xs tptp.nil_list_a))) (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (= (@ (@ (@ tptp.lexordp_eq_a Less) Xs) tptp.nil_a) (= Xs tptp.nil_a))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Ys2 tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) tptp.nil_list_a) Ys2)) (forall ((Less (-> tptp.a tptp.a Bool)) (Ys2 tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) tptp.nil_a) Ys2)) (= tptp.lexordp_eq_a tptp.lexordp_eq_a) (forall ((Less (-> tptp.a tptp.a Bool)) (Xs tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) Xs) Xs)) (forall ((A3 tptp.list_a) (P (-> tptp.list_a Bool))) (= (@ (@ tptp.member_list_a2 A3) (@ tptp.collect_list_a P)) (@ P A3))) (forall ((A3 tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a2 A3) (@ tptp.collect_a P)) (@ P A3))) (forall ((A4 tptp.set_list_a)) (= (@ tptp.collect_list_a (lambda ((X4 tptp.list_a)) (@ (@ tptp.member_list_a2 X4) A4))) A4)) (forall ((A4 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X4 tptp.a)) (@ (@ tptp.member_a2 X4) A4))) A4)) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (@ (@ Less X3) Y) (@ (@ (@ tptp.lexordp_eq_list_a Less) (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.cons_list_a Y) Ys2)))) (forall ((Less (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ Less X3) Y) (@ (@ (@ tptp.lexordp_eq_a Less) (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2)))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.lexordp_eq_list_a Less))) (=> (not (@ (@ Less X3) Y)) (=> (not (@ (@ Less Y) X3)) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.cons_list_a Y) Ys2))))))) (forall ((Less (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.lexordp_eq_a Less))) (=> (not (@ (@ Less X3) Y)) (=> (not (@ (@ Less Y) X3)) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2))))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (Ys2 tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) tptp.nil_list_a) Ys2)) (forall ((Less (-> tptp.a tptp.a Bool)) (Ys2 tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) tptp.nil_a) Ys2)) (forall ((R (-> tptp.a tptp.list_a Bool)) (X3 tptp.a) (Y tptp.list_a) (Xs tptp.list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.listrelp_a_list_a R))) (=> (@ (@ R X3) Y) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_list_a Y) Ys2)))))) (forall ((R (-> tptp.list_a tptp.a Bool)) (X3 tptp.list_a) (Y tptp.a) (Xs tptp.list_list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.listrelp_list_a_a R))) (=> (@ (@ R X3) Y) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2)))))) (forall ((R (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.listre1221556159list_a R))) (=> (@ (@ R X3) Y) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.cons_list_a Y) Ys2)))))) (forall ((R (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Y tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.listrelp_a_a R))) (=> (@ (@ R X3) Y) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2)))))) (forall ((R (-> tptp.a tptp.list_a Bool))) (@ (@ (@ tptp.listrelp_a_list_a R) tptp.nil_a) tptp.nil_list_a)) (forall ((R (-> tptp.list_a tptp.a Bool))) (@ (@ (@ tptp.listrelp_list_a_a R) tptp.nil_list_a) tptp.nil_a)) (forall ((R (-> tptp.list_a tptp.list_a Bool))) (@ (@ (@ tptp.listre1221556159list_a R) tptp.nil_list_a) tptp.nil_list_a)) (forall ((R (-> tptp.a tptp.a Bool))) (@ (@ (@ tptp.listrelp_a_a R) tptp.nil_a) tptp.nil_a)) (forall ((F (-> tptp.a tptp.list_a)) (A3 tptp.a) (As2 tptp.list_a) (Bs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.map_ta41997947list_a F))) (= (@ (@ _let_1 (@ (@ tptp.cons_a A3) As2)) Bs2) (@ (@ _let_1 As2) (@ (@ tptp.cons_list_a (@ F A3)) Bs2))))) (forall ((F (-> tptp.list_a tptp.a)) (A3 tptp.list_a) (As2 tptp.list_list_a) (Bs2 tptp.list_a)) (let ((_let_1 (@ tptp.map_ta2002079599st_a_a F))) (= (@ (@ _let_1 (@ (@ tptp.cons_list_a A3) As2)) Bs2) (@ (@ _let_1 As2) (@ (@ tptp.cons_a (@ F A3)) Bs2))))) (forall ((F (-> tptp.list_a tptp.list_a)) (A3 tptp.list_a) (As2 tptp.list_list_a) (Bs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.map_ta982122357list_a F))) (= (@ (@ _let_1 (@ (@ tptp.cons_list_a A3) As2)) Bs2) (@ (@ _let_1 As2) (@ (@ tptp.cons_list_a (@ F A3)) Bs2))))) (forall ((F (-> tptp.a tptp.a)) (A3 tptp.a) (As2 tptp.list_a) (Bs2 tptp.list_a)) (let ((_let_1 (@ tptp.map_tailrec_rev_a_a F))) (= (@ (@ _let_1 (@ (@ tptp.cons_a A3) As2)) Bs2) (@ (@ _let_1 As2) (@ (@ tptp.cons_a (@ F A3)) Bs2))))) (forall ((F (-> tptp.a tptp.a)) (Bs2 tptp.list_a)) (= (@ (@ (@ tptp.map_tailrec_rev_a_a F) tptp.nil_a) Bs2) Bs2)) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (A1 tptp.list_list_a) (A2 tptp.list_list_a)) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) A1) A2) (=> (not (= A1 tptp.nil_list_a)) (=> (forall ((X tptp.list_a)) (=> (exists ((Xs2 tptp.list_list_a)) (= A1 (@ (@ tptp.cons_list_a X) Xs2))) (forall ((Y3 tptp.list_a)) (=> (exists ((Ys3 tptp.list_list_a)) (= A2 (@ (@ tptp.cons_list_a Y3) Ys3))) (not (@ (@ Less X) Y3)))))) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (=> (= A1 (@ (@ tptp.cons_list_a X) Xs2)) (forall ((Ys3 tptp.list_list_a)) (=> (= A2 (@ (@ tptp.cons_list_a Y3) Ys3)) (=> (not (@ (@ Less X) Y3)) (=> (not (@ (@ Less Y3) X)) (not (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs2) Ys3))))))))))))) (forall ((Less (-> tptp.a tptp.a Bool)) (A1 tptp.list_a) (A2 tptp.list_a)) (=> (@ (@ (@ tptp.lexordp_eq_a Less) A1) A2) (=> (not (= A1 tptp.nil_a)) (=> (forall ((X tptp.a)) (=> (exists ((Xs2 tptp.list_a)) (= A1 (@ (@ tptp.cons_a X) Xs2))) (forall ((Y3 tptp.a)) (=> (exists ((Ys3 tptp.list_a)) (= A2 (@ (@ tptp.cons_a Y3) Ys3))) (not (@ (@ Less X) Y3)))))) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (=> (= A1 (@ (@ tptp.cons_a X) Xs2)) (forall ((Ys3 tptp.list_a)) (=> (= A2 (@ (@ tptp.cons_a Y3) Ys3)) (=> (not (@ (@ Less X) Y3)) (=> (not (@ (@ Less Y3) X)) (not (@ (@ (@ tptp.lexordp_eq_a Less) Xs2) Ys3))))))))))))) (= tptp.lexordp_eq_list_a (lambda ((Less2 (-> tptp.list_a tptp.list_a Bool)) (A12 tptp.list_list_a) (A22 tptp.list_list_a)) (or (exists ((Ys tptp.list_list_a)) (and (= A12 tptp.nil_list_a) (= A22 Ys))) (exists ((X4 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X4) Xs3)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys)) (@ (@ Less2 X4) Y2))) (exists ((X4 tptp.list_a) (Y2 tptp.list_a) (Xs3 tptp.list_list_a) (Ys tptp.list_list_a)) (and (= A12 (@ (@ tptp.cons_list_a X4) Xs3)) (= A22 (@ (@ tptp.cons_list_a Y2) Ys)) (not (@ (@ Less2 X4) Y2)) (not (@ (@ Less2 Y2) X4)) (@ (@ (@ tptp.lexordp_eq_list_a Less2) Xs3) Ys)))))) (= tptp.lexordp_eq_a (lambda ((Less2 (-> tptp.a tptp.a Bool)) (A12 tptp.list_a) (A22 tptp.list_a)) (or (exists ((Ys tptp.list_a)) (and (= A12 tptp.nil_a) (= A22 Ys))) (exists ((X4 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X4) Xs3)) (= A22 (@ (@ tptp.cons_a Y2) Ys)) (@ (@ Less2 X4) Y2))) (exists ((X4 tptp.a) (Y2 tptp.a) (Xs3 tptp.list_a) (Ys tptp.list_a)) (and (= A12 (@ (@ tptp.cons_a X4) Xs3)) (= A22 (@ (@ tptp.cons_a Y2) Ys)) (not (@ (@ Less2 X4) Y2)) (not (@ (@ Less2 Y2) X4)) (@ (@ (@ tptp.lexordp_eq_a Less2) Xs3) Ys)))))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (X12 tptp.list_list_a) (X23 tptp.list_list_a) (P (-> tptp.list_list_a tptp.list_list_a Bool))) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) X12) X23) (=> (forall ((X_1 tptp.list_list_a)) (@ (@ P tptp.nil_list_a) X_1)) (=> (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (@ (@ Less X) Y3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3)))) (=> (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a) (Ys3 tptp.list_list_a)) (=> (not (@ (@ Less X) Y3)) (=> (not (@ (@ Less Y3) X)) (=> (@ (@ (@ tptp.lexordp_eq_list_a Less) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_list_a X) Xs2)) (@ (@ tptp.cons_list_a Y3) Ys3))))))) (@ (@ P X12) X23)))))) (forall ((Less (-> tptp.a tptp.a Bool)) (X12 tptp.list_a) (X23 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (@ (@ (@ tptp.lexordp_eq_a Less) X12) X23) (=> (forall ((X_1 tptp.list_a)) (@ (@ P tptp.nil_a) X_1)) (=> (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys3 tptp.list_a)) (=> (@ (@ Less X) Y3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)))) (=> (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a) (Ys3 tptp.list_a)) (=> (not (@ (@ Less X) Y3)) (=> (not (@ (@ Less Y3) X)) (=> (@ (@ (@ tptp.lexordp_eq_a Less) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3))))))) (@ (@ P X12) X23)))))) (= (@ tptp.product_lists_list_a tptp.nil_list_list_a) _let_14) (= (@ tptp.product_lists_a tptp.nil_list_a) _let_13) (= (@ tptp.subseqs_list_a tptp.nil_list_a) _let_14) (= (@ tptp.subseqs_a tptp.nil_a) _let_13) (forall ((A1 tptp.list_nat) (A2 tptp.list_nat)) (=> (@ (@ tptp.ord_lexordp_eq_nat A1) A2) (=> (not (= A1 tptp.nil_nat)) (=> (forall ((X tptp.nat)) (=> (exists ((Xs2 tptp.list_nat)) (= A1 (@ (@ tptp.cons_nat X) Xs2))) (forall ((Y3 tptp.nat)) (=> (exists ((Ys3 tptp.list_nat)) (= A2 (@ (@ tptp.cons_nat Y3) Ys3))) (not (@ (@ tptp.ord_less_nat X) Y3)))))) (not (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= A1 (@ (@ tptp.cons_nat X) Xs2)) (forall ((Ys3 tptp.list_nat)) (=> (= A2 (@ (@ tptp.cons_nat Y3) Ys3)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (=> (not (@ (@ tptp.ord_less_nat Y3) X)) (not (@ (@ tptp.ord_lexordp_eq_nat Xs2) Ys3))))))))))))) (= tptp.ord_lexordp_eq_nat (lambda ((A12 tptp.list_nat) (A22 tptp.list_nat)) (or (exists ((Ys tptp.list_nat)) (and (= A12 tptp.nil_nat) (= A22 Ys))) (exists ((X4 tptp.nat) (Y2 tptp.nat) (Xs3 tptp.list_nat) (Ys tptp.list_nat)) (and (= A12 (@ (@ tptp.cons_nat X4) Xs3)) (= A22 (@ (@ tptp.cons_nat Y2) Ys)) (@ (@ tptp.ord_less_nat X4) Y2))) (exists ((X4 tptp.nat) (Y2 tptp.nat) (Xs3 tptp.list_nat) (Ys tptp.list_nat)) (and (= A12 (@ (@ tptp.cons_nat X4) Xs3)) (= A22 (@ (@ tptp.cons_nat Y2) Ys)) (not (@ (@ tptp.ord_less_nat X4) Y2)) (not (@ (@ tptp.ord_less_nat Y2) X4)) (@ (@ tptp.ord_lexordp_eq_nat Xs3) Ys)))))) (forall ((X12 tptp.list_nat) (X23 tptp.list_nat) (P (-> tptp.list_nat tptp.list_nat Bool))) (=> (@ (@ tptp.ord_lexordp_eq_nat X12) X23) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P tptp.nil_nat) X_1)) (=> (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat X) Y3) (@ (@ P (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (=> (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (=> (not (@ (@ tptp.ord_less_nat Y3) X)) (=> (@ (@ tptp.ord_lexordp_eq_nat Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3))))))) (@ (@ P X12) X23)))))) (forall ((Y tptp.list_a)) (not (@ (@ tptp.member_list_a tptp.nil_list_a) Y))) (forall ((Y tptp.a)) (not (@ (@ tptp.member_a tptp.nil_a) Y))) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (Y tptp.list_a)) (= (@ (@ tptp.member_list_a (@ (@ tptp.cons_list_a X3) Xs)) Y) (or (= X3 Y) (@ (@ tptp.member_list_a Xs) Y)))) (forall ((X3 tptp.a) (Xs tptp.list_a) (Y tptp.a)) (= (@ (@ tptp.member_a (@ (@ tptp.cons_a X3) Xs)) Y) (or (= X3 Y) (@ (@ tptp.member_a Xs) Y)))) (forall ((X3 tptp.list_list_a) (Xa tptp.list_list_a) (Y tptp.list_list_a)) (=> (= (@ (@ tptp.splice_list_a X3) Xa) Y) (=> (=> (= X3 tptp.nil_list_a) (not (= Y Xa))) (not (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X))) (=> (= X3 (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice_list_a Xa) Xs2))))))))))) (forall ((X3 tptp.list_a) (Xa tptp.list_a) (Y tptp.list_a)) (=> (= (@ (@ tptp.splice_a X3) Xa) Y) (=> (=> (= X3 tptp.nil_a) (not (= Y Xa))) (not (forall ((X tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X))) (=> (= X3 (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice_a Xa) Xs2))))))))))) (forall ((X3 tptp.a) (Xs tptp.list_a) (F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.bind_a_a (@ (@ tptp.cons_a X3) Xs)) F) (@ (@ tptp.append_a (@ F X3)) (@ (@ tptp.bind_a_a Xs) F)))) (forall ((X3 tptp.a) (Xs tptp.list_a) (F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.bind_a_list_a (@ (@ tptp.cons_a X3) Xs)) F) (@ (@ tptp.append_list_a (@ F X3)) (@ (@ tptp.bind_a_list_a Xs) F)))) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.bind_list_a_a (@ (@ tptp.cons_list_a X3) Xs)) F) (@ (@ tptp.append_a (@ F X3)) (@ (@ tptp.bind_list_a_a Xs) F)))) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.bind_list_a_list_a (@ (@ tptp.cons_list_a X3) Xs)) F) (@ (@ tptp.append_list_a (@ F X3)) (@ (@ tptp.bind_list_a_list_a Xs) F)))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs2)) (= Ys2 Zs2)))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs2)) (= Ys2 Zs2)))) (forall ((Ys2 tptp.list_a) (Xs tptp.list_a) (Zs2 tptp.list_a)) (= (= (@ (@ tptp.append_a Ys2) Xs) (@ (@ tptp.append_a Zs2) Xs)) (= Ys2 Zs2))) (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a) (Zs2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Ys2) Xs) (@ (@ tptp.append_list_a Zs2) Xs)) (= Ys2 Zs2))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (= (@ (@ tptp.append_a (@ _let_1 Ys2)) Zs2) (@ _let_1 (@ (@ tptp.append_a Ys2) Zs2))))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (= (@ (@ tptp.append_list_a (@ _let_1 Ys2)) Zs2) (@ _let_1 (@ (@ tptp.append_list_a Ys2) Zs2))))) (forall ((A3 tptp.list_a) (B tptp.list_a) (C tptp.list_a)) (let ((_let_1 (@ tptp.append_a A3))) (= (@ (@ tptp.append_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_a B) C))))) (forall ((A3 tptp.list_list_a) (B tptp.list_list_a) (C tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a A3))) (= (@ (@ tptp.append_list_a (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_list_a B) C))))) (forall ((A3 tptp.list_list_a)) (= (@ (@ tptp.append_list_a A3) tptp.nil_list_a) A3)) (forall ((A3 tptp.list_a)) (= (@ (@ tptp.append_a A3) tptp.nil_a) A3)) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys2) tptp.nil_list_a) (and (= Xs tptp.nil_list_a) (= Ys2 tptp.nil_list_a)))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) tptp.nil_a) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= tptp.nil_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (and (= Xs tptp.nil_list_a) (= Ys2 tptp.nil_list_a)))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= tptp.nil_a (@ (@ tptp.append_a Xs) Ys2)) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))) (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a)) (= (= Ys2 (@ (@ tptp.append_list_a Xs) Ys2)) (= Xs tptp.nil_list_a))) (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (= (= Ys2 (@ (@ tptp.append_a Xs) Ys2)) (= Xs tptp.nil_a))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys2) Ys2) (= Xs tptp.nil_list_a))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) Ys2) (= Xs tptp.nil_a))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= Xs (@ (@ tptp.append_list_a Xs) Ys2)) (= Ys2 tptp.nil_list_a))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= Xs (@ (@ tptp.append_a Xs) Ys2)) (= Ys2 tptp.nil_a))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys2) Xs) (= Ys2 tptp.nil_list_a))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) Xs) (= Ys2 tptp.nil_a))) (forall ((Xs tptp.list_list_a)) (= (@ (@ tptp.append_list_a Xs) tptp.nil_list_a) Xs)) (forall ((Xs tptp.list_a)) (= (@ (@ tptp.append_a Xs) tptp.nil_a) Xs)) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (= (@ (@ tptp.splice_list_a Xs) Ys2) tptp.nil_list_a) (and (= Xs tptp.nil_list_a) (= Ys2 tptp.nil_list_a)))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.splice_a Xs) Ys2) tptp.nil_a) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))) (forall ((Xs tptp.list_list_a)) (= (@ (@ tptp.splice_list_a Xs) tptp.nil_list_a) Xs)) (forall ((Xs tptp.list_a)) (= (@ (@ tptp.splice_a Xs) tptp.nil_a) Xs)) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (F (-> tptp.nat tptp.list_a))) (= (@ (@ tptp.listIn1753026346list_a Xs) (@ (@ tptp.listIn1753026346list_a Ys2) F)) (@ (@ tptp.listIn1753026346list_a (@ (@ tptp.append_list_a Xs) Ys2)) F))) _let_12 (forall ((Xs tptp.list_list_a) (X3 tptp.list_a) (Ys2 tptp.list_list_a) (Y tptp.list_a)) (= (= (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a)) (@ (@ tptp.append_list_a Ys2) (@ (@ tptp.cons_list_a Y) tptp.nil_list_a))) (and (= Xs Ys2) (= X3 Y)))) (forall ((Xs tptp.list_a) (X3 tptp.a) (Ys2 tptp.list_a) (Y tptp.a)) (= (= (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X3) tptp.nil_a)) (@ (@ tptp.append_a Ys2) (@ (@ tptp.cons_a Y) tptp.nil_a))) (and (= Xs Ys2) (= X3 Y)))) (forall ((X3 tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys2 tptp.list_nat)) (= (@ (@ tptp.ord_lexordp_eq_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)) (or (@ (@ tptp.ord_less_nat X3) Y) (and (not (@ (@ tptp.ord_less_nat Y) X3)) (@ (@ tptp.ord_lexordp_eq_nat Xs) Ys2))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a) (Ts tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) Ys2) (@ (@ tptp.append_a Zs2) Ts)) (exists ((Us tptp.list_a)) (let ((_let_1 (@ tptp.append_a Us))) (or (and (= Xs (@ (@ tptp.append_a Zs2) Us)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append_a Xs) Us) Zs2) (= Ys2 (@ _let_1 Ts)))))))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a) (Ts tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) Ys2) (@ (@ tptp.append_list_a Zs2) Ts)) (exists ((Us tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Us))) (or (and (= Xs (@ (@ tptp.append_list_a Zs2) Us)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append_list_a Xs) Us) Zs2) (= Ys2 (@ _let_1 Ts)))))))) (forall ((Xs tptp.list_a) (Xs1 tptp.list_a) (Zs2 tptp.list_a) (Ys2 tptp.list_a) (Us2 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys2 (@ (@ tptp.append_a Xs1) Us2)) (= (@ _let_1 Ys2) (@ (@ tptp.append_a Zs2) Us2)))))) (forall ((Xs tptp.list_list_a) (Xs1 tptp.list_list_a) (Zs2 tptp.list_list_a) (Ys2 tptp.list_list_a) (Us2 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys2 (@ (@ tptp.append_list_a Xs1) Us2)) (= (@ _let_1 Ys2) (@ (@ tptp.append_list_a Zs2) Us2)))))) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (= (@ (@ tptp.append_list_a (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.append_list_a Xs) Ys2))))) (forall ((X3 tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ (@ tptp.append_a (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.append_a Xs) Ys2))))) (forall ((X3 tptp.list_a) (Xs1 tptp.list_list_a) (Ys2 tptp.list_list_a) (Xs tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs (@ (@ tptp.append_list_a Xs1) Zs2)) (= (@ _let_1 Xs) (@ (@ tptp.append_list_a Ys2) Zs2)))))) (forall ((X3 tptp.a) (Xs1 tptp.list_a) (Ys2 tptp.list_a) (Xs tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs (@ (@ tptp.append_a Xs1) Zs2)) (= (@ _let_1 Xs) (@ (@ tptp.append_a Ys2) Zs2)))))) (forall ((A3 tptp.list_list_a)) (= (@ (@ tptp.append_list_a tptp.nil_list_a) A3) A3)) (forall ((A3 tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) A3) A3)) (forall ((Ys2 tptp.list_list_a)) (= (@ (@ tptp.append_list_a tptp.nil_list_a) Ys2) Ys2)) (forall ((Ys2 tptp.list_a)) (= (@ (@ tptp.append_a tptp.nil_a) Ys2) Ys2)) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (= Xs Ys2) (= Xs (@ (@ tptp.append_list_a tptp.nil_list_a) Ys2)))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (= Xs Ys2) (= Xs (@ (@ tptp.append_a tptp.nil_a) Ys2)))) (forall ((Less (-> tptp.list_a tptp.list_a Bool)) (U tptp.list_list_a) (V tptp.list_list_a)) (@ (@ (@ tptp.lexordp_eq_list_a Less) U) (@ (@ tptp.append_list_a U) V))) (forall ((Less (-> tptp.a tptp.a Bool)) (U tptp.list_a) (V tptp.list_a)) (@ (@ (@ tptp.lexordp_eq_a Less) U) (@ (@ tptp.append_a U) V))) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (= (@ (@ tptp.splice_list_a (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.splice_list_a Ys2) Xs))))) (forall ((X3 tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ (@ tptp.splice_a (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.splice_a Ys2) Xs))))) (forall ((Ys2 tptp.list_list_a)) (= (@ (@ tptp.splice_list_a tptp.nil_list_a) Ys2) Ys2)) (forall ((Ys2 tptp.list_a)) (= (@ (@ tptp.splice_a tptp.nil_a) Ys2) Ys2)) (forall ((Xs tptp.list_list_a) (P (-> tptp.list_list_a Bool))) (=> (not (= Xs tptp.nil_list_a)) (=> (forall ((X tptp.list_a)) (@ P (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (=> (not (= Xs2 tptp.nil_list_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_list_a Xs2) (@ (@ tptp.cons_list_a X) tptp.nil_list_a)))))) (@ P Xs))))) (forall ((Xs tptp.list_a) (P (-> tptp.list_a Bool))) (=> (not (= Xs tptp.nil_a)) (=> (forall ((X tptp.a)) (@ P (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (forall ((X tptp.a) (Xs2 tptp.list_a)) (=> (not (= Xs2 tptp.nil_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_a Xs2) (@ (@ tptp.cons_a X) tptp.nil_a)))))) (@ P Xs))))) (forall ((Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a) (X3 tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a X3) Xs))) (= (= (@ (@ tptp.append_list_a Ys2) Zs2) _let_1) (or (and (= Ys2 tptp.nil_list_a) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_list_a)) (and (= Ys2 (@ (@ tptp.cons_list_a X3) Ys4)) (= (@ (@ tptp.append_list_a Ys4) Zs2) Xs))))))) (forall ((Ys2 tptp.list_a) (Zs2 tptp.list_a) (X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a X3) Xs))) (= (= (@ (@ tptp.append_a Ys2) Zs2) _let_1) (or (and (= Ys2 tptp.nil_a) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_a)) (and (= Ys2 (@ (@ tptp.cons_a X3) Ys4)) (= (@ (@ tptp.append_a Ys4) Zs2) Xs))))))) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a X3) Xs))) (= (= _let_1 (@ (@ tptp.append_list_a Ys2) Zs2)) (or (and (= Ys2 tptp.nil_list_a) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_list_a)) (and (= (@ (@ tptp.cons_list_a X3) Ys4) Ys2) (= Xs (@ (@ tptp.append_list_a Ys4) Zs2)))))))) (forall ((X3 tptp.a) (Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a X3) Xs))) (= (= _let_1 (@ (@ tptp.append_a Ys2) Zs2)) (or (and (= Ys2 tptp.nil_a) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_a)) (and (= (@ (@ tptp.cons_a X3) Ys4) Ys2) (= Xs (@ (@ tptp.append_a Ys4) Zs2)))))))) (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (not (forall ((Ys3 tptp.list_list_a) (Y3 tptp.list_a)) (not (= Xs (@ (@ tptp.append_list_a Ys3) (@ (@ tptp.cons_list_a Y3) tptp.nil_list_a)))))))) (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (not (forall ((Ys3 tptp.list_a) (Y3 tptp.a)) (not (= Xs (@ (@ tptp.append_a Ys3) (@ (@ tptp.cons_a Y3) tptp.nil_a)))))))) (forall ((P (-> tptp.list_list_a Bool)) (Xs tptp.list_list_a)) (=> (@ P tptp.nil_list_a) (=> (forall ((X tptp.list_a) (Xs2 tptp.list_list_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_list_a Xs2) (@ (@ tptp.cons_list_a X) tptp.nil_list_a))))) (@ P Xs)))) (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (@ P tptp.nil_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_a Xs2) (@ (@ tptp.cons_a X) tptp.nil_a))))) (@ P Xs)))) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (= (@ (@ tptp.append_list_a (@ _let_1 tptp.nil_list_a)) Xs) (@ _let_1 Xs)))) _let_11 (forall ((X3 tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (@ (@ tptp.ord_lexordp_eq_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)))) (forall ((X3 tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (=> (not (@ (@ tptp.ord_less_nat Y) X3)) (=> (@ (@ tptp.ord_lexordp_eq_nat Xs) Ys2) (@ (@ tptp.ord_lexordp_eq_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)))))) (forall ((F (-> tptp.a tptp.list_a)) (X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.maps_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs))))) (forall ((F (-> tptp.a tptp.list_list_a)) (X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.maps_a_list_a F))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.append_list_a (@ F X3)) (@ _let_1 Xs))))) (forall ((F (-> tptp.list_a tptp.list_a)) (X3 tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.maps_list_a_a F))) (= (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.append_a (@ F X3)) (@ _let_1 Xs))))) (forall ((F (-> tptp.list_a tptp.list_list_a)) (X3 tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.maps_list_a_list_a F))) (= (@ _let_1 (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.append_list_a (@ F X3)) (@ _let_1 Xs))))) (forall ((Xss2 tptp.list_list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a)) (let ((_let_1 (= Xss2 tptp.nil_list_list_a))) (= (= (@ tptp.concat_list_a Xss2) (@ (@ tptp.append_list_a Ys2) Zs2)) (and (=> _let_1 (and (= Ys2 tptp.nil_list_a) (= Zs2 tptp.nil_list_a))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_list_a) (Xs3 tptp.list_list_a) (Xs4 tptp.list_list_a) (Xss22 tptp.list_list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_list_a Xss1) (@ (@ tptp.cons_list_list_a (@ (@ tptp.append_list_a Xs3) Xs4)) Xss22))) (= Ys2 (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xss1)) Xs3)) (= Zs2 (@ (@ tptp.append_list_a Xs4) (@ tptp.concat_list_a Xss22)))))))))) (forall ((Xss2 tptp.list_list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a)) (let ((_let_1 (= Xss2 tptp.nil_list_a))) (= (= (@ tptp.concat_a Xss2) (@ (@ tptp.append_a Ys2) Zs2)) (and (=> _let_1 (and (= Ys2 tptp.nil_a) (= Zs2 tptp.nil_a))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_a) (Xs3 tptp.list_a) (Xs4 tptp.list_a) (Xss22 tptp.list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_a Xss1) (@ (@ tptp.cons_list_a (@ (@ tptp.append_a Xs3) Xs4)) Xss22))) (= Ys2 (@ (@ tptp.append_a (@ tptp.concat_a Xss1)) Xs3)) (= Zs2 (@ (@ tptp.append_a Xs4) (@ tptp.concat_a Xss22)))))))))) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (= (@ tptp.rotate1_list_a (@ _let_1 Xs)) (@ (@ tptp.append_list_a Xs) (@ _let_1 tptp.nil_list_a))))) (forall ((X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (= (@ tptp.rotate1_a (@ _let_1 Xs)) (@ (@ tptp.append_a Xs) (@ _let_1 tptp.nil_a))))) (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (= (@ tptp.butlast_list_a (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a))) Xs)) (forall ((Xs tptp.list_a) (X3 tptp.a)) (= (@ tptp.butlast_a (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X3) tptp.nil_a))) Xs)) (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (= (@ tptp.last_list_a (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a))) X3)) (forall ((Xs tptp.list_a) (X3 tptp.a)) (= (@ tptp.last_a (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X3) tptp.nil_a))) X3)) (forall ((Kl tptp.list_list_a) (K tptp.list_a) (Kl2 tptp.set_list_list_a)) (=> (@ (@ tptp.member_list_list_a (@ (@ tptp.append_list_a Kl) (@ (@ tptp.cons_list_a K) tptp.nil_list_a))) Kl2) (@ (@ tptp.member_list_a2 K) (@ (@ tptp.bNF_Gr1046450207list_a Kl2) Kl)))) (forall ((Kl tptp.list_a) (K tptp.a) (Kl2 tptp.set_list_a)) (=> (@ (@ tptp.member_list_a2 (@ (@ tptp.append_a Kl) (@ (@ tptp.cons_a K) tptp.nil_a))) Kl2) (@ (@ tptp.member_a2 K) (@ (@ tptp.bNF_Greatest_Succ_a Kl2) Kl)))) (forall ((K tptp.list_a) (Kl2 tptp.set_list_list_a) (Kl tptp.list_list_a)) (=> (@ (@ tptp.member_list_a2 K) (@ (@ tptp.bNF_Gr1046450207list_a Kl2) Kl)) (@ (@ tptp.member_list_list_a (@ (@ tptp.append_list_a Kl) (@ (@ tptp.cons_list_a K) tptp.nil_list_a))) Kl2))) (forall ((K tptp.a) (Kl2 tptp.set_list_a) (Kl tptp.list_a)) (=> (@ (@ tptp.member_a2 K) (@ (@ tptp.bNF_Greatest_Succ_a Kl2) Kl)) (@ (@ tptp.member_list_a2 (@ (@ tptp.append_a Kl) (@ (@ tptp.cons_a K) tptp.nil_a))) Kl2))) (forall ((Xs tptp.list_list_a)) (= (= (@ tptp.rotate1_list_a Xs) tptp.nil_list_a) (= Xs tptp.nil_list_a))) (forall ((Xs tptp.list_a)) (= (= (@ tptp.rotate1_a Xs) tptp.nil_a) (= Xs tptp.nil_a))) (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a)) (=> (= Ys2 tptp.nil_list_a) (= (@ tptp.last_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ tptp.last_list_a Xs)))) (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (=> (= Ys2 tptp.nil_a) (= (@ tptp.last_a (@ (@ tptp.append_a Xs) Ys2)) (@ tptp.last_a Xs)))) (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a)) (=> (not (= Ys2 tptp.nil_list_a)) (= (@ tptp.last_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ tptp.last_list_a Ys2)))) (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (=> (not (= Ys2 tptp.nil_a)) (= (@ tptp.last_a (@ (@ tptp.append_a Xs) Ys2)) (@ tptp.last_a Ys2)))) (forall ((Xs tptp.list_list_list_a) (Ys2 tptp.list_list_list_a)) (= (@ tptp.concat_list_a (@ (@ tptp.append_list_list_a Xs) Ys2)) (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xs)) (@ tptp.concat_list_a Ys2)))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (@ tptp.concat_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ (@ tptp.append_a (@ tptp.concat_a Xs)) (@ tptp.concat_a Ys2)))) (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ (@ tptp.append_list_a (@ tptp.butlast_list_a Xs)) (@ (@ tptp.cons_list_a (@ tptp.last_list_a Xs)) tptp.nil_list_a)) Xs))) (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ (@ tptp.append_a (@ tptp.butlast_a Xs)) (@ (@ tptp.cons_a (@ tptp.last_a Xs)) tptp.nil_a)) Xs))) (= (@ tptp.butlast_list_a tptp.nil_list_a) tptp.nil_list_a) (= (@ tptp.butlast_a tptp.nil_a) tptp.nil_a) (forall ((Xs tptp.list_list_a) (X3 tptp.list_a) (Ys2 tptp.list_list_a)) (= (= (@ (@ tptp.append_list_a Xs) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a)) Ys2) (and (not (= Ys2 tptp.nil_list_a)) (= (@ tptp.butlast_list_a Ys2) Xs) (= (@ tptp.last_list_a Ys2) X3)))) (forall ((Xs tptp.list_a) (X3 tptp.a) (Ys2 tptp.list_a)) (= (= (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X3) tptp.nil_a)) Ys2) (and (not (= Ys2 tptp.nil_a)) (= (@ tptp.butlast_a Ys2) Xs) (= (@ tptp.last_a Ys2) X3)))) (= (@ tptp.rotate1_list_a tptp.nil_list_a) tptp.nil_list_a) (= (@ tptp.rotate1_a tptp.nil_a) tptp.nil_a) (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (let ((_let_1 (@ tptp.last_list_a (@ (@ tptp.cons_list_a X3) Xs)))) (let ((_let_2 (= Xs tptp.nil_list_a))) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ tptp.last_list_a Xs))))))) (forall ((Xs tptp.list_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.last_a (@ (@ tptp.cons_a X3) Xs)))) (let ((_let_2 (= Xs tptp.nil_a))) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ tptp.last_a Xs))))))) (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (=> (= Xs tptp.nil_list_a) (= (@ tptp.last_list_a (@ (@ tptp.cons_list_a X3) Xs)) X3))) (forall ((Xs tptp.list_a) (X3 tptp.a)) (=> (= Xs tptp.nil_a) (= (@ tptp.last_a (@ (@ tptp.cons_a X3) Xs)) X3))) (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ tptp.last_list_a (@ (@ tptp.cons_list_a X3) Xs)) (@ tptp.last_list_a Xs)))) (forall ((Xs tptp.list_a) (X3 tptp.a)) (=> (not (= Xs tptp.nil_a)) (= (@ tptp.last_a (@ (@ tptp.cons_a X3) Xs)) (@ tptp.last_a Xs)))) (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.last_list_a (@ (@ tptp.append_list_a Xs) Ys2)))) (let ((_let_2 (= Ys2 tptp.nil_list_a))) (and (=> _let_2 (= _let_1 (@ tptp.last_list_a Xs))) (=> (not _let_2) (= _let_1 (@ tptp.last_list_a Ys2))))))) (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.last_a (@ (@ tptp.append_a Xs) Ys2)))) (let ((_let_2 (= Ys2 tptp.nil_a))) (and (=> _let_2 (= _let_1 (@ tptp.last_a Xs))) (=> (not _let_2) (= _let_1 (@ tptp.last_a Ys2))))))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (exists ((Ss tptp.list_list_a) (Xs5 tptp.list_list_a) (Ys5 tptp.list_list_a)) (and (= Xs (@ (@ tptp.append_list_a Xs5) Ss)) (= Ys2 (@ (@ tptp.append_list_a Ys5) Ss)) (or (= Xs5 tptp.nil_list_a) (= Ys5 tptp.nil_list_a) (not (= (@ tptp.last_list_a Xs5) (@ tptp.last_list_a Ys5))))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (exists ((Ss tptp.list_a) (Xs5 tptp.list_a) (Ys5 tptp.list_a)) (and (= Xs (@ (@ tptp.append_a Xs5) Ss)) (= Ys2 (@ (@ tptp.append_a Ys5) Ss)) (or (= Xs5 tptp.nil_a) (= Ys5 tptp.nil_a) (not (= (@ tptp.last_a Xs5) (@ tptp.last_a Ys5))))))) (forall ((Xs tptp.list_list_a) (X3 tptp.list_a)) (let ((_let_1 (@ tptp.cons_list_a X3))) (let ((_let_2 (@ tptp.butlast_list_a (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_list_a))) (and (=> _let_3 (= _let_2 tptp.nil_list_a)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_a Xs))))))))) (forall ((Xs tptp.list_a) (X3 tptp.a)) (let ((_let_1 (@ tptp.cons_a X3))) (let ((_let_2 (@ tptp.butlast_a (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_a))) (and (=> _let_3 (= _let_2 tptp.nil_a)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_a Xs))))))))) _let_10 _let_8 (forall ((X3 tptp.list_list_a) (Xs tptp.list_list_list_a)) (= (@ tptp.concat_list_a (@ (@ tptp.cons_list_list_a X3) Xs)) (@ (@ tptp.append_list_a X3) (@ tptp.concat_list_a Xs)))) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a)) (= (@ tptp.concat_a (@ (@ tptp.cons_list_a X3) Xs)) (@ (@ tptp.append_a X3) (@ tptp.concat_a Xs)))) (forall ((Ys2 tptp.list_list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Xs))) (let ((_let_2 (@ tptp.butlast_list_a (@ _let_1 Ys2)))) (let ((_let_3 (= Ys2 tptp.nil_list_a))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_list_a Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_a Ys2))))))))) (forall ((Ys2 tptp.list_a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.append_a Xs))) (let ((_let_2 (@ tptp.butlast_a (@ _let_1 Ys2)))) (let ((_let_3 (= Ys2 tptp.nil_a))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_a Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_a Ys2))))))))) (forall ((F (-> tptp.a tptp.list_list_a))) (= (@ (@ tptp.maps_a_list_a F) tptp.nil_a) tptp.nil_list_a)) (forall ((F (-> tptp.list_a tptp.list_a))) (= (@ (@ tptp.maps_list_a_a F) tptp.nil_list_a) tptp.nil_a)) (forall ((F (-> tptp.list_a tptp.list_list_a))) (= (@ (@ tptp.maps_list_a_list_a F) tptp.nil_list_a) tptp.nil_list_a)) (forall ((F (-> tptp.a tptp.list_a))) (= (@ (@ tptp.maps_a_a F) tptp.nil_a) tptp.nil_a)) (forall ((Xss2 tptp.list_list_list_a) (Ys2 tptp.list_list_a) (Zs2 tptp.list_list_a)) (=> (= (@ tptp.concat_list_a Xss2) (@ (@ tptp.append_list_a Ys2) Zs2)) (=> (not (= Xss2 tptp.nil_list_list_a)) (exists ((Xss12 tptp.list_list_list_a) (Xs2 tptp.list_list_a) (Xs5 tptp.list_list_a) (Xss23 tptp.list_list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_list_a Xss12) (@ (@ tptp.cons_list_list_a (@ (@ tptp.append_list_a Xs2) Xs5)) Xss23))) (= Ys2 (@ (@ tptp.append_list_a (@ tptp.concat_list_a Xss12)) Xs2)) (= Zs2 (@ (@ tptp.append_list_a Xs5) (@ tptp.concat_list_a Xss23)))))))) (forall ((Xss2 tptp.list_list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a)) (=> (= (@ tptp.concat_a Xss2) (@ (@ tptp.append_a Ys2) Zs2)) (=> (not (= Xss2 tptp.nil_list_a)) (exists ((Xss12 tptp.list_list_a) (Xs2 tptp.list_a) (Xs5 tptp.list_a) (Xss23 tptp.list_list_a)) (and (= Xss2 (@ (@ tptp.append_list_a Xss12) (@ (@ tptp.cons_list_a (@ (@ tptp.append_a Xs2) Xs5)) Xss23))) (= Ys2 (@ (@ tptp.append_a (@ tptp.concat_a Xss12)) Xs2)) (= Zs2 (@ (@ tptp.append_a Xs5) (@ tptp.concat_a Xss23)))))))) (forall ((Kl2 tptp.set_list_list_a) (K tptp.list_a)) (let ((_let_1 (@ tptp.member_list_list_a tptp.nil_list_a))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member_list_a2 K) (@ (@ tptp.bNF_Gr1046450207list_a Kl2) tptp.nil_list_a)) (@ _let_1 (@ (@ tptp.bNF_Gr1972240547list_a Kl2) K)))))) (forall ((Kl2 tptp.set_list_a) (K tptp.a)) (let ((_let_1 (@ tptp.member_list_a2 tptp.nil_a))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member_a2 K) (@ (@ tptp.bNF_Greatest_Succ_a Kl2) tptp.nil_a)) (@ _let_1 (@ (@ tptp.bNF_Greatest_Shift_a Kl2) K)))))) (forall ((Kl2 tptp.set_list_list_a) (K tptp.list_a) (Kl tptp.list_list_a)) (= (@ (@ tptp.bNF_Gr1046450207list_a (@ (@ tptp.bNF_Gr1972240547list_a Kl2) K)) Kl) (@ (@ tptp.bNF_Gr1046450207list_a Kl2) (@ (@ tptp.cons_list_a K) Kl)))) (forall ((Kl2 tptp.set_list_a) (K tptp.a) (Kl tptp.list_a)) (= (@ (@ tptp.bNF_Greatest_Succ_a (@ (@ tptp.bNF_Greatest_Shift_a Kl2) K)) Kl) (@ (@ tptp.bNF_Greatest_Succ_a Kl2) (@ (@ tptp.cons_a K) Kl)))) (= tptp.concat_list_a (lambda ((Xss3 tptp.list_list_list_a)) (@ (@ (@ tptp.foldr_769741863list_a tptp.append_list_a) Xss3) tptp.nil_list_a))) (= tptp.concat_a (lambda ((Xss3 tptp.list_list_a)) (@ (@ (@ tptp.foldr_list_a_list_a tptp.append_a) Xss3) tptp.nil_a))) (forall ((F (-> tptp.list_a tptp.list_a tptp.list_a)) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a) (A3 tptp.list_a)) (let ((_let_1 (@ tptp.foldr_list_a_list_a F))) (= (@ (@ _let_1 (@ (@ tptp.append_list_a Xs) Ys2)) A3) (@ (@ _let_1 Xs) (@ (@ _let_1 Ys2) A3))))) (forall ((Kl tptp.list_list_a) (Kl2 tptp.set_list_list_a) (K tptp.list_a)) (=> (@ (@ tptp.member_list_list_a Kl) (@ (@ tptp.bNF_Gr1972240547list_a Kl2) K)) (@ (@ tptp.member_list_list_a (@ (@ tptp.cons_list_a K) Kl)) Kl2))) (forall ((Kl tptp.list_a) (Kl2 tptp.set_list_a) (K tptp.a)) (=> (@ (@ tptp.member_list_a2 Kl) (@ (@ tptp.bNF_Greatest_Shift_a Kl2) K)) (@ (@ tptp.member_list_a2 (@ (@ tptp.cons_a K) Kl)) Kl2))) _let_6 _let_5 (forall ((X3 tptp.nat) (Y tptp.nat) (Us2 tptp.list_nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Us2))) (=> (@ (@ tptp.ord_less_nat X3) Y) (@ (@ tptp.ord_lexordp_nat (@ _let_1 (@ (@ tptp.cons_nat X3) Xs))) (@ _let_1 (@ (@ tptp.cons_nat Y) Ys2)))))) (forall ((X3 tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys2 tptp.list_nat)) (= (@ (@ tptp.ord_lexordp_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)) (or (@ (@ tptp.ord_less_nat X3) Y) (and (not (@ (@ tptp.ord_less_nat Y) X3)) (@ (@ tptp.ord_lexordp_nat Xs) Ys2))))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ tptp.hd_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ tptp.hd_list_a Xs)))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ tptp.hd_a (@ (@ tptp.append_a Xs) Ys2)) (@ tptp.hd_a Xs)))) (forall ((Xs tptp.list_nat)) (=> (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))) (not (@ (@ tptp.ord_lexordp_nat Xs) Xs)))) (forall ((X21 tptp.list_a) (X22 tptp.list_list_a)) (= (@ tptp.hd_list_a (@ (@ tptp.cons_list_a X21) X22)) X21)) (forall ((X21 tptp.a) (X22 tptp.list_a)) (= (@ tptp.hd_a (@ (@ tptp.cons_a X21) X22)) X21)) (forall ((Xs tptp.list_list_list_a)) (let ((_let_1 (@ tptp.hd_list_list_a Xs))) (=> (not (= Xs tptp.nil_list_list_a)) (=> (not (= _let_1 tptp.nil_list_a)) (= (@ tptp.hd_list_a (@ tptp.concat_list_a Xs)) (@ tptp.hd_list_a _let_1)))))) (forall ((Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.hd_list_a Xs))) (=> (not (= Xs tptp.nil_list_a)) (=> (not (= _let_1 tptp.nil_a)) (= (@ tptp.hd_a (@ tptp.concat_a Xs)) (@ tptp.hd_a _let_1)))))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.hd_list_a (@ (@ tptp.append_list_a Xs) Ys2)))) (let ((_let_2 (= Xs tptp.nil_list_a))) (and (=> _let_2 (= _let_1 (@ tptp.hd_list_a Ys2))) (=> (not _let_2) (= _let_1 (@ tptp.hd_list_a Xs))))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.hd_a (@ (@ tptp.append_a Xs) Ys2)))) (let ((_let_2 (= Xs tptp.nil_a))) (and (=> _let_2 (= _let_1 (@ tptp.hd_a Ys2))) (=> (not _let_2) (= _let_1 (@ tptp.hd_a Xs))))))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (exists ((Ps tptp.list_list_a) (Xs5 tptp.list_list_a) (Ys5 tptp.list_list_a)) (let ((_let_1 (@ tptp.append_list_a Ps))) (and (= Xs (@ _let_1 Xs5)) (= Ys2 (@ _let_1 Ys5)) (or (= Xs5 tptp.nil_list_a) (= Ys5 tptp.nil_list_a) (not (= (@ tptp.hd_list_a Xs5) (@ tptp.hd_list_a Ys5)))))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (exists ((Ps tptp.list_a) (Xs5 tptp.list_a) (Ys5 tptp.list_a)) (let ((_let_1 (@ tptp.append_a Ps))) (and (= Xs (@ _let_1 Xs5)) (= Ys2 (@ _let_1 Ys5)) (or (= Xs5 tptp.nil_a) (= Ys5 tptp.nil_a) (not (= (@ tptp.hd_a Xs5) (@ tptp.hd_a Ys5)))))))) (forall ((X3 tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat X3) Y) (@ (@ tptp.ord_lexordp_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)))) (forall ((X3 tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y)) (=> (not (@ (@ tptp.ord_less_nat Y) X3)) (=> (@ (@ tptp.ord_lexordp_nat Xs) Ys2) (@ (@ tptp.ord_lexordp_nat (@ (@ tptp.cons_nat X3) Xs)) (@ (@ tptp.cons_nat Y) Ys2)))))) (forall ((Xs tptp.list_nat) (Us2 tptp.list_nat) (Vs2 tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Xs))) (=> (@ (@ tptp.ord_lexordp_nat (@ _let_1 Us2)) (@ _let_1 Vs2)) (=> (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (@ (@ tptp.ord_lexordp_nat Us2) Vs2))))) (forall ((A1 tptp.list_nat) (A2 tptp.list_nat)) (=> (@ (@ tptp.ord_lexordp_nat A1) A2) (=> (=> (= A1 tptp.nil_nat) (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (not (= A2 (@ (@ tptp.cons_nat Y3) Ys3))))) (=> (forall ((X tptp.nat)) (=> (exists ((Xs2 tptp.list_nat)) (= A1 (@ (@ tptp.cons_nat X) Xs2))) (forall ((Y3 tptp.nat)) (=> (exists ((Ys3 tptp.list_nat)) (= A2 (@ (@ tptp.cons_nat Y3) Ys3))) (not (@ (@ tptp.ord_less_nat X) Y3)))))) (not (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= A1 (@ (@ tptp.cons_nat X) Xs2)) (forall ((Ys3 tptp.list_nat)) (=> (= A2 (@ (@ tptp.cons_nat Y3) Ys3)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (=> (not (@ (@ tptp.ord_less_nat Y3) X)) (not (@ (@ tptp.ord_lexordp_nat Xs2) Ys3))))))))))))) (= tptp.ord_lexordp_nat (lambda ((A12 tptp.list_nat) (A22 tptp.list_nat)) (or (exists ((Y2 tptp.nat) (Ys tptp.list_nat)) (and (= A12 tptp.nil_nat) (= A22 (@ (@ tptp.cons_nat Y2) Ys)))) (exists ((X4 tptp.nat) (Y2 tptp.nat) (Xs3 tptp.list_nat) (Ys tptp.list_nat)) (and (= A12 (@ (@ tptp.cons_nat X4) Xs3)) (= A22 (@ (@ tptp.cons_nat Y2) Ys)) (@ (@ tptp.ord_less_nat X4) Y2))) (exists ((X4 tptp.nat) (Y2 tptp.nat) (Xs3 tptp.list_nat) (Ys tptp.list_nat)) (and (= A12 (@ (@ tptp.cons_nat X4) Xs3)) (= A22 (@ (@ tptp.cons_nat Y2) Ys)) (not (@ (@ tptp.ord_less_nat X4) Y2)) (not (@ (@ tptp.ord_less_nat Y2) X4)) (@ (@ tptp.ord_lexordp_nat Xs3) Ys)))))) (forall ((X12 tptp.list_nat) (X23 tptp.list_nat) (P (-> tptp.list_nat tptp.list_nat Bool))) (=> (@ (@ tptp.ord_lexordp_nat X12) X23) (=> (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_nat Y3) Ys3))) (=> (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat X) Y3) (@ (@ P (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (=> (forall ((X tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (=> (not (@ (@ tptp.ord_less_nat Y3) X)) (=> (@ (@ tptp.ord_lexordp_nat Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3))))))) (@ (@ P X12) X23)))))) (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_lexordp_nat Xs) Ys2) (=> (=> (= Xs tptp.nil_nat) (forall ((Y3 tptp.nat) (Ys5 tptp.list_nat)) (not (= Ys2 (@ (@ tptp.cons_nat Y3) Ys5))))) (=> (forall ((X tptp.nat)) (=> (exists ((Xs5 tptp.list_nat)) (= Xs (@ (@ tptp.cons_nat X) Xs5))) (forall ((Y3 tptp.nat)) (=> (exists ((Ys5 tptp.list_nat)) (= Ys2 (@ (@ tptp.cons_nat Y3) Ys5))) (not (@ (@ tptp.ord_less_nat X) Y3)))))) (not (forall ((X tptp.nat) (Xs5 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X) Xs5)) (forall ((Ys5 tptp.list_nat)) (=> (= Ys2 (@ (@ tptp.cons_nat X) Ys5)) (not (@ (@ tptp.ord_lexordp_nat Xs5) Ys5))))))))))) (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat) (P (-> tptp.list_nat tptp.list_nat Bool))) (=> (@ (@ tptp.ord_lexordp_nat Xs) Ys2) (=> (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_nat Y3) Ys3))) (=> (forall ((X tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat X) Y3) (@ (@ P (@ (@ tptp.cons_nat X) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (=> (forall ((X tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X))) (=> (@ (@ tptp.ord_lexordp_nat Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ _let_1 Xs2)) (@ _let_1 Ys3)))))) (@ (@ P Xs) Ys2)))))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (= (@ tptp.distinct_adj_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (and (@ tptp.distinct_adj_list_a Xs) (@ tptp.distinct_adj_list_a Ys2) (or (= Xs tptp.nil_list_a) (= Ys2 tptp.nil_list_a) (not (= (@ tptp.last_list_a Xs) (@ tptp.hd_list_a Ys2))))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (@ tptp.distinct_adj_a (@ (@ tptp.append_a Xs) Ys2)) (and (@ tptp.distinct_adj_a Xs) (@ tptp.distinct_adj_a Ys2) (or (= Xs tptp.nil_a) (= Ys2 tptp.nil_a) (not (= (@ tptp.last_a Xs) (@ tptp.hd_a Ys2))))))) (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ tptp.rotate1_list_a Xs) (@ (@ tptp.append_list_a (@ tptp.tl_list_a Xs)) (@ (@ tptp.cons_list_a (@ tptp.hd_list_a Xs)) tptp.nil_list_a))))) (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ tptp.rotate1_a Xs) (@ (@ tptp.append_a (@ tptp.tl_a Xs)) (@ (@ tptp.cons_a (@ tptp.hd_a Xs)) tptp.nil_a))))) (forall ((P (-> tptp.list_a tptp.list_a Bool)) (Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (let ((_let_1 (@ tptp.successively_list_a P))) (= (@ _let_1 (@ (@ tptp.append_list_a Xs) Ys2)) (and (@ _let_1 Xs) (@ _let_1 Ys2) (or (= Xs tptp.nil_list_a) (= Ys2 tptp.nil_list_a) (@ (@ P (@ tptp.last_list_a Xs)) (@ tptp.hd_list_a Ys2))))))) (forall ((P (-> tptp.a tptp.a Bool)) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.successively_a P))) (= (@ _let_1 (@ (@ tptp.append_a Xs) Ys2)) (and (@ _let_1 Xs) (@ _let_1 Ys2) (or (= Xs tptp.nil_a) (= Ys2 tptp.nil_a) (@ (@ P (@ tptp.last_a Xs)) (@ tptp.hd_a Ys2))))))) (forall ((X3 tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y) Xs))) (= (@ tptp.distinct_adj_list_a (@ (@ tptp.cons_list_a X3) _let_1)) (and (not (= X3 Y)) (@ tptp.distinct_adj_list_a _let_1))))) (forall ((X3 tptp.a) (Y tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y) Xs))) (= (@ tptp.distinct_adj_a (@ (@ tptp.cons_a X3) _let_1)) (and (not (= X3 Y)) (@ tptp.distinct_adj_a _let_1))))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ tptp.tl_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ (@ tptp.append_list_a (@ tptp.tl_list_a Xs)) Ys2)))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ tptp.tl_a (@ (@ tptp.append_a Xs) Ys2)) (@ (@ tptp.append_a (@ tptp.tl_a Xs)) Ys2)))) (forall ((Xs tptp.list_list_a)) (=> (not (= Xs tptp.nil_list_a)) (= (@ (@ tptp.cons_list_a (@ tptp.hd_list_a Xs)) (@ tptp.tl_list_a Xs)) Xs))) (forall ((Xs tptp.list_a)) (=> (not (= Xs tptp.nil_a)) (= (@ (@ tptp.cons_a (@ tptp.hd_a Xs)) (@ tptp.tl_a Xs)) Xs))) (forall ((List tptp.list_list_a)) (=> (not (= List tptp.nil_list_a)) (= (@ (@ tptp.cons_list_a (@ tptp.hd_list_a List)) (@ tptp.tl_list_a List)) List))) (forall ((List tptp.list_a)) (=> (not (= List tptp.nil_a)) (= (@ (@ tptp.cons_a (@ tptp.hd_a List)) (@ tptp.tl_a List)) List))) (forall ((X21 tptp.list_a) (X22 tptp.list_list_a)) (= (@ tptp.tl_list_a (@ (@ tptp.cons_list_a X21) X22)) X22)) (forall ((X21 tptp.a) (X22 tptp.list_a)) (= (@ tptp.tl_a (@ (@ tptp.cons_a X21) X22)) X22)) (= (@ tptp.tl_list_a tptp.nil_list_a) tptp.nil_list_a) (= (@ tptp.tl_a tptp.nil_a) tptp.nil_a) (forall ((X3 (-> tptp.list_a tptp.list_a Bool)) (Xa tptp.list_list_a)) (=> (not (@ (@ tptp.successively_list_a X3) Xa)) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_list_a X) _let_1)) (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_list_a X3) _let_1)))))))) (forall ((X3 (-> tptp.a tptp.a Bool)) (Xa tptp.list_a)) (=> (not (@ (@ tptp.successively_a X3) Xa)) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_a X) _let_1)) (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_a X3) _let_1)))))))) (forall ((P (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a) (Y tptp.list_a) (Xs tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y) Xs))) (let ((_let_2 (@ tptp.successively_list_a P))) (= (@ _let_2 (@ (@ tptp.cons_list_a X3) _let_1)) (and (@ (@ P X3) Y) (@ _let_2 _let_1)))))) (forall ((P (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Y tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y) Xs))) (let ((_let_2 (@ tptp.successively_a P))) (= (@ _let_2 (@ (@ tptp.cons_a X3) _let_1)) (and (@ (@ P X3) Y) (@ _let_2 _let_1)))))) (forall ((P (-> tptp.list_a tptp.list_a Bool))) (@ (@ tptp.successively_list_a P) tptp.nil_list_a)) (forall ((P (-> tptp.a tptp.a Bool))) (@ (@ tptp.successively_a P) tptp.nil_a)) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (@ tptp.distinct_adj_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ tptp.distinct_adj_list_a Xs))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ tptp.distinct_adj_a (@ (@ tptp.append_a Xs) Ys2)) (@ tptp.distinct_adj_a Xs))) (forall ((Xs tptp.list_list_a) (Ys2 tptp.list_list_a)) (=> (@ tptp.distinct_adj_list_a (@ (@ tptp.append_list_a Xs) Ys2)) (@ tptp.distinct_adj_list_a Ys2))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ tptp.distinct_adj_a (@ (@ tptp.append_a Xs) Ys2)) (@ tptp.distinct_adj_a Ys2))) (@ tptp.distinct_adj_list_a tptp.nil_list_a) (@ tptp.distinct_adj_a tptp.nil_a) (forall ((X3 tptp.list_a) (Xs tptp.list_list_a)) (=> (@ tptp.distinct_adj_list_a (@ (@ tptp.cons_list_a X3) Xs)) (@ tptp.distinct_adj_list_a Xs))) (forall ((X3 tptp.a) (Xs tptp.list_a)) (=> (@ tptp.distinct_adj_a (@ (@ tptp.cons_a X3) Xs)) (@ tptp.distinct_adj_a Xs))) (forall ((Xs tptp.list_a)) (= (@ tptp.butlast_a (@ tptp.tl_a Xs)) (@ tptp.tl_a (@ tptp.butlast_a Xs)))) (forall ((Xs tptp.list_list_a)) (= (= (@ tptp.tl_list_a Xs) tptp.nil_list_a) (or (= Xs tptp.nil_list_a) (exists ((X4 tptp.list_a)) (= Xs (@ (@ tptp.cons_list_a X4) tptp.nil_list_a)))))) (forall ((Xs tptp.list_a)) (= (= (@ tptp.tl_a Xs) tptp.nil_a) (or (= Xs tptp.nil_a) (exists ((X4 tptp.a)) (= Xs (@ (@ tptp.cons_a X4) tptp.nil_a)))))) (forall ((Xs tptp.list_list_a)) (= (= tptp.nil_list_a (@ tptp.tl_list_a Xs)) (or (= Xs tptp.nil_list_a) (exists ((X4 tptp.list_a)) (= Xs (@ (@ tptp.cons_list_a X4) tptp.nil_list_a)))))) (forall ((Xs tptp.list_a)) (= (= tptp.nil_a (@ tptp.tl_a Xs)) (or (= Xs tptp.nil_a) (exists ((X4 tptp.a)) (= Xs (@ (@ tptp.cons_a X4) tptp.nil_a)))))) (forall ((List tptp.list_list_a) (List2 tptp.list_list_a)) (let ((_let_1 (= List2 tptp.nil_list_a))) (let ((_let_2 (= List tptp.nil_list_a))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (and (= (@ tptp.hd_list_a List) (@ tptp.hd_list_a List2)) (= (@ tptp.tl_list_a List) (@ tptp.tl_list_a List2))))) (= List List2)))))) (forall ((List tptp.list_a) (List2 tptp.list_a)) (let ((_let_1 (= List2 tptp.nil_a))) (let ((_let_2 (= List tptp.nil_a))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (and (= (@ tptp.hd_a List) (@ tptp.hd_a List2)) (= (@ tptp.tl_a List) (@ tptp.tl_a List2))))) (= List List2)))))) (forall ((Xs tptp.list_list_a)) (let ((_let_1 (@ tptp.tl_list_a Xs))) (=> (or (= Xs tptp.nil_list_a) (not (= _let_1 tptp.nil_list_a))) (= (@ tptp.last_list_a _let_1) (@ tptp.last_list_a Xs))))) (forall ((Xs tptp.list_a)) (let ((_let_1 (@ tptp.tl_a Xs))) (=> (or (= Xs tptp.nil_a) (not (= _let_1 tptp.nil_a))) (= (@ tptp.last_a _let_1) (@ tptp.last_a Xs))))) (forall ((P (-> tptp.list_a tptp.list_a Bool)) (X3 tptp.list_a)) (@ (@ tptp.successively_list_a P) (@ (@ tptp.cons_list_a X3) tptp.nil_list_a))) (forall ((P (-> tptp.a tptp.a Bool)) (X3 tptp.a)) (@ (@ tptp.successively_a P) (@ (@ tptp.cons_a X3) tptp.nil_a))) (forall ((X3 (-> tptp.list_a tptp.list_a Bool)) (Xa tptp.list_list_a) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ (@ tptp.successively_list_a X3) Xa) Y) (=> (=> (= Xa tptp.nil_list_a) _let_1) (=> (=> (exists ((X tptp.list_a)) (= Xa (@ (@ tptp.cons_list_a X) tptp.nil_list_a))) _let_1) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_list_a X) _let_1)) (= Y (not (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_list_a X3) _let_1))))))))))))) (forall ((X3 (-> tptp.a tptp.a Bool)) (Xa tptp.list_a) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ (@ tptp.successively_a X3) Xa) Y) (=> (=> (= Xa tptp.nil_a) _let_1) (=> (=> (exists ((X tptp.a)) (= Xa (@ (@ tptp.cons_a X) tptp.nil_a))) _let_1) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_a X) _let_1)) (= Y (not (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_a X3) _let_1))))))))))))) (forall ((X3 (-> tptp.list_a tptp.list_a Bool)) (Xa tptp.list_list_a)) (=> (@ (@ tptp.successively_list_a X3) Xa) (=> (not (= Xa tptp.nil_list_a)) (=> (forall ((X tptp.list_a)) (not (= Xa (@ (@ tptp.cons_list_a X) tptp.nil_list_a)))) (not (forall ((X tptp.list_a) (Y3 tptp.list_a) (Xs2 tptp.list_list_a)) (let ((_let_1 (@ (@ tptp.cons_list_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_list_a X) _let_1)) (not (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_list_a X3) _let_1))))))))))) (forall ((X3 (-> tptp.a tptp.a Bool)) (Xa tptp.list_a)) (=> (@ (@ tptp.successively_a X3) Xa) (=> (not (= Xa tptp.nil_a)) (=> (forall ((X tptp.a)) (not (= Xa (@ (@ tptp.cons_a X) tptp.nil_a)))) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (=> (= Xa (@ (@ tptp.cons_a X) _let_1)) (not (and (@ (@ X3 X) Y3) (@ (@ tptp.successively_a X3) _let_1))))))))))) (forall ((X3 tptp.list_a)) (@ tptp.distinct_adj_list_a (@ (@ tptp.cons_list_a X3) tptp.nil_list_a))) (forall ((X3 tptp.a)) (@ tptp.distinct_adj_a (@ (@ tptp.cons_a X3) tptp.nil_a))) (forall ((List tptp.list_a)) (=> (not (= List tptp.nil_a)) (= List (@ (@ tptp.cons_a (@ tptp.hd_a List)) (@ tptp.tl_a List))))) (forall ((P (-> tptp.a tptp.a Bool)) (X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.successively_a P))) (= (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (or (= Xs tptp.nil_a) (and (@ (@ P X3) (@ tptp.hd_a Xs)) (@ _let_1 Xs)))))) (forall ((X3 tptp.a) (Xs tptp.list_a)) (= (@ tptp.distinct_adj_a (@ (@ tptp.cons_a X3) Xs)) (or (= Xs tptp.nil_a) (and (not (= X3 (@ tptp.hd_a Xs))) (@ tptp.distinct_adj_a Xs))))) (forall ((Z tptp.a) (Zs2 tptp.list_a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.shuffles_a Xs))) (let ((_let_2 (@ tptp.member_list_a2 Zs2))) (= (@ (@ tptp.member_list_a2 (@ (@ tptp.cons_a Z) Zs2)) (@ _let_1 Ys2)) (or (and (not (= Xs tptp.nil_a)) (= (@ tptp.hd_a Xs) Z) (@ _let_2 (@ (@ tptp.shuffles_a (@ tptp.tl_a Xs)) Ys2))) (and (not (= Ys2 tptp.nil_a)) (= (@ tptp.hd_a Ys2) Z) (@ _let_2 (@ _let_1 (@ tptp.tl_a Ys2))))))))) (forall ((Xs tptp.list_a) (F (-> tptp.a tptp.a tptp.a)) (Y tptp.a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.map2_a_a_a F))) (=> (not (= Xs tptp.nil_a)) (= (@ (@ _let_1 Xs) (@ (@ tptp.cons_a Y) Ys2)) (@ (@ tptp.cons_a (@ (@ F (@ tptp.hd_a Xs)) Y)) (@ (@ _let_1 (@ tptp.tl_a Xs)) Ys2)))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (= (@ (@ tptp.member_list_a2 tptp.nil_a) (@ (@ tptp.shuffles_a Xs) Ys2)) (and (= Xs tptp.nil_a) (= Ys2 tptp.nil_a)))) (forall ((Zs2 tptp.list_a) (Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (@ (@ tptp.member_list_a2 Zs2) (@ (@ tptp.shuffles_a Xs) Ys2)) (=> (=> (= Zs2 Xs) (not (= Ys2 tptp.nil_a))) (=> (=> (= Zs2 Ys2) (not (= Xs tptp.nil_a))) (=> (forall ((X tptp.a) (Xs5 tptp.list_a)) (=> (= Xs (@ (@ tptp.cons_a X) Xs5)) (forall ((Z2 tptp.a) (Zs3 tptp.list_a)) (=> (= Zs2 (@ (@ tptp.cons_a Z2) Zs3)) (=> (= X Z2) (not (@ (@ tptp.member_list_a2 Zs3) (@ (@ tptp.shuffles_a Xs5) Ys2)))))))) (not (forall ((Y3 tptp.a) (Ys5 tptp.list_a)) (=> (= Ys2 (@ (@ tptp.cons_a Y3) Ys5)) (forall ((Z2 tptp.a) (Zs3 tptp.list_a)) (=> (= Zs2 (@ (@ tptp.cons_a Z2) Zs3)) (=> (= Y3 Z2) (not (@ (@ tptp.member_list_a2 Zs3) (@ (@ tptp.shuffles_a Xs) Ys5)))))))))))))) (forall ((F (-> tptp.a tptp.a tptp.a)) (X3 tptp.a) (Xs tptp.list_a) (Y tptp.a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.map2_a_a_a F))) (= (@ (@ _let_1 (@ (@ tptp.cons_a X3) Xs)) (@ (@ tptp.cons_a Y) Ys2)) (@ (@ tptp.cons_a (@ (@ F X3) Y)) (@ (@ _let_1 Xs) Ys2))))) (forall ((Zs2 tptp.list_a) (Xs tptp.list_a) (Ys2 tptp.list_a) (Z tptp.a)) (let ((_let_1 (@ tptp.cons_a Z))) (=> (@ (@ tptp.member_list_a2 Zs2) (@ (@ tptp.shuffles_a Xs) Ys2)) (@ (@ tptp.member_list_a2 (@ _let_1 Zs2)) (@ (@ tptp.shuffles_a (@ _let_1 Xs)) Ys2))))) (forall ((Zs2 tptp.list_a) (Xs tptp.list_a) (Ys2 tptp.list_a) (Z tptp.a)) (let ((_let_1 (@ tptp.cons_a Z))) (let ((_let_2 (@ tptp.shuffles_a Xs))) (=> (@ (@ tptp.member_list_a2 Zs2) (@ _let_2 Ys2)) (@ (@ tptp.member_list_a2 (@ _let_1 Zs2)) (@ _let_2 (@ _let_1 Ys2))))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (= Xs tptp.nil_a) (=> (= Ys2 tptp.nil_a) (@ (@ tptp.member_list_a2 tptp.nil_a) (@ (@ tptp.shuffles_a Xs) Ys2))))) (forall ((Xs tptp.list_a) (F (-> tptp.a tptp.a tptp.a)) (Y tptp.a) (Ys2 tptp.list_a)) (let ((_let_1 (@ tptp.map2_a_a_a F))) (let ((_let_2 (@ (@ _let_1 Xs) (@ (@ tptp.cons_a Y) Ys2)))) (let ((_let_3 (= Xs tptp.nil_a))) (and (=> _let_3 (= _let_2 tptp.nil_a)) (=> (not _let_3) (= _let_2 (@ (@ tptp.cons_a (@ (@ F (@ tptp.hd_a Xs)) Y)) (@ (@ _let_1 (@ tptp.tl_a Xs)) Ys2))))))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a)) (=> (or (= Xs tptp.nil_a) (= Ys2 tptp.nil_a) (not (= (@ tptp.last_a Xs) (@ tptp.hd_a Ys2)))) (= (@ tptp.remdups_adj_a (@ (@ tptp.append_a Xs) Ys2)) (@ (@ tptp.append_a (@ tptp.remdups_adj_a Xs)) (@ tptp.remdups_adj_a Ys2))))) (forall ((Xs_1 tptp.list_a) (X3 tptp.a) (Xs_2 tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (let ((_let_2 (@ _let_1 Xs_2))) (let ((_let_3 (@ tptp.append_a Xs_1))) (= (@ tptp.remdups_adj_a (@ _let_3 _let_2)) (@ (@ tptp.append_a (@ tptp.remdups_adj_a (@ _let_3 (@ _let_1 tptp.nil_a)))) (@ tptp.tl_a (@ tptp.remdups_adj_a _let_2)))))))) (forall ((Xs tptp.list_a)) (= (= (@ tptp.remdups_adj_a Xs) tptp.nil_a) (= Xs tptp.nil_a))) (forall ((X3 tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.cons_a X3))) (let ((_let_2 (@ tptp.remdups_adj_a (@ _let_1 Xs)))) (= (@ _let_1 (@ tptp.tl_a _let_2)) _let_2)))) (forall ((X3 tptp.list_a) (Y tptp.list_a)) (=> (= (@ tptp.remdups_adj_a X3) Y) (=> (=> (= X3 tptp.nil_a) (not (= Y tptp.nil_a))) (=> (forall ((X tptp.a)) (let ((_let_1 (@ (@ tptp.cons_a X) tptp.nil_a))) (=> (= X3 _let_1) (not (= Y _let_1))))) (not (forall ((X tptp.a) (Y3 tptp.a) (Xs2 tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y3) Xs2))) (let ((_let_2 (@ tptp.cons_a X))) (let ((_let_3 (= X Y3))) (=> (= X3 (@ _let_2 _let_1)) (not (and (=> _let_3 (= Y (@ tptp.remdups_adj_a (@ _let_2 Xs2)))) (=> (not _let_3) (= Y (@ _let_2 (@ tptp.remdups_adj_a _let_1)))))))))))))))) (forall ((X3 tptp.a)) (let ((_let_1 (@ (@ tptp.cons_a X3) tptp.nil_a))) (= (@ tptp.remdups_adj_a _let_1) _let_1))) (= (@ tptp.remdups_adj_a tptp.nil_a) tptp.nil_a) (forall ((X3 tptp.a) (Y tptp.a) (Xs tptp.list_a)) (let ((_let_1 (@ (@ tptp.cons_a Y) Xs))) (let ((_let_2 (@ tptp.cons_a X3))) (let ((_let_3 (@ tptp.remdups_adj_a (@ _let_2 _let_1)))) (let ((_let_4 (= X3 Y))) (and (=> _let_4 (= _let_3 (@ tptp.remdups_adj_a (@ _let_2 Xs)))) (=> (not _let_4) (= _let_3 (@ _let_2 (@ tptp.remdups_adj_a _let_1)))))))))) (forall ((Xs tptp.list_a) (X3 tptp.a) (Y tptp.a)) (let ((_let_1 (@ (@ tptp.cons_a Y) tptp.nil_a))) (let ((_let_2 (@ tptp.cons_a X3))) (let ((_let_3 (@ tptp.append_a Xs))) (= (@ tptp.remdups_adj_a (@ _let_3 (@ _let_2 _let_1))) (@ (@ tptp.append_a (@ tptp.remdups_adj_a (@ _let_3 (@ _let_2 tptp.nil_a)))) (@ (@ (@ tptp.if_list_a (= X3 Y)) tptp.nil_a) _let_1))))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (F (-> tptp.a tptp.a tptp.a)) (X3 tptp.a) (Y tptp.a)) (let ((_let_1 (@ tptp.map2_a_a_a F))) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys2)) (= (@ (@ _let_1 (@ (@ tptp.append_a Xs) (@ (@ tptp.cons_a X3) tptp.nil_a))) (@ (@ tptp.append_a Ys2) (@ (@ tptp.cons_a Y) tptp.nil_a))) (@ (@ tptp.append_a (@ (@ _let_1 Xs) Ys2)) (@ (@ tptp.cons_a (@ (@ F X3) Y)) tptp.nil_a)))))) (forall ((N tptp.nat) (Xs tptp.list_a)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (not (= Xs tptp.nil_a)))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (P (-> tptp.list_a tptp.list_a Bool))) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys2)) (=> (@ (@ P tptp.nil_a) tptp.nil_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys3 tptp.list_a)) (=> (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3))))) (@ (@ P Xs) Ys2))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a) (P (-> tptp.list_a tptp.list_a tptp.list_a Bool))) (let ((_let_1 (@ tptp.size_size_list_a Ys2))) (=> (= (@ tptp.size_size_list_a Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_a Zs2)) (=> (@ (@ (@ P tptp.nil_a) tptp.nil_a) tptp.nil_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys3 tptp.list_a) (Z2 tptp.a) (Zs tptp.list_a)) (let ((_let_1 (@ tptp.size_size_list_a Ys3))) (=> (= (@ tptp.size_size_list_a Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_a Zs)) (=> (@ (@ (@ P Xs2) Ys3) Zs) (@ (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)) (@ (@ tptp.cons_a Z2) Zs))))))) (@ (@ (@ P Xs) Ys2) Zs2))))))) (forall ((Xs tptp.list_a) (Ys2 tptp.list_a) (Zs2 tptp.list_a) (Ws2 tptp.list_a) (P (-> tptp.list_a tptp.list_a tptp.list_a tptp.list_a Bool))) (let ((_let_1 (@ tptp.size_size_list_a Zs2))) (let ((_let_2 (@ tptp.size_size_list_a Ys2))) (=> (= (@ tptp.size_size_list_a Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_a Ws2)) (=> (@ (@ (@ (@ P tptp.nil_a) tptp.nil_a) tptp.nil_a) tptp.nil_a) (=> (forall ((X tptp.a) (Xs2 tptp.list_a) (Y3 tptp.a) (Ys3 tptp.list_a) (Z2 tptp.a) (Zs tptp.list_a) (W tptp.a) (Ws3 tptp.list_a)) (let ((_let_1 (@ tptp.size_size_list_a Zs))) (let ((_let_2 (@ tptp.size_size_list_a Ys3))) (=> (= (@ tptp.size_size_list_a Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_a Ws3)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs) Ws3) (@ (@ (@ (@ P (@ (@ tptp.cons_a X) Xs2)) (@ (@ tptp.cons_a Y3) Ys3)) (@ (@ tptp.cons_a Z2) Zs)) (@ (@ tptp.cons_a W) Ws3))))))))) (@ (@ (@ (@ P Xs) Ys2) Zs2) Ws2))))))))) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X3 tptp.list_a) (Y tptp.list_a)) (= (@ (@ (@ tptp.if_list_a false) X3) Y) Y)) (forall ((X3 tptp.list_a) (Y tptp.list_a)) (= (@ (@ (@ tptp.if_list_a true) X3) Y) X3)) _let_4 true))))))))))))))))))))))))))))))))))
% 0.87/1.10 )
% 0.87/1.10 % SZS output end Proof for ITP100^1
% 0.87/1.11 % cvc5---1.0.5 exiting
% 0.87/1.11 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------